™ | B DATE: SUBJECT: TO: FROM: OAK RIDGE NATIONAL LABORATORY OPERATED BY UNION CARBIDE CORPORATION NUCLEAR DIVISION UNION CARBIDE POST OFFICE BOX X OAK RIDGE, TENNESSEE 37830 March 2, 1970 Calculation of Stresses During a Thermal Transient in a MSBR Outlet Nozzle Distribution J. L. Spoormaker* ABSTRACT Internal Use Only ORNL CENTRAL FILES NUMBER 70~3-2 COPY NO. 41 Information is given about the thermal stresses devel- oped in the outlet nozzles of a reactor vessel for a 1000 Mw(e) Molten-Salt Breeder Reactor for several step changes in the salt temperature. Calculation of the temperature distri- butions, as well as of the stresses, was carried out by finite element computer programs. Step temperature changes of 1300 to 1400°F, 1300 to 1600°F, 1300 to 1800°F, 1300 to 1200°F, and 1300 to 1100°F were considered. For each step change the number of cycles to fallure was estimated and an estimation of whether or not gross cyclic yielding would occur was made. *¥On assignment to ORNL from Delft Technological University, The Netherlands, under a fellowship program sponsored by the Dutch Government. NOTICE This document contains information of a preliminary nature and was prepared primarily for internal use at the Oak Ridge National Laboratory. It is subject to revision or correction and therefore does not represent a final report. The information is only for official use and no release to the public shall be made without the approval of the Legal and Information Control Depart- ment of Union Carbide Corporation, Nuclear Division. 1. 2. O 0 I O INTRODUCTION 3 CONTENTS LIST OF FIGURES NOMENC LATURE DESCRIPTION OF CONFIGURATION AND FINITE ELEMENT IDEALIZATTION 2.1, Configuration .....ceeevevereneerecnecenescacocnans 2.2. Finite Flement MeSh .. ¢veeeeeecececsocecaocacsancs TEMPERATURE DISTRIBUTION CAICULATIONS ¢vvevececccosceoocens STRESS ANALYSTS 4.1, 4.2, 5.1. 5.2. 5.3. 5.4. 5.5. 5.6. CONCLUSIONS REFERENCES ACKNOWLEDGEMENTS . General Remarks Evaluation of Stresses RESULTS OF STRESS COMPUTATIONS .... Steady-State Condition ... Step Change 1300 Step Change 1300 Step Change 1300 Step Change 1300 Step Change 1300 — 1400°F — 1600°F @ @ 0 0 0 0 0 ¢ 0 & 0 0 0 0 0 0 &6 0 0 0 0 0 9 e 0 @ 0 0 0 0 0 ¢ 0 06 0 0 0 0 0 O ¢ 0 ¢ 0 0 ¢ OOOOOOOOOOOOOOOOOOOOOOO 000000000000000000000000 000000000000000000000000 000000000000000000000000 OOOOOOOOOOOOOOOOOOOOOOOO ........................ OOOOOOOOOOOOOOOOOOOOOOOO o . o 06 6 06 ¢ o 0 o o . e . . o0 [ 2 ® o e o e o o 11 12 12 12 13 14 14 14 17 17 17 18 18 19 20 20 21 22 23 Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. O ¢ I O bt A W N - O '_.l '_.l 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22 . 23. 24 LIST OF FIGURES MSBR Reactor Vessel Flow Schematic. MSBR Reactor Vessel Simplified Outlet Configuration. MSBR Reactor Vessel Simplified Outlet Nozzle Detail. Plot of the Outline of the Configuration. Subplot of the Subplot of the Subplot of the Subplot of the Design Fatigue Various Criteria for the for INOR-8. Temperature Condition. Temperature Condition. Temperature Condition. Temperature Condition. Temperature Condition. Temperature Condition. Distribution Distribution Distribution Distribution Distribution Distribution Element Idealization Element Idealization Element Idealization Element Idealization (Pipe Region). (Intersection Region). (Nozzle Wall Region). (Flat Plate). Strength, Sa’ for Ni-Mo—Cr Alloy. Determination of the Design Stresses Across Section A-A in the Steady-State Across Section Across Section Across Section Across Section Across Section Stress Distribution Across Section A-A Condition. Stress Distribution Across Section B-B Condition. Stress Distribution Across Section C=C Condition. Stress Distribution Across Section D-D Condition. Stress Distribution Across Section E-E Condition. B-B in the Steady-State C-C in the Steady-State D-D in the Steady=State E-E in the Steady-State F-F in the Steady-State in in in in in the Steady-State the Steady-State the Steady-State the Steady-State the Steady-State Temperature Distribution Across Section A-A After the Step Change 1300 — 1400°F. Temperature Distribution Across Section B-B After the Step Change 1300 — 1400°F. Temperature Distribution Across §ection C-C After the Step Change 1300 — 1400°F. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. 25. 26. 27 . 28. 29. 30. 31. 32. 33. 34, 35. 36. 37. 38. 39. 40. 41, 42. 43, 4ts 45, Temperature Distribution Across Section D-D After the Change 1300 — 1400°F. Temperature Distribution Across Section E-E After the Change Stress 1300 — Stress 1300 - Stress 1300 — Stress 1300 — Stress Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 Stress Distribution Across Section 1300 — 1600° 1300 — 1400°F Distribution Across 1400°F. Distribution Across 1400°F. Distribution Across Section C-C After the Step 1400° Distribution Across Section D-D After the Step 1400°F. Distribution Across 1300 — 1400° F. F. Distribution Across - 1600 oFc Distribution Across — 1600°F. Distribution Across — 1600°F. Distribution Across — 1600°F, Distribution Across - 1600 °F| o F. Section A-A After the Step Section B-B After the Step section E-E After the Step Section A-A After the Section B-B After the section C-C After the Section D-D After the section E-E After the A-A After the Step Stress Distribution Across Section B-B After the Step 1300 — 1600°F. Stress Distribution Across 1300 — 1600°F. otress Distribution Across 1300 — 1600°F. Stress Distribution Across 1300 — 1600° Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 F. Distribution Across — 1800°F. Distribution Across — 1800°F. Distribution Across — 1800°F. Distribution Across — 1800°F. Section Section C-C After the Step Section D-D After the Step E-E After the Step Section A-A After the Section B-B After the ocection C-C After the oection D-D After the Step Step Change Change Change Change Change Step Step Step Step Step Change Change Change Change Change Step Step Step Step s Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. 46, 47, 48, 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 6l. 62. 63. 64 . 65. 66. Temperature Distribution Across Section E-E After the Change 1300 Stress Distribution Across — 1800°F. 1300 — 1800°F. Stress Distribution Across 1300 — 1800°F. Stress Distribution Across 1300 — 1800°F. Stress Distribution Across 1300 — 1800°F. Stress Distribution Across 1300 — 1800° Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 Stress Distribution Across 1300 — 1200° Stress Distribution Across F. Distribution Across — 1200°F. Distribution Across — 1200°F. Distribution Across — 1200°F. Distribution Across — 1200°F, Distribution Across — 1200°F. F. 1300 — 1200°F. Stress Distribution Across 1300 — 1200° Stress Distribution Across 1300 — 1200° F. F. Section Section Section Section Section Section A-A After the Section A-A After the Section B-B After the A-A After B-B After C-C After D-D After E-E After Section B-B After the Section C-C After the Section D-D After the Stress Distribution Across Section E-E After the 1300 — 1200° Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 Temperature Change 1300 F. Distribution Across Section — 1100°F. DiStribution Across Section — 1100°F. Distribution Across Section — 1100°F. Distribution Across Section — 1100°F. Distribution Across Section — 1100°F. A-A After B-B After C-C After D-D After E-E After otep Step Section C-C After the Step Section D-D After the Step Section E-E After the Step the the the the the otep Step Step otep Step the the the the the Step Change Change Change Change Change otep Step Step Step Step Change Change Change Change Change Step Step Step Step Step Fig. Fig. Fig. Fig. Fig. 67 . 68. 69. 70. 71. Stress Distribution 1300 — 1100°F. Across Section Stress Distribution Across Section 1300 — 1100°F. Stress Distribution 1300 — 1100°F. Stress Distribution 1300 - 1100°F. Stress Distribution 1300 — 1100°F. Across Across Across Section Section Section A-A After the Step Change B-B After the Step Change C-C After the Step Change D-D After the Step Change E-E After the Step Change 0 T ™ = Q alt ES @ chn N ch HQ < Q Q Q ks N min Q max Q NOMENCLATURE Modulus of elasticity Biot's number Allowable elastically calculated stress amplitude Amplitude of stress fluctuation Uniaxial yield strength Coefficient of thermal expansion Temperature Temperature difference Poisson's ratio Radial stress Circumferential stress Axial stress Shear stress Minimum stress in meridional plane Maximum stress in meridional plane Surface stress 11 1. INTRODUCTION In a MSBR of 1000 Mw(e) the salt enters at a temperature of 1050°F and will rise about 250°F as it passes the core. Under normal conditions it is assumed that the salt temperature in and around the outlet nozzle will be at 1300°F. There are, however, circumstances in which the salt from the core changes rapidly in temperature. Shortly after such a change, high tem- perature gradients, and hence high thermal stresses, will occur near the inner surface of the outlet nozzle and the connected pipe. Because the heat dissipates through the structure, discontinuity stresses are ailso produced at the intersection of the pipe and the nozzle since the nozzle is relatively thick in comparison with the pipe. Information about the structural damage produced by rapid changes in salt temperature is needed for the design of a MSBR. Consequently, the thermal stresses were computed after five different step changes in salt temperature. The step changes were: Downward Upward 1300 — 1200°F 1300 — 1400°F 1300 — 1100°F 1300 — 1600°F 1300 — 1800°F It was assumed that these transients would not last longer than 10 seconds, since measures could be taken in that amount of time to bring the salt temperature back to normal. The time at which the highest sur- face and discontinuity stresses would occur was determined by a number of stress computations at different time points for the step change 1300 — 1600°F. From the results of these computations at 1, 3, 5, 7, and 9 seconds, it was learned that the highest surface stresses in the pipe occur at about 1 second, and in the nozzle wall they occur at about 9 seconds. The highest discontinuity stresses occur at about 9 seconds. Since the temperature distributions were similar for all step changes, and since the differences between the stresses produced at 1 and 3 seconds and at 7 and 9 seconds were not large, computations were carried out only at 1 and 9 seconds for the remaining step changes. 12 With the results obtained from the stress computations, estimates were made of the number of cycles to failure for each condition. A judgement was also made regarding the likelihood of gross cyclic yielding at the intersection between the pipe and the nozzle. 2. DESCRIPTION OF CONFIGURATION AND FINITE ELEMENT IDEALIZATION 2.1. Configuration The outlet nozzles are attached to a cylindrical vessel about 22 ft in diameter. The diameter of the outlet nozzles at the connection is 23 in. (Fig. 1). Most of the salt flows directly from the inlet through the core to the outlet nozzles, but some salt from the inlet‘flows through the gap between the cylindrical wall and the reflector (see Fig. 2). oince the highest stresses expected are due to thermal loading, the nozzles were considered to be attached to a flat plate rather than to a cylindrical shell. With this simplification it was possible to consider an axisymmetric problem for the thermal loading. Since the vessel diameter to nozzle diameter ratio is about 12:1, the results were ex- pected to be reasonably accurate. The configuration, as shown in Fig. 3, was extended as far as possible in order to approximate the real situation. The flat plate was taken suf- ficlently large for the degree of restraint against thermal expansion to closely approximate that of the cylindrical wall. The criterion for the length of the connected pipevwas that the discontinuity stresses should be damped out to 10% at the end of the pipe. 2.2. Finite Element Mesh The configuration shown in Fig. 3 was divided into a number of tri- angular ring elements. A fine mesh was taken in regions where high sStresses were expected. Although for the calculation of the temperature distribution the mesh in some regions was finer than necessary, the same mesh was used as for the stress analysis. Plots and subplots of the mesh are given in Figs. 4 through 8. \» 13 3. TEMPERATURE DISTRIBUTION CALCULATIONS The determination of the temperature distribution was carried out by a finite element computer program.l The program calculates the tempera- ture of the nodal points situated at the vertices of the elements into which the body has been divided. The temperature of the centroid of an element is obtained by taking the average of the temperatures of the nodal points. The difference of the centroid temperature and a reference tem- perature 1s multiplied by the coefficient of thermal expansion, and the resulting numbers are the input data for the SAFE-PCRS stress analysis program. %’ 3 | The following simplifications were made for these calculations: 1. The problem is axisymmetric. 2. Under normal conditions, the salt temperature is at 1300°F. 3. The temperature of the salt in the gap between the wall and the reflector does not change. 4. Except along boundaries where the configuration is in contact with the salt, 1t was assumed to be insulated. 5. The material properties are temperature independent. - The material properties used are: Conductivity coefficient: 12.7 Btu/hr-ft-F Heat capacity: 75.8 Btu-ft3-F The film coefficients are: In the nozzle: 1600 Btu/hr-ft2-F In the gap: 150 Btu/hr-ftz-F The heat source strengths due to gamma radiation are: Perpendicular to nozzle wall: 27.4 exp (—0.818x) Btu/hr-in.°> Perpendicular to vessel wall: 30.2 exp (—0.818x) Btu/hr-in.3 , where x 1s the distance, in inches, from the wall. Although the intensity of the gamma radiation changes during a transient, this effect was not taken into account, since the time considered was relatively short. The steady-state temperature distribution was first calculated be- cause it was not uniform due to the internal heat generation. 14 4. STRESS ANALYSIS 4.1. General Remarks The stress computations were carried out by a stress analysis finite element computer program which determines the elastic stresses in an axi- symmetric body. Where the value of the "stress'" exceeds the yield strength, the results from these computations must be interpreted as strain times Young's modulus. Further discussion will be in terms of stress, since the fatigue curves and Section III of the ASME Boiler and Pressure Vessel Code are based on these elastically calculated stresses. As already mentioned, in the first 10 seconds after the step change in the salt temperature, high local surface stresses and high bending stresses will occur. The surface stresses are high in the pipe and the nozzle wall, while the bending stresses are dominant in the intersection between the pipe and the nozzle. The stresses in these regions develop as follows: l. The Pipe. This rather thin and flexible part of the structure changes rapidly in temperature. The highest surface stresses occur here in the first seconds after the step change. These stresses quickly de- crease because of the dissipation of heat. 2. The Nozzle Wall. This is a relatively thick and stiff part of the structure and thus does not change as rapidly in temperature as does the pipe. At 9 seconds after the step change, a region only 0.5 in. deep is at a significantly different temperature from that in the steady-state condition. The highest surface stresses occur at this time. 3. The Intersection. Due to the difference in thermal expansion be- tween the pipe and the nozzle wall, high bending stresses occur here. These stresses are classified as discontinuity stresses and can cause cyclic yielding. The stresses produced by the pressure loading are also of interest here. 4.2. Evaluation of Stresses The stresses obtained by the finite element calculations were .. o o o o . and o in each element. T 7> %9 9%y Opin? max hese stresses are assumed o 15 to be constant within each element. Especially where steep thermal gradients occur, the actual stresses vary significantly across an element and the type of element (constant stress) which was used will not give very accurate results unless a very fine mesh is employed. Higher order elements or a finer mesh near the inside surface of the nozzle would im- prove the results. For practical reasons these solutions were not applied. According to Zienkiewicz (page 35, Ref. 4) the calculated stresses should be assigned to the centroids of the elements. For a section consisting of a row of elements, it is then possible to plot the stress components at the centroids against the radius of these centroids. The curve through these plotted points then gives a reasonable approximation of the stress distribution through the wall in that section. An approximation expression given by Manson’ enables us to check the highest surface stress in the pipe and the nozzle wall. This expression, which takes the Biot number into account, has the form G:me{ 1 s 1-=v 1.35 4+ 3fi25'— 3 0.5 e'lé/B] and gives the maximum surface stress due to a step change in fluid tem- perature on one side of a thin restrained flat plate. This case is essen- tially the same as a thin, infinitely long, cylindrical shell. Generally, there was good agreement when the stresses in the steady-state condition at the surface were taken into account. For the evaluation of the stresses it was necessary to use a strength theory since a triaxial stress condition existed. Because of its accepted use in Section IIT of the ASME Code, the maximum shear theory was used. The stress intensity was thus determined by taking the largest algebraic difference between any of the two principal stresses at a point. ©Since the thickness of the pipe and the nozzle wall was small in comparison with the diameter of the nozzle, G, was expected to beASmall. From the results of the stress computations it was found that C, was small through- out the wall. Since o, is equal to zero at the surface, it was set equal to zero everywhere. With this simplification the stress intensity was just the highest stress component in absolute value. 16 The high local surface stresses were considered to be peak stresses which could damage the surface by fatigue cracking. For the evaluation of these stresses the amplitude of the stress fluctuation must be deter- mined. This amplitude was found by taking the algebraic difference be- tween the highest occurring surface stress in the structure and the sur- face stress in the steady-state condition for the same spot. The amplitude of the stress fluctuation was then half the difference of the stresses. The mean stress and hold-time effects were not taken into account because they were of no significance for the cases considered. The number of cycles to failure for each step change was determined from the fatigue curves in Fig. 9. The evaluation of the bending stresses in the intersection between the pipe and the nozzle was more complicated. In addition to the thermal loading, the pressure loading should be taken into account. The internal pressure in the nozzle was, however, low (14 psig), and hence the effect of this loading was not expected to be significant. In order to deter- mine the order of magnitude of the stresses produced by the pressure load- ing, a simplified calculation was carried out. For this calculation it was assumed that the pressure in the pipe was 30 psig and that the radial stress at the edge of the plate was equal to the circumferential stress in the vessel wall for the same internal pressure. A higher pressure than 14 psig was taken since no end plate (causing an axial membrane stress in the nozzle) was added to the configuration. The end plate was neglected since the relatively thin flat plate behaves differently from a cylindrical shell. It was found, from this calculation, that the stress intensity in nearly the entire intersection was lower than 1 ksi. The error in the determination of the thermal stresses was several times larger than this, and hence the stresses produced by the pressure loading were neglected. In order to estimate whether or not serious cyclic yielding would occur in the intersection, it was determined over what percentage of the section a higher stress intensity than ZSy occurs, where Sy is the yleld strength and is given in Fig. 10 as a function of temperature. 4 17 5. RESULTS OF STRESS COMPUTATIONS In this chapter the results of the stress computations for different conditions are presented. From these results estimates of the number of cycles to failure have been made, and also it has been determined, for each condition, whether or not gross cyclic yielding might occur. The temperature distributions presented have been obtained by plotting the nodal point values against the distance from the centerline. The procedure by which the stress distributions were obtained was described in Chapter 4. The stress component presented for each section is the highest component occurring there, and since C. has been set equal to zero this stress component is also the stress intensity. 5.1. Steady-State Condition The temperature distributions through the wall at sections A-A, B-B, C-C, D-D, E-E, and F-TF are presented in Figs. 11 through 16, respectively. The stress distributions through the wall in the first five sectlons are shown in Figs. 17 through Z21. These stress distributions are necessary to determine the amplitude of the stress fluctuation for the other conditions. 5.2. Step Change 1300 — 1400°F The temperature distributions through the wall at sections A-A, B-B, C-C, D-D, and E-E are presented in Figs. 22 through 26, respectively. The stress distributions in the same sections are shown in Figs. 27 through 31. The surface stress that gives the highest amplitude of stress fluctu- ation occurs in section D-D, and at this spot we have: The circumferential stress: 21 ksi The surface temperature: 1380°F The circumferential stress in the 7 ksi steady-state condition: The amplitude of the stress fluctuation: 14 ksi From the fatigue curves in Fig. 9 we find that fatigue cracking is unlikely for this condition. 18 For section B-B, where the highest discontinuity stresses occur, we have at 9 seconds after the step change: The average temperature: 1350°F The yield strength at 1350°F: 20 ksi From the stress distribution in Fig. 28 we find that no yielding will occur. 5.3. Step Change 1300 — 1600°F The temperature distributions throfigh the wall in sections A-A, B-B, C-C, D-D, and E-E are presented in Figs. 32 through 36, respectively. The stress distributions in the same sections are shown in Figs. 37 through 41. | The surface stress that gives the highest amplitude of the stress fluctuation occurs in section D-D, and at this spot we have: The circumferential stress: 70 ksi The surface temperature: 1540°F The circumferential stress in the 7 ksi steady-state condition: : The amplitude of the stress fluctuation: 38.5 ksi From the fatigue curves in Fig. 9 we find that the number of cycles to failure might be as low as 90. For section B-B, where the highest discontinuity stresses occur, we have, at 9 seconds after the step change: The average temperature: 1450 °F The yield strength at 1450°F: 20 ksi From the stress distribution in Fig. 38 we find that the stress intensity is higher than ZSy in about 30% of this section. It can thus be suspected that gross cyclic yielding might occur in this section. 5.4. Step Change 1300 — 1800°F The temperature distributiens through the wall in sections A-A, B-B, C-C, D-D, and E-E are presented in Figs. 42 through 46, reSpectively. The stress distributions in the same sections are shown in Figs. 47 through 51. The surface stress that gives the highest amplitude of the stress fluctuation occurs in section D-D, and at this spot we have: 19 The circumferential stress: —-118 ksi The surface temperature. 1700°F The circumferential stress in the "7 ksi - steady-state condition: | | The amplitude of the stress fluctuation: 62.5 ksi There are presently no fatigue data available for 1700°F, but since Saltis very high it is estimated that cracking might occur after only one or two cycles. For section B-B, where the highest discontinuity stresses occur, we have, at 9 seconds after the step change: The average temperature: | 1550°F The yield strength at 1550°F: 20 ksi From the stress distribution in Fig. 48 we find that the stress intensity is higher than 2Sy in about 55% of this section. It can be concluded that gross cyclic yielding will occur for this condition. 5.5. Step Change 1300 — 1200°F The temperature distributions through the Wall:in sections A-A, B-B, C-C, D-D, and E-E are presented in Figs. 52 through 56, respectively. | The stress distributions in the same sections are shown in Figs. 57 through 6l. The surface stress that gives the highest amplitude of the stress fluctuation occurs in section D-D, and at this spot we have: The circumferential stress: 34 ksi The surface temperature: 1225°F The circumferential stress in the 7 ksi steady-state condition: The amplitude of the stress fluctuation: 13.5 ksi From the fatigue curves in Fig. 9 we find that fatigue cracking is unlikely for this condition. For section B-B, where the highest discontinuity stresses occur, we have, at 9 seconds after the step changei The average temperature: 1250°F The yield strength at 1250°F: 20 ksi From the stress distribution in Fig. 58 we find that no yielding will occur at the intersection. 20 5.6. Step Change 1300 — 1100°F The temperature distribution through the wall in sections A-A, B-B, C-C, D-D, and E-E are presented in Figs. 62 through 66, respectively. The stress distributions in the same sections are shown in Figs. 67 through 71. The surface stress that gives the highest amplitude of the stress fluctuation occurs in section D-D, and at this spot we have: The circumferential stress: | 58 ksi The surface temperature: 1145°F The circumferential stress in the 7 ksi steady-state condition: The amplitude of the stress fluctuation: 25.5 ksi From the fatigue curves in Fig. 9 we find that the number of cycles to failure might be as low as 2 X 10°. For section B-B, where the highest discontinuity stresses occur, we have, at 9 seconds after the step change: The average temperature: 1220°F The yield strength at 1220°F: 20 ksi From the stress distribution in Fig. 68 we find that the stress intensity is higher than ZSy in about 10% of this section. It can be concluded that no gross cyclic yilelding will occur for this condition. 6. CONCLUSIONS From the results of the stress calculations it was found that: 1. A step change of 100°F in the salt temperature upward or downward will not cause any damage to the configuration. 2. The step change 1300 — 1100°F might possibly cause fatigue crack- ing after a large number of cycles, but no gross cyclic yielding would occur. 3. A step change from 1300 — 1600°F would cause fatigue cracking after about 90 cycles and gross cyclic yielding might occur in the inter- section between the pipe and the nozzle. 4. The step change 1300 — 1800°F is likely to cause cracks after a very few cycles and gross cyclic yielding will occur in the intersection between the nozzle and the pipe. " 21 7. REFERENCES J. L. Spoormaker, "Application of the Finite Element Method to the Computation of Temperature Distributions in Axisymmetric Bodies," USAEC Report ORNL-TM-2894, Oak Ridge National Laboratory (to be published). Y. R. Rashid, "Finite Element Analysis of Axisymmetric Composite Structures," USAEC Report GA-6303, General Atomic, June 4, 1965. D. C. Cornell, "SAFE-PCRS — A Computer Program for the Stress Analysis of Composite Bodies of Revolution, Input Instructions,' USAEC Report GA-6588, General Atomic, August 1, 1965. 0. C. Zienkiewicz, The Finite Element Method in Structural and Con- tinuum Mechanics, McGraw-Hill, 1967. D. J. Lewis, E. J. Chubb, and H. A. Money, "Factors Affecting Thermal Stress in a Power Plant," International Conference on Thermal Stresses and Thermal Fatigue, Berkeley Nuclear Laboratories, September 23-26, 1969. 22 8. ACKNOWLEDGEMENTS The author wishes to express his appreciation to R. B. Briggs of the Director's Division for his overall direction and guidance. Members of the Reactor Division Design Department, including J. R. McWherter, C. W. Collins, W. K. Furlong, and H. A. McLain, supplied the necessary MSBR information and made helpful suggestions. Finally, the author acknowledges the help of J. M. Corum of the Reactor Division Applied Mechanics Section in performing the stress analyses and evaluating the results, and of W. G. Dodge of the Applied Mechanics Section in writing the heat conduction computer programn. 23 9. FIGURES 25 ORNL-DWG 70-2354 +— w22 FT DIA. —» * Fig. INLET 1050° F. 1. OUTLET (4) 0 1300° F MSBR Reactor Vessel Flow Schematic. 26 ORNL-DWG 70-2355 20 IN. DIA. ~— “ 19 IN. DIA. 1 _JL_ /4 IN. CLEARANCE MSBR Reactor Vessel Simplified Outlet Configuration. Fig. 2. 27 ORNL-DWG 70-2356 2 IN.-=| |=5 IN* Yo S /5 R 19 IN. 1. D. 20 IN. O. D. ! J ~ Fig. 30° _ ’ 3. MSBR Reactor Vessel Simplified Outlet Nozzle Detail. 28 ORNL-DWG. 70-2357 MSBR OUTLET NOZZLE (SIMPLIFIED VEWSION 1 30. 25 F s £ E — = 20. b b & 5 & 5* = c 2 15. B B & 8 4 10, A 4+ A S. 0. - _ 10. 1S. 20. Radius (inches) Fig. 4. Plot of the Outline of the Configuration. 29 ORVL-DWG 70-2358 MSBR OUTLET NOZZLE (SIMPLIFIED VEWSIOM 1) . | 13. w12, < & B S e llo & 5 & 3 T 9. 8. 1 G 7. Radius (inches) Fig. 5. Subplot of the Element Idealization (Pipe Region). 30 ORNL-DWG 70-2359 MSBR OUTLET NOZZLE (SIMPLIFIED VEWSIOW 1 | 1S.8 | 15.6 { 15.4 ~ 15.2 2 E 4 15.0 = : ] £ 14.8 3 14.6 4.4 ‘ 14.2 14.0 - 9.6 9.8 10.0 10.2 10.4 10.6 Radius (inches) Fig. 6. Subplot of the Element Idealization (Intersection Region). 31 ORNL-DWG 70-2360 MSOR MTLFT NOZZLE (SIMPLIFIED VERSIOW 23.[ 22. 2l. £ 0. ' & < qg* 4 7 19. fi g fi & ( § ( 5 18, « A { 17. { J q Y T - 16. 1S. - 10. 1. 12. Radius (inches) Fig. 7. Subplot of the Element Idealization (Nozzle Wall Region). Distance from end of pipe (inches) X ;g . » 22. 10. Fig. 8. ORNL-DWG 70-2361 MSBR OUTLET NOZZLE (SIMPLIFIED VERSION) 12. 13. . 18. 19. Radius (inches) Subplot of the Element Idealization (Flat Plate). 43 1/2€ (E) Values of S;, psi (Sa 108 108 104 10 W 5 U ONDO- ORNL-DWG 70-3301 1 2 3 4 567891 2 3 4 567891 2 3 4 567891 3 4 567891 2 3 4 567891 W P U OO NNOOO L\ W S U ONOD- n N 10 102 10° 104 10° 108 Number of Cycles Fig. 9. Design Fatigue Strength, Sa, for Ni-Mo—Cr Alloy. €€ 3k ORNL-LR-DWG 46316 30,000 | | ’ ‘ ‘ tx ULTIMATE TENSILE STRENGTH 25,000 ———— | - T ~ 2 xYIEm ‘QLSTRENGTH | 20,000 . T(0\2% OFFSET) < .U—, §\§\\§§~ B DESIGN STRESS— "Q"\\ \ 0 15,000 FOR 316 STAINLESS 2 ~ L) STEEL \fli‘\" {5 & | {\\» STRESS FOR 10,000 | . RUPTURE IN — STRESS FOR 1% CREEP IN—— =X\ 4 100,000hr 100,000hr \ | | % 2000 STRESS FOR 10° % /hr M.C. R————/ N . L] 0 400 800 1200 1600 TEMPERATURE (°F) Various Criteria for the Determination of the Design Stresses for INOR-8. Fig. 10. Various Criteria for the Determination of the Design Stresses for INOR-8. v 35 ORNL-DWG 70-2363 TEMPERATURE 0O0I1STRiIBDVTIOM L THRoOVOGHN THE WALL I M | :' Sgcriony A -AR :" . Fig. 11. Temperature Distribution « A3 . Across Section A-A in the Steady-State - 3 Condition. N < < % N by Y s Q T & w W " 4300 ~ q.5 10 DISTANCE FROWNM CENTERLINE, INCHES Fig. 12. Condition. ORNL-DWG 70-2364 TEMPERATVUVRE DISTRIBUT joN THROVGH THE WwWALL I NV Secrio¥vN B-B8B 1350 Temperature Distribution Across Section B-B in the Steady-State 1300 95 §0. *r TEMPERATVRE DISTANCE FROM CENTERL |NE, |NCHES ORNL-DWG. 70-2365 TEMPERATYRE D I1STRIBUTION 1350 p— THROVGHN THE wWALL N sSEcTiow C-C fih " 1300 —— 4.5 10 DISTANCE FROM CENTERLINE Fig. 13. Temperature Distribution Across Section C-C in the Steady-State Condition. °c TEMPERAT VR E 36 ORNL-DWG 70-2366 .l TEMPEBERATURE ODISTR IBVTION . THROIVON THE WALL I~V SECTioN D-D §q35 : 513 0 ~ < « U a /"——_——7 w - 1300 a5 DISTANCE FRON ceEwvTERLINE Fig. 1l4. Temperature Distribution Across Section D-D in the Steady- State Condition. ORNL-DWG. 70-2367 e v T TEMPERATURE DISTRIBUT/o N THROVGH THNE WALL IN SECTION E -E 1350 / _— ff’ffd 1300 9.5 10 n DISTANCE FROM CENTERLINE, /incHES Fig. 15. Temperature Distribution Across Section E-E in the Steady- State Condition. ORNL-DWG 70-2368 @ TEMPERATVRE DISTR | BVT I8N THROUOG N ° TNE WALL |~ SEcTrionv F - F w X | D 4350 4+ ~ . i ( x—r « // { r : — | t W = ‘ i | ; o 4300 : + - 0 DISTANCE FROnNM FRomMm S VRF ALE IN CO NTACT WITH SALT INCHES Fig. 16. Temperature Distribution Across Section F-F in the Steady- State Condition. 37 ORNL-DWG 70-2369 _ CIRCUOMFERENT/IAL STRESS OLISTR I8 vTrow TwROyCw THE wALL /N YT secriom A-A N “ \ *. . @ of——N Q s = v \ | DISTANCE FRroNMm CEVNTEORLINVE, I WCNES -1 l | L Fig. 17. Stress Distribution Across Section A-A in the Steady-State Condition. ORNL-DWG 70-2370 AXIAL STRESS DISTRIBUVUTION THRODUGH THE WALL 1 S6criow B-RB 10 \\ o . q.5 \\. 10. DISTANCE FRom CENTERLINE \ STRESSs , KkKsS I -10 Fig. 18. Stress Distribution Across Section B-B in the Steady-State Condition. 38 ORNL-DWG 70-2371 CIRCUNFERENTIAL STRESS D!STRIB8VT/ON ,L_ THROUG ™ Tw€ WALL ' SECTIioN (C -C : 2 Fig. 19. Stress Distribution X Across Section C-C in the Steady- . NN 30 State Condition. w o -~ " \ “ W 4.5 \\ « ~ -2 — A DISTANCE FRom CO”T‘!LINE‘ INCHwES -5 | | | | i | ORNL-DWG 70-2372 CIRLUMPERENTIAL STRESS DISTRIBVYTION THROUGN THNHE WALL |N SECTION D-D 10 +——o - o o o o v \ Fig. 20. Stress Distribution «x ‘\ Across Section D-D in the Steady- “ ~——_ State Condition. “ T . 45 1o. 1. " DISTANCE FRONM CENTERLINE INCHES - 10 ORNL-DWG 70-2373 CIRCUMFERENT,AL STRES S OI1STRI)BVTIOWN — THNROVGHW THE WwWALL IN SECTIiON E -E - ~ T~ 5 10. : DISTANCE P ROM CENTERLINE , INcHES — 11 2 \© STRESS KSI > Fig. 21. Stress Distribution Across Section E-E in the Steady-State Condition. ORNL-DWG 70-2374 39 TEMPERATURE DISTRIBVTIoN 4 W TRovenw WwALL )~ sectiov R-AR ® 1400 i : W ? - « 3 ~ < « ; : | e i t w1300 ; 45 Y DISTANCE FROr CENTERLINE, INCHES Fig. 22. Temperature Distribu- tion Across Section A-A After the Step Change 1300 — 1L400°F. ORNL-DWG 70-2375 TEMPERATURE THROUGH THE WALL DISTRIBUTION IN SecTion B-B 1400 Fig. 23. Temperature Distribution Across Section B-B After the Step Change 1300 — 1L00°F. 4300 9.5 DRSTANCE FROM CENTERLINE INCHES 1s | 9¢ \\- 10 ORNL-DWG 70-2376 l 4400 \. | | | 1 { 1 [ I | TEMPERATURE DISTRIBVTION | i | i | " THROUGCH THE wALL In SEcTion C~-C 4 ! ; | ! e sm— e sovann] \gs 15 1 = 1300 E 45 10.5 DISTANCE FROM CENTERL/INE, INCHES Fig. 24. Temperature Distribution Across * Section C-C After the Step Change 1300 — 1L400Q°F. °F TEMPERATVRE Lo ORNL-DWG 70-2377 TEMNPERATVRE ODISTR I BUOTION :L THRovVGH THNE WALL 1N~ SECTION D-D « _ X d ~ ¢ 1400 Y g Q X W W~ 1300 g5 10. 11, DISTANCE FROM CENTERLINE ,INCHES Fig. 25. Temperature Distribution Across Section D-D After the Step Change 1300 — 1L400°F. ORNL-DWG 70-2378 TEMPERATURE DISTRIBVYUT!ION ! THROUGH THE WALL IN SECTION E-E e -] 1400 1300 9s 10 11 42 DISTANCE FRON CENTERLINE INCHES Fig. 26. Temperature Distribution Across Section E-E After the Step : Change 1300 — 1L400°F. KSI STRESS, ORNL-DWG 70-2380 T T AXIAL STRESS DISTRIBUVTION THROVeW THE WALL I1N SEcTion B-8 Tn ORNL-DWG 70-2379 20 CIRCUMFERENTIAL STRESS DISTRIBVTION | THROUGH YHE WALL IN SECTIiON A-R / SV 10 10 / 9s ; - X / o y A /-_ A ‘ P )}f; “ ‘///” T 0 € o , . (' 9.5 10 . g / o DISTANCE FROM ‘ 1s DISTANCE FROM CENTERLINE K INCNES CENTERLINE, INCHES ,‘ // -10 -0 //// -10& -2.0 Fig. 27. Stress Distribution Across Section Fig. 28. Stress Distribution Across Section B-B After A-A After the Step Change 1300 — 1L00°F. the Step Change 1300 — 1400°F. 57R£Sses.i<$I ORNL-DWG 70-2381 ] ~ T HROUGH THE wnhAll o L IN SECTION | CIRCUMFERENTIAL S TRESS DISTRI BUTION, ¢-C 10 «20 9s _ < \\ 10.5 T OISTANCE FRor CENTERLINE , INCHE 11 Fig. 29. Stress Distribution Across Section C-C After the Sept Change 1300 — 1400°F. o STRESSEs , KSI ORNL-DWG 70-2382 D-D After the Step Change 1300 — 1L400°F. CIRCUMFERENTINAL STRESS DPISTRIBVTION THROVGH THE WALL IN SEcTien D-D | | ( | ; ; ; ? z ! | 5 i ! : ! ) ‘ ; ? é } T 0 — — s q.5 10 | | " DISTANCE FROM CENTERLINE , INCHES | | % Tf ; ? i : i : é | =10 | | | ! ? 5 ? | | | | ! e i — ; | 1 1 | Fig. 30. Stress Distribution Across Section of L3 ORNL-DWG 70-2383 T ] CIRCUMFBRENTIAL STRESS DISTRIBUT(ON THROVGEH THE wAallt i1~ secTI10n# E-E 1¢ “ N g _ m‘ / \ \ w . . ‘ , n - 10 11 W « DISTANCE FROM CENTERL(NE.INCHES - e b e — " -20 Fig. 31. Stress Distribution Across Section E-E After the Step Change 1300 — 1L00°F. Lh ORNL-DWG 70-2384 600 t—m— *F TEMPERATURE 1500 TEMPERRATVRAE DISTRIBUTION THROVUGH THE wALlL 1N SEcTIioNn AR-A 1400 gs- 5s 1s 1300 N g.5 10 DISTANCE FROM CENTERLINE , INCHES Fig. 32. Temperature Distribution Across Sectlon A-A After the Step Change 1300 - 1600°F. TEMPERAT vRE °F ORNL-DWG 70-2386 V4boot—— 1500 \ SECTiIoN C-C TEMPERATURE DISTRIBUTION THROUGH THE wAall 1~ 1400 9ds 5s 1s é—- {300 q.5 10 10.5 DISTANCE FROM LENTERLINE ,INCHES ORNL-DWG 70-2385 1600 b= e HMPERATURE DISTRIBUTION TROUGH THE WALL IN SEcTion B-8B i 1500 \ W 9s e W : 1400 e c « Y Ss T w b~ 1s 1 300 q.5 40 DISTANCE FROM CENTERL/NE Fig. 33. Temperature Dis- tribution Across Section B-B After the Step Change 1300 — 1600°F. Fig. 3L4. Temperature Dis- tribution Across Section C-C After the Step Change 1300 — 1600°F. oL TE/MMPERATVRE °F TEMPERATURE TENPERATURE DISTRIBUTION 1600 L—-— THROVGH THE WALL I SECTION D-D 1500 1400 5s 14300 9.5 10 11 L5 ORNL-IWG '70-2387 DISTANCE Fig. 35. FRolM cENVNTERLINE K TNCHES D-D After the Step Change 1300 — 1600°F. 1.8 Temperature Distribution Across Section ORNL-DWG 70-2388 1600F——— 1500 /00 TEMPERATURE DISTR THAODUVGHN THE WALL )BvTION IN SEcTion [F-E 9s 5s 1300 q.s 10 41 [y DISTANCE FROM THE CENTERLINE , 1\NCHES E-E After the Step Change 1300 — 1600°F. Fig. 36. Temperature Distribution Across Section L6 ORNL-DWG 70-2389 CIRCUMFERENTIAL STRESS DISTRIBUTION THRoUGHM THE WALL IN SeEcTion R-A 40 30 LY STRESS, KST -10 -20 ~30 \\‘? Ss as -50 -n| Fig. 37. Stress Distribution Across Section A-A After the Step Change 1300 — 1600°F. b7 ORNL-DWG 70-2390 R¥lAaL STRESS DISTRIBUTION THROVGH THE wWAHll IN SECTION B-B 70 6o 40 /. w A ., / a T - w - - X g5 10 W 1s _ DISTANCE FROM CENTERLINE ,LINCHES. v w -40 £ o F / // N -20 / Ss / 9s - 40 - éo .70 Fig. 38. Stress Distribution Across Section B-B After the Step Change 1300 — 1600°F. L8 ORNL-DWG 70-2391 CIRCUMFERENTIAL STRESS DISTRIBUTION T HROUgH THE WALL IN SEcTioN C-C 20 gs A 5¢ \ S/ . | s .\ \ \ q.5 10.5 DISTANCE FROM CENTERLINE, INCHES H - 0 X o« 10 n W « - Vi 1] 55 -20 // 9s -30 / -40 -50 -60 Fig. 39. ©Stress Distribution Across Section C-C After the Step Change 1300 — 1600°F 49 ORNL-DWG 70-2392 Circumferential Stress Distribution Through the Wall in Section D-D 10 R g5 | 10.5 T~ \ DISTANCE FROM CENTER LINE ,INCHES s STReEss KkKSI le] - 30 -40 -50 -60 - 70 Fig. 40. ©Stress Distribution Across Section D-D After the Step Change 1300 — 1600°F. >0 ORNL-DWG 70-2393 CIRCUMFERENTIAL STRESS DISTRV'BUTION 20 THROUGH THE WALL IN SeEcTion E-F 10 \1 e ———————— 10 1 12 2.8 DISTANCE FROM CENTERLINE, INCHES sTress , KS I -10 -40 -60 %7 ] // | Fig. 41. Stress Distribution Across Section E-E After the Step Change 1300 — 1600°F. °f TEMPERATURE tribution Across Section A-A After the Step Change 1300 — 1800°F. °g TEMPERATURE ol ORNL-DWG 70-23% ORNL-DWG 70-2395 TEMPERATUYURE DISTRIBUTION TEMPERATUVURE DISTRIB UTION THROUVUGC i THE WALL I'N THROUVGHKH THE WALL I N sgcrTion A-A SEcT)oNn B-B 1800 1800 1700 1700 w \ o w 4 o > < 500 1500 g :‘ 95 s s Q. p Y 1400 w 1400 : - 12\\\\~__ :>\\\\- 1300 + 1300 - 95 10. 45 10. DISTANCE FRoN DISTANCE FRort CENTERLINE INCHES CENTERLINE ,INCHES Fig. 42. Temperature Dis- Fig. 43. Temperature Distribution 1800 1700 ORNL-DWG 70-2396 TEMPERATUVRE DISTRIBVTION THROUGH THE wWALL IN SECTIOoN T -C VS, 1500 O\ \ 1300 9 N .3 10 DISTANCE FROM CENTERLINE INCHES Across Section B-B After the Step Change 1300 — 1800°F. Fig. L4h. Temperature Dis- tribution Across Section C-C After the Step Change 1300 — 1800°F. TEMPERARTURE °F TEMPERATUVRE °F 52 ORNL-DWG 70-2397 TEMPERATURE DI1ISTRIBVTION 18004 THROUGH THE WALL IN section D-D 1700 e 1500 9 < ¥ 1300 q.5 10. A4. DISTANCE FRONM CENTERLINE ,INCHES Fig. 45. Temperature Distribution Across Section D-D After the Step Change 1300 — 1800°F. ORNL-DWG 70-2398 TEMPERATURE DISTRIBUVUTION THROVGHM THE WwWALL IN SEcTioN E-E 1500 ; x 1300 a5 10. 11 2 DiISTANCE FROM CENTERLINE A LNCHES Fig. 46. Temperature Distribution Across Section E-E After the Step Change 1300 — 1800°F. STRESS, KSI >3 ORNL-DWG 70-2399 CIRCUMFERENTIAL STRESS OISTRIBUTION THROUGHN THE WALL IN &SEgcTioN A-A 9s 20 /] o 10 DISTANCE FROM CENTERLINE ,INCNES P ) -20 - &0 -60 -80 Fig. 47. Stress Distribution Across Section A-A After the Step Change 1300 — 1800°F. 54 ORNL-DWG 70-2400 STRESS, KS1 AXIAL STRESS DISTRIBUVTION THROVENW THE WALL 18 SEcTiON B-B 400 - I 4°~L A e 0 , ///' 10 101 DISTANCE FRopmM CENTERLINE INCHES 201} | 501 / 100 % Fig. 48. Stress Distribution Across Section B-B After the Step Change 1300 — 1800°F. 55 ORNL-DWG 70-2401 CIRCUMFERENT |AL S TRESS DISTRiIBVTION yol- THRoven TwE WALL I~ SEcTion C-C oI 0 4 ; : . 95 1o 10.5 DISTANCE FRonm CENTERL/INE —p—————arel 0 STRESS,6KS1 -20 - 40 - bo - 80 -Qo Fig. 49. Stress Distribution Across Section C-C After the Step Change 1300 — 1800°F. 56 ORNL-DWG 70-2402 CIRCUMFERENTIAL STRESS DISTRIBVTION THROUGH THE WALL '~ sEcTtionNnv D-D 20 X 0o j . . 11 . 95 / “ DISTANCE FRoOM CENTERLINE, K INCNHES W < . “ s -20 -40 -60 - 80 ~-100 -410 L Fig. 50. Stress Distribution Across Section D-D Atfter the Step Change 1300 — 1800°F. o7 ORNL-DWG 70-2403 90 1 — CIRCUMFERENTIAL STRESS OISTRIBVTIDON THROUGH THE WALL AT SEcCTIioN E-E 10 9¢ / - o ‘ \ , — X 4.5 10 11 12, DISTANCE FROM CENTERLINE ZLNCHES = _ 20 @ 2 X v “ «l oL - “"/0 ~ 60 ~-80 ] ~100 - (20 Fig. 51. Stress Distribution Across Section E-E After the Step Change 1300 — 1800°F. 58 ORNL-DWG 70-2404 TEMPERATVRE DISTRIBYUTION u THROUGH THE WALL I1~¥# SECTIion A-A . ° g 1300 i Fig. 52. Temperature Dis- § 1 tribution Across Section A-A After % the Step Change 1300 — 1200°F. . - 3 QY qQ v W * 4200 — 9.5 10. DISTANCE FROM CENTERLINE , INCHES ORNL-DWG 70-2405 TEMPERATUVRE DISTRIBUTION THROUGM THE wWALL W& SeEcTtiov B-8B Fig. 53. Temperature Distribution Across Section B-B After the Step Change | 1s 1300 — 1200°F. 1200 — 9.5 10 DI STANCE FROM CENTERLINVE , INCHES ORNL-DWG 70-2406 TEMPERATURE DISTRIBUTION :L THROUGH THE WALL IN SECTIDN C-C w _ | Fig. 54. Temperature Dis- © Lapo P . tribution Across Section C-C After 2 the Step Change 1300 — 1200°F. 1 i o | Ww Q. r w 40.5 = j200—n ; - DISTANCE PROM CENTERLINE ,INCHES 9.5 °F TEMPERAT URE 59 ORNL-DWG 70-2407 °f 1300 | T EMNMPERATURE DISTRIBVUT joN THROUGHW THME WALL |1~ sE&cTioN~¥ D-D s _— | — 1200 TEMPERATUVRE w ] w 45 10 14. DisTANCE FROMT CENTERLINE, INCHES Fig. 55. Temperature Distribution Across Section D-D After the Step Change 1300 — 1200°F. ORNL-DWG 70-2408 1300 TEMPERATUVURE DISTRIBvTionNn THROVE N TNE WALL 1~ SEcrionNn E -F 1200 /4 9.5 10. 14 12 DiSTANCE FRomMm CENTERLINEG, K |NCKHES Fig. 56. Temperature Distribution Across Section E-E After the Step Change 1300 — 1200°F. 60 ORNL-DWG 70-2409 CIRCUMFERENTIAL STRESS DISTRIBUT ION THROUGH THE wALL IN Secrion A-ARA 20 10 ~ v X wn A 9 X 1s 9s =~ 0 ’ - v\ sis 10 -10 T_. DISTANCE FRO M CENTERL INE ,INCHES Fig. 57. Stress Distribution Across Section A-A After the Step Change 1300 — 1200°F. 61 ORNL-DWG 70-2410 10\ ARXIAL STRESS DISTRIBUTION 30— THROUGH THE WALL IN S ECTiIOWN ’ N\ OISTANCE PROM CENTERLINE, INCHWHES STRESS KS 1 -10 1s A W 10 -10 \ -3 Fig. 58. Stress Distribution Across Section B-B After the . Step Change 1300 — 1200°F. ORNL-DWG 70-2411 CIRCLUMFERENTIAL STRESS DISTRIBVTION THROUGH THE wALL N SeEcTiov C-C 20 10 10.5 STRESS ,KSIT 0 N — ’ . a5 \Dlsrnwcf FROM CENTERLINE LWNCHES P \ . \__ - 10 1s Fig. 59. Stress Distribution Across Section C-C After the Step Change 1300 — 1200°F. ORNL-DWG 70-2412 o C CIRCUMFERENTIAL STRESS DISTRIBUT O N THROVUGHN THE WALL 1N Sgction D-D 30 20 i 17, X 10 w v . ¢ « 1s - " { ) ' ! ’ 9.5 10 — | | DISTANCE FROM CENTEHERLINE |, INCHES - 10 Fig. 60. Stress Distribution Across Section D-D After the Step Change 1300 — 1200°F. ¢9 k SI STRES S , 63 ORNL-DWG 70-2413 CIRCUMPERAENTIAL S5TRESS DISTRiIBVTION THROUGN THE wnl.'l. ‘N S ECTIon E-E 10. DISTANCE FROM CENTERLINE | INCHES Fig. 6l1. Stress Distribution Across Section E-E After the Step Change 1300 — 1200°F. ORNL-DWG 70-2414 TEMPERATVRE DISTR)BvT/ N rHROUGH THE wall I1n SeEcTion A-R 1s uw o W 9s o > o < L 4 w a C w - 1100 95 10. DISTANCE FROM CENTERLINE, INCH ES Fig. 62. Temperature Dis- tribution Across Section A-A After the Step Change 1300 — 1100°F. TEMPERATURE °F 6k ORNL-DWG 70-2415 | TEMPERATVRE DISTRIBUT!(ON THROUEHN THE WALL )~ SECTtonv B-8 n 1300 Ts ] W ° w o 9s > - < . / w a L w - 1100 95 10. OISTANCE FRo»Mm CENTER.L /VE , /INCHES Fig. 63. Across Section B-B After the Step Change 1300 — 1100°F. Temperature Distribution ORNL-DWG 70-2416 | T T TEMPERATURE DISTRIBVTION THROUGH THNE WALL IN SECTIoN C-C 00 — — 13 1s ~ 9s 1100 95 10.5 DISTANCE FROM Fig. 64. CENTERL 1wg INCHES > C-C After the Step Change 1300 — 1100°F. Temperature Distribution Across Section v °F TEMPERATURE . I K ° 9s O Y, d ~ < [ Q Q r w - 1100 . + , 4.5 10. 11. 65 ORNL-DWG 70-2417 TEMPERATURE DISTRIBuUTId®N THROUGH THE WALL IN SEcT/iON D-D Fig. 65. Temperature Distribution Across Section D-D After the Step Change 1300 — 1100°F. ORNL-DWG 70-2418 TEMPERATURE DISTRIBVTION THROvVEN THE WALL IN SEcTiON E-E — 1300 {-1s / 9s 1100 9.5 DISTANCE Fig. 10 | 11 12 FROM CENTERLINE, INCHES 66. Temperature Distribution Across Section E-E After the Step Change 1300 — 1100°F. 66 ORNL-DWG 70-2419 I | | 01— CIRCUMFBRENTIAL STARESS DISTRIBVUTION _ THMROUGH THE WALL 1N SEcTioN A-R 30 ol -4 " X 10 ‘. A w « - " DISTANCE FROM CENTERLINE, INCHES OTas \ ) is -10 ! 9 -20 Fig. 67. ©Stress Distribution Across Section A-A After the Step Change 1300 — 1100°F. € 67 ORNL-DWG 70-2420 ) . l ' l 40 AXIRL STRESS DISTAIBUTION THROUGN THE WALL IN SECTION B-B 30 20 \ 9¢ 1s 10 : Tl Y X " : \ DISTANCE FROM CENTERLINE (INCHES o A « 5 . 9 \ 10 " & '10 \ A -20 -30 -40 Fig. 68. Stress Distribution Across Section B-B After the Step Change 1300 — 1100°F. 68 ORNL-DWG T0-2421 50 CIRCUMFERENTIAL STRESS DISTRIBUTION 0| THROUGM THE waLL IN SEcTioN (-C 30 20 10 9s ODISTANCE FRon CENTERLINE, i1NCHES 0 \ . _ 9.5 \ 10.5 /L—/ - ls o \ N — STRESS, KSI -20 Fig. 69. Stress Distribution Across Section C-C After the Step Change 1300 — 1100°F. < 69 ORNL-DWG 70-2422 ! | | I 401 ——— CIRCUMPERENTIAL STRESS DISTRIBUTION THROUG THE WALL 18 seEcTioNn D-D 50 40 9s 30 20 1s 10 \ -4 wn x w w w a ~ “ .5 ___..—-————_'4 DISTANCE FROM CENTERLINE, INCHES 10 Fig. T70. Stress Distribution Across Section D-D After the Step Change 1300 — 1100°F. sTReEss, KSI T0 ORNL-DWG 70-2423 50| CIRCYMFERENT IAL STRESS DISTRIBVUTION THROVEM THE wall IN section E-E 40 9¢ 30 20 1 10 DISTANCE FRoM CENTERLINE, INCHES . ) . | ) ' .$ 095 \ \ e -10 Fig. 71l. ©Stress Distribution Across Section E-E After Step Change 1300 — 1100°F. the