42 MPA-SEMINAR 2016, October 4 and

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1 Plastic buckling of thin-walled pipes with D/t > 50 and conclusions for the nuclear design codes Henry Schau, Angelika Huber TÜV SÜD Energietechnik GmbH, Mannheim, Germany 42 nd MPA-Seminar October 4 th and 5 th 2016 TÜV SÜD Energietechnik GmbH

2 Abstract The B 2 stress indices of thin-walled straight pipes with D/t-ratios (D - outside diameter, t - wall thickness) up to 140 are determined using nonlinear FE analyses. The analyses were performed for pipes made of ideal elastic-plastic materials and for a few chosen steels. For the calculation of the B 2 indices an earlier derived equation is used. The analyses show that the type of imperfection, the D/t ratio, the modulus of elasticity and the yield stress have significant influence on the B 2 indices. Straight pipes with D/t 40 fail with a simple kink. Pipes with D/t > 40 fail (mostly) by plastic buckling with some wrinkles. The transition between both cases is not defined clearly. The numerical failure shapes are in good agreement with the experimentally obtained shapes. For pipes with D/t > and an out of roundness around of 0.5% the nominal bending stress is for higher yield stresses at the point of instability smaller than the yield stress. In these cases, the failure occurs by local (plastic) buckling and in the elastic range of the nominal bending stress with small rotation angles. This is in agreement with the experimental results in the literature. Curves for the dependence of B 2 indices on the type of imperfection, the D/t ratio, the modulus of elasticity and the yield stress are given. In general, there is a good formal agreement between the calculated values and the values of the ASME Code. The analyses indicate a different temperature dependence of the B 2 indices. Finally, the influence of the secondary stresses from disabled thermal expansion and anchor movements on failure by buckling and on the safety of piping systems with D/t > 50 is discussed. TÜV SÜD Energietechnik GmbH Folie 2

3 1. Introduction The design of piping components for primary loads in modern nuclear codes, such as the ASME Boiler and Pressure Vessel Code (further the ASME Code) [1], the French RCC-M [2] and the German KTA [3] and [4], are based on the formula B 1 D p 2 t + B 2 D M 2 I σ allow with I = π 64 D4 d 4 (1) B 1 and B 2 are the (primary) stress indices for the internal pressure p and the primary bending moment M (d - inside diameter, I - moment of inertia, σ allow - allowable stress). Initially, the stress indices were only valid for piping components with dimensions D/t 50. With the 2008 Addendum to the 2007 Edition of the ASME Code the range for the dimensions was extended to D/t 100. For the range 50 < D/t 100 the B 1 indices in Table NB-3681(a)-1 are valid and the B 2 indices should be multiplied by a correction factor 1/(X Y) given in the NB (c) (T - design temperature in C): X = DΤt (2) Y = T for ferritic materials and Y = 1.0 for other materials The same corrections are given in the NC (class 2) und ND (class 3). These enhancements were included in the 2013 Editions of the German KTA and The background for these corrections is that the failure of thin-walled piping with D/t > 50 occurs predominantly by (local) plastic buckling. Therefore, the failure and particularly the (plastic) buckling of straight thin-walled pipes are studied using static and dynamic nonlinear FE analyses. The stress design formulas in the nuclear codes will be discussed for the case of thin-walled pipes with D/t > 50. TÜV SÜD Energietechnik GmbH Folie 3

4 2. Determination of the B 2 indices and FE Analyses The ASME Code does not give an appropriate method for determining the stress indices. A new method to calculate the B 2 stress index is given by Matzen and Tan [5]. In [6] this method was applied on thinwalled straight pipes with D/t > 50. For an ideal elastic-plastic material the following equation for the calculation of the B 2 indices from the instability moment is given: B 2 = σ y Z pl M IL = M pl M IL with Z pl = 1 6 D3 d 3 (3) (M IL - instability moment, σ y - yield stress) The instability moment M IL is defined in the NB of the ASME Code. For materials not exhibiting a definite yield point the 0.2% offset yield stress (proof stress) is used. This yield stress is rather an empirical approach and from a mechanical or theoretical point of view difficult to justify. To verify this approach, the dependence of the B 2 index on the D/t ratio is to be determined. The obtained B 2 indices must converge to 1.0 for small D/t ratios. Otherwise, the yield stress is to be corrected. It is noted, that the ASME Code uses a similar method to derive the factor X in Equation (2). For this purpose, the data for M max /M pl from the General Electric Report [7] were used. The factor Y is based on the temperature dependencies of the allowable compressive stresses in the Section II, Part D, Subpart 3 of the ASME Code and of the yield stresses. TÜV SÜD Energietechnik GmbH Folie 4

5 The analyses were performed with the FE program Abaqus [8]. Geometric nonlinearities (large displacement and strain) are taken into account. The FE models use S4 shell elements and are symmetric to the plane of bending. The mesh is downsized axially to the centre. The considered pipes have an outside diameter of 200 mm and lengths of 1000 mm, 2000 mm, 4000 mm and 8000 mm. The D/t ratio varies from 20 to 140. The following imperfections are used in the analyses: - scaled buckling modes from elastic buckling analyses - analytically defined single dents The single dents are defined by the following expression: δr = α cos π z λ + 1 cos β φ (4) r is the radial deviation from the ideal circular geometry (z - axial coordinate from the middle, - circumferential angle to the plane of bending). The parameter is the half wavelength for elastic buckling given by Timoshenko and Gere [9]. The geometric parameter is derived from the numerical obtained elastic buckling modes. The size of the local deviation from the ideal circular cross section is characterized by the out of roundness: O = D max D min ΤD 100% (5) (D min, D max - minimum and maximum outside diameter) The ASME Code, Section I, PG states Pipe having a tolerance of ±1% on either the O.D. or the I.D.. The KTA and specify a maximal deviation of 2% for pipes. The ASTM A530 gives a maximal out of roundness of 1.5% for thin-walled pipes with D/t > 33. The EN ISO 1127 specifies tolerances for the outer diameter between 0.5 and 1.5%. Consequently, a local out of roundness of about 0.5 1% is for pipes a usual technical tolerance. TÜV SÜD Energietechnik GmbH Folie 5

6 For the following calculations the ideal elastic-plastic material model and the real material models for some steels are used. Table 1 shows the material properties for these steels (E - modulus of elasticity, σ u - ultimate tensile strength). Table 1: Important material properties of the steels Material E in GPa σ y in MPa σ u in MPa Material data X6CrNiNb Mutz [10] AISI 304L Wilkins [11] 22NiMoCr Bernauer et al. [12] 20MnMoNi Reicherter [13] TÜV SÜD Energietechnik GmbH Folie 6

7 3. Results For the first calculations pipes made of ideal elastic-plastic material are used. Figures 1 and 2 show typical failure modes for pipes (length L = 2000 mm, E = 200 GPa, σ y = 500 MPa, single dent with O = 0.5%) with D/t = 30 and 90. The pipe with D/t = 90 fails by plastic buckling with multiple wrinkles. These shapes are in a good agreement with the shapes in [14-18]. Figure 1: Failure mode for an imperfect, ideal elastic-plastic pipe with D/t = 30 Figure 2: Failure mode for an imperfect, ideal elastic-plastic pipe with D/t = 90 TÜV SÜD Energietechnik GmbH Folie 7

8 Figure 3 displays experimental data (M max - maximum moment) for ferritic pipes and the linear approach (green line) from the General Electric Report [7]. The yield stresses are between 336 and 586 MPa. The linear fit of the data in the range of 39 D/t gives: M max ΤM pl = DΤt (6) Figure 4 shows the numerical results for an ideal elastic-plastic pipe with a yield stress of 500 MPa for various imperfections. The slopes from to for the curves in the range 40 D/t 120 with a yield stress of 500 MPa and O = 0.5% are in a good agreement with the slope of of the experimental data in Figure 3. Therefore, further studies are mostly performed for pipes having a single dent O = 0.5% as an imperfection. Figure 3: Experimental data for M max /M pl for some ferritic pipes as a function of the D/t ratio from [7] Figure 4: M IL /M pl ratio for an ideal elastic-plastic pipe as a function of the D/t-ratio for various imperfections TÜV SÜD Energietechnik GmbH Folie 8

9 Figure 5 demonstrates the M IL /M pl ratio as a function of the D/t ratio for ideal elastic-plastic pipes (E = 200 GPa, σ y = 500 MPa, single dent with O = 1.0%) with different pipe lengths. There are no relevant differences between the results for pipes with lengths from 2000 to 8000 mm. For a 1000 mm long pipe the suppression of the ovalisation at the ends stabilizes the pipe and the boundary conditions have a greater influence. Figure 6 shows the M/M pl ratio for an ideal elastic-plastic pipe (E = 200 GPa, σ y = 500 MPa) with D/t = 100 as a function of the rotation angle for various out of roundness. The dashed blue lines are the curves for infinitely long pipes without an imperfection. The red line represents the moment for the first yield. Figure 5: M IL /M pl for an ideal elastic-plastic pipe (E = 200 GPa, σ y = 500 MPa) as a function of the D/t-ratio for different lengths Figure 6: M/M pl ratio for an ideal elastic-plastic pipe with D/t = 100 as a function of the rotation angle TÜV SÜD Energietechnik GmbH Folie 9

10 The B 2 indices for ideal elastic-plastic pipes depend also on the yield stress and the elastic modulus. Figure 7 shows the B 2 indices for ideal elastic-plastic pipes with D/t = 100 and O = 0.5% as a function of the yield stress. Figure 8 gives the results for pipes with similar geometry as a function of the elastic modulus. The B 2 indices are larger with increasing yield stress and decreasing elastic modulus. Figure 7: B 2 index for ideal elastic-plastic pipes (E = 200 GPa) with D/t = 100 and O = 0.5% as a function of the yield stress Figure 8: B 2 index for ideal elastic-plastic pipes with D/t = 100 and O = 0.5% as a function of the elastic modulus TÜV SÜD Energietechnik GmbH Folie 10

11 Figure 9: B 2 index for ideal elastic-plastic pipes with O = 0.5% as a function of the D/t ratio for two yield stresses Figure 10: M/M y ratio for an ideal elastic-plastic pipe with O = 0.5% of the D/t ratio Figure 10 shows the B 2 indices for ideal elastic-plastic pipes (E = 200 GPa) with O = 0.5% as a function of the D/t ratio for a yield stress of 250 and 500 MPa. The B 2 indices depend (almost perfectly) linearly on the D/t ratio in the range from 40 to 120. The slopes are for the yield stress of 250 MPa and for 500 MPa. It should be noted, that yield stresses of about 250 MPa are typical for austenitic and 500 MPa for ferritic steels. Figure 11 indicates that for pipes with a yield stress of 250 MPa and D/t > 100 and for pipes with a yield stress of 500 MPa and D/t > 70 the failure occurs in the elastic range of the nominal bending stress. TÜV SÜD Energietechnik GmbH Folie 11

12 Additional analyses were performed for pipes made of the austenitic steels X6CrNiNb18-10 and AISI 304L and of the ferritic steels 22NiMoCr3-7 and 20MnMoNi5-5. For pipes with D/t > and higher yield stresses (for ferritic pipes) the failure occurs in the elastic range of the nominal bending stress with small rotation angles. This is in agreement with the experiments by Elchalakani et al. [14] and Sherman [18]. A comparison for real and ideal elastic-plastic pipes is given in Table 2. There are only small differences between the real and the ideal material properties. Table 2: B 2 indices for real and ideal elastic-plastic pipes with D/t = 100 and O = 0.5% Material real B 2 for D/t = 100 ideal X6CrNiNb AISI 304L NiMoCr MnMoNi TÜV SÜD Energietechnik GmbH Folie 12

13 4. Conclusions for the design For pipes with D/t > (especially ferritic pipes) the failure occurs in the elastic range of the (nominal) bending stress with small rotation angles. The B 2 indices depend strongly from the D/t ratio, the out of roundness, the elastic modulus und the yield stress. Previously obtained numerical results indicate that the temperature dependency is small and the B 2 indices at room temperature are conservative. The yield stress and the elastic modulus decrease with increasing temperature. The B 2 indices decrease with lower yield stresses and increase with lower elastic moduli. The numerical analyses for austenitic pipes give B 2 = for O = 0.5% and B 2 = for O = 1%. The ASME Code states B 2 = The numerical analyses for ferritic pipes give B 2 = for O = 0.5% and B 2 = for O = 1%. The ASME Code, Subsection NB gives the following limits for the primary stresses: D p 4 t + B D M 2 2 I 1.5 S m σ y for Level 0, A (9) D p 4 t + B D M 2 2 I min 3 S m; 2 σ y 2 σ y for Level D (10) The allowable stress for Level A may be equal to σ y. It has already been stated, that the failure for pipes with yield stresses around 500 MPa, D/t ~ 100 and p ~ 0 occurs for nominal stresses smaller/equal the yield stress (see also Figure 10). The pressure term and B 2 index give always a particular margin against failure. On the other hand, the safety margin in Level 0 /A against failure for a pipe with D/t 50 is higher than 2 (comparison with Level D). An additional (or possibly necessary) safety factor for D/t > 50 could be calculated with help of these considerations and depends primarily on the yield stresses. TÜV SÜD Energietechnik GmbH Folie 13

14 The ASME Code, Subsection NB or NC gives the following limits for the secondary stresses from disabled thermal expansion and anchor movements: C 2 i D M 2 I 3 S m 2 σ y with C 2 = 1.0 for straight pipes - NB-3653 (11) D M 2 I S A 1.5 σ y with i = 1.0 for straight pipes - NC-3653 (12) The allowable moment for secondary stresses might be higher than the first yield moment. A failure by plastic buckling only by secondary loads is therefore also possible. The following points are under discussion: The moments from disabled thermal expansion and anchor movements have the same effect in relation to a failure due to (plastic) buckling as the primary moments and must be taken into account. The B 2 indices at room temperature are conservative also for higher temperatures. A correction factor for higher temperatures is not necessary. Calculation of an additional safety factor. The corrections of the B 2 -indices are based only on straight pipes, therefore the B 2 indices are also to be determined for other components (especially elbows). TÜV SÜD Energietechnik GmbH Folie 14

15 5. Summary Ideal elastic-plastic pipes with D/t 40 fail with a simple kink. Pipes with D/t > fail by (plastic) buckling with some wrinkles. The numerical obtained failure shapes are in a good agreement with the experimental shapes. The B 2 index significantly depends on the D/t ratio, the elastic modulus and the yield stress. The imperfections have a considerable influence on the B 2 index. For ideal elastic-plastic pipes with D/t = 100 and a usual out of roundness of 0.5% typical values for the B 2 index are 1.3 for a yield stress of 250 MPa and 1.5 for 500 MPa. The differences between the B 2 indices for ideal and real materials are small and therefore without practical importance. A comparison of the numerical obtained B 2 indices with experimental results indicates an out of roundness of 0.5%. Final statements are not possible, because the required information about the experiments is not completely available. For an out of roundness of 0.5% the obtained values of the B 2 index are overall in a formal good agreement with the values stated in the ASME Code. Some analyses show differences with respect to the temperature dependence and the additional correction factor. Some conclusions for the design or the design equations are given. TÜV SÜD Energietechnik GmbH Folie 15

16 References 1. ASME, 2015, Boiler and Pressure Vessel Code, Section III, Division 1. The American Society of Mechanical Engineers. 2. AFCEN, 2012, RCC-M, Design and Conception Rules for Mechanical Components of PWR Nuclear Islands (English version). 3. KTA , , Components of the Reactor Coolant Pressure Boundary of Light Water Reactors; Part 2: Design and Analysis. Nuclear Safety Standards Commission (KTA), Germany. 4. KTA , , Pressure and Activity Retaining Components of Systems Out-side the Primary Circuit; Part 2: Design and Analysis. Nuclear Safety Standards Commission (KTA), Germany. 5. Matzen, V. C., and Tan, Y., 2000, The History of the B2 Stress Index and a New Margin-Consistent Procedure for Its Calculation, 2000 ASME Pressure Vessels and Piping Conference, Seattle, Washington, PVP-Vol. 399, pp Schau, H., Mkrtchyan, L., and Geier, M The Influence of Imperfections and Nonlinearities on the Failure and B2 Stress Index of Thin-Walled Pipes, Journal of Pressure Vessel Technology, 137(6), DOI: / General Electric Report, 1978, Functional Capability Criteria for Essential Mark II Piping, Report No. NEDO Abaqus, Version 6.13, SIMULIA (ABAQUS Inc., Providence, USA). 9. Timoshenko, S. P., and Gere, J. M., 2013, Theory of Elastic Stability. Dover Publications, Mineola/New York. TÜV SÜD Energietechnik GmbH Folie 16

17 10. Mutz, A., 2011, Structural Assessment of Piping Components and Systems in Energy Conversion Facilities Considering the Real Material Characteristic. Dissertation on the Materials Testing Institute, University of Stuttgart. 11. Wilkins, J. K., 2002, Experimental and Analytical Investigation into the Non-Linear Behavior of 2 and 4, 90, Large Radius, Schedule 10, Stainless Steel Elbows Under Monotonic, Cyclic and Rate Dependent Loading. Master Thesis, North Carolina State University. 12. Bernauer, G., Brocks, W., Mühlich, U., Steglich, D. and Werwer, M. (1999). Hinweise zur Anwendung des GURSON-TVERGAARD-NEEDLEMAN-Modells, GKSS/WMG/99/10, Geesthacht. 13. Reicherter, B. (2011). Determination of material behaviour in the low cycle fatigue regime for improved lifetime assessment. Dissertation on the Materials Testing Institute, University of Stuttgart. 14. Elchalakani, M., Zhao, X. L., and Grzebieta, R., 2002, Bending Tests to Determine Slenderness Limits for Cold-Formed Circular Hollow Sections, J. Constr. Steel Res., 58(11), pp Houliara, S., and Karamanos, S. A., 2011, Buckling of Thin-Walled Long Steel Cylinders Subjected to Bending, ASME J. Pressure Vessel Technol., 133(1), p Dama, E., Gresnigt, A. M., and Karamanos, S. A., 2006, Failure of Locally Buckled Pipelines, ASME J. Pressure Vessel Technol., 129(2), pp Guo, L., Yang, S., and Jiao, H., 2013, Behavior of Thin-Walled Circular Hollow Section Tubes Subjected to Bending, Thin-Walled Struct., 73, pp Sherman, D. R., 1976, Tests of circular steel tubes in bending, Journal of the Structural Division (ASCE), 102(11), pp TÜV SÜD Energietechnik GmbH Folie 17

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