- Email: [email protected]
Correlation of test and FEA results for elbows subjected to out-of-plane loading
Nuclear Engineering and Design 217 (2002) 213– 224 www.elsevier.com/locate/nucengdes
Correlation of test and FEA results for elbows subjected to out-of-plane loading Ying Tan, Kevin Wilkins, Vernon Matzen * Center for Nuclear Power Plant Structures, Equipment and Piping, North Carolina State Uni6ersity, Raleigh, NC 27695 -7908, USA Received 10 October 2001; received in revised form 1 February 2002; accepted 8 March 2002
Abstract The objective of this study is to validate a finite element analysis (FEA) simulation methodology to predict the out-of-plane behavior of piping elbows. Two out-of-plane elbow experiments and the corresponding FEA shell and elbow element models are presented. For load–displacements results, all the FEA predictions showed excellent agreement with measured experimental results, and for load– strain behavior, the shell FEA model results correlated quite well with the experimental results. © 2002 Elsevier Science B.V. All rights reserved.
1. Introduction
2. Background
In previous publications (Tan et al., 2002; Tan and Matzen, 2002), finite element analysis (FEA) procedures were developed and used to successfully simulate the behavior of eight physical tests: two four-point-bending tests on straight pipes, four in-plane closing bending tests and two inplane opening bending tests on 90° long-radius stainless steel (SS) elbows. The purpose of this study is to determine if out-of-plane behavior can be equally well simulated.
The study of pipe bends began with von Karman (1911). Since then Hovgaard (1930), Turner and Ford (1957) developed comprehensive theories for curved tubes under in-plane bending. Beskin (1945) extended von Karman’s theory and Smith (1967) adapted Turner and Ford’s analysis to deal with out-of-plane bending. All the studies above were based on elastic and small-deflection assumptions. In addition to theoretical studies, extensive experimental investigations have been performed. Smith and Ford (1967) carried out an experimental investigation on three individual pipe bends subjected to three-dimensional loading, one for in-plane bending, one for out-of-plane bending and one for combined in-plane and out-of-plane bending. Deflections, cross-sectional distortions and strains were measured. In 1978, results from
* Corresponding author. Tel.: +1-919-515-7736; fax: + 1919-515-5301. E-mail address: [email protected] (V. Matzen).
0029-5493/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 9 - 5 4 9 3 ( 0 2 ) 0 0 1 3 2 - 2
214
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
20 elbow tests were presented by Greenstreet (1978), of which five were out-of-plane tests, some with internal pressure and some without. Imazu et al. (1979) tested a thin-walled 304SS elbow at 600 °C using out-of-plane bending. In Prost et al.’s (1983) experimental study, three out-of-plane elbow tests were conducted at room temperature with and without internal pressure and one at elevated temperature (340 °C). Hilsenkopf et al. (1988) presented the results of two series of tests performed on 90° large-radius elbows, among which six were out-of-plane tests. Each series consisted of three tests. One was out-of-plane bending at room temperature without internal pressure, one was without internal pressure but at 120 °C, and one was at room temperature but with internal pressure. The moment– rotation relationships and the ovalization modes were recorded and illustrated. All of the work cited above was based on experiments— FEA simulation was not involved. Natarajan and Mirza (1981) described a finite element procedure for the analysis of a piping system subjected to out-of-plane moments. Basavaraju and Lee (1993) utilized ANSYS (1989) to study stress intensification factors and the C2 stress index for in-plane and out-of-plane moment, in which linear elastic analysis was used. To determine the stress for an elbow which has a stiffener closer than one pipe radius from the
Fig. 2. Test setup for Pipe-2. (a) Schematic; (b) Photograph.
Fig. 1. Test setup for Pipe-1 (from Figure 2 of Greenstreet, 1978).
elbow, Machida et al. (1995) carried out elastic stress analyzes using FEA for a 90° elbow subjected to out-of-plane moment. Mourad and Younan (2000a) using ABAQUS (1989) and taking geometric and material non-linearities into account, performed non-linear analyzes of elbows subjected to out-of-plane moment and internal pressure. All the works above focused exclusively on FEA study and the computed results were not confirmed by experimental data. Some reconciliation work has been conducted to bridge the experimental and FEA investiga-
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
215
data by 13–21% for out-of-plane forces and they attributed the discrepancies to ‘the geometric irregularities of the test models’. Kussmaul et al. (1995) reported a 90° elbow subjected to out-ofplane bending without internal pressure, and a FEA using ABAQUS ELBOW31 to simulate the test. Their computed forces differed by up to 15–20% compared with experimental results. They attributed the discrepancies to inaccurate material properties. Mourad and Younan (2000b), in a second 2000 paper, concentrated on the effect of FEA modeling parameters for pipe bends subjected to out-of-plane moment and internal pressure. They verified their FEA models by comparing their computed results to measured test data reported by Greenstreet (1978). Their correlations are quite good. Curiously, the Greenstreet data they present vary by 8–9% from what Greenstreet has in his report, although this deviation would appear to have little effect on the correlation assessment. The strain correlation for what they call their ‘connected model’ is also quite good, but they display the results in a moment –strain graph whereas Greenstreet gave his results in load–strain coordinates and so it is difficult for a casual observer to correlate their results directly with the original Greenstreet curve. They conclude that using the ‘closest in properties to a real elastic-plastic strain-hardening material’ (Mourad and Younan, 2000a) is very important for correlations between FEA and tests. As described above, even though much research has been performed on elbows subjected to outof-plane bending, the problem of simulating test
Fig. 3. Specimen dimensions for Pipe-2.
Fig. 4. Measured cross-sections. (a) Cross-section location; (b) pipe cross-section.
tions. Fujimoto and Soh (1988) analyzed very thin-walled pipe bends under in-plane and out-ofplane moments and compared their FEA stress distributions with experimental measurements. The experimental values are less than their FEA Table 1 Measured outside diameters and wall thicknesses for Pipe-2 Plane no.
P-1
P-2
P-3
P-4
P-5
Average
Unit
(in)
(cm)
(in)
(cm)
(in)
(cm)
(in)
(cm)
(in)
(cm)
(in)
(cm)
Do Flank–Flank t-Flank t-Flank Do Intra–Extra t-Intrados t-Extrados
2.380 0.132 0.135 2.375 0.131 0.119
6.045 0.335 0.343 6.033 0.333 0.302
2.385 0.130 0.131 2.365 0.141 0.120
6.058 0.330 0.333 6.007 0.358 0.305
2.376 0.130 0.135 2.370 0.139 0.117
6.035 0.330 0.343 6.020 0.353 0.297
2.382 0.130 0.138 2.377 0.141 0.119
6.050 0.330 0.351 6.038 0.358 0.302
2.380 0.132 0.142 2.377 0.128 0.120
6.045 0.335 0.361 6.038 0.325 0.305
2.381 0.131 0.136 2.373 0.136 0.119
6.047 0.332 0.345 6.027 0.345 0.302
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
216
Table 2 Average outside diameters and wall thicknesses for Pipe-2 Do Segments of test specimens
Elbow Straight pipe
Average t
(in) (cm) (in) (cm)
Average
0.133 0.338 0.110 0.279
Do/t
Extrados–Intrados
Flank–Flank
Average
2.373 6.027 – –
2.381 6.047 – –
2.377 6.038 2.375 6.033
17.9 21.6
Table 3 Material properties of Pipe-1 Carbon steel SA106 Grade B
Sy
Pipe-1 (Greenstreet, 1978, Table 1) Base curve (ANSYS, 1999, Table 3)
Su
E
(ksi)
(MPa)
(ksi)
(MPa)
(ksi)
(GPa)
50.0 42.5
345 293
73.6 69.7
507 480
30,100 42,922
208 296
ey (%)
eu (%)
N/A 0.2
N/A 20
Table 4 Material properties of Pipe-2 Stainless steel 304
Sy
Segments of test specimens
(ksi)
(Mpa)
(ksi)
(MPa)
(ksi)
(GPa)
35.4 39.5 38.4
244 272 265
81.0 82.2 85.8
558 567 592
N/A N/A 29,000
N/A N/A 200
Manufacturer’s report NCSU ASTM test
Elbow Straight pipe Straight pipe
and FEA results accurately has not been fully solved. This paper describes an investigation into this problem and a resolution to it.
Su
E
3. Experiments
to as Pipe-1 in this paper). The test information is illustrated in Fig. 1. Measured specimen dimensions were not presented and only the following nominal dimensions were reported in Greenstreet (1978): Do = 6.625 in (16.83 cm) and t=0.280 in (0.711 cm) for a Do/t ratio of 23.7.
3.1. Pipe-1
3.2. Pipe-2
The first set of data used to verify the FEA procedure described in Tan et al. (2002), Tan and Matzen (2002) is from an out-of-plane bending test on 6¦ schedule 40 long radius carbon steel elbow, reported by Greenstreet (1978), (called Test No. PE-3 in Greenstreet (1978), and referred
At North Carolina State University (NCSU), an elbow specimen, designated Pipe-2, was tested (Wilkins et al., 2001) under out-of-plane loading, as shown in Fig. 2. The specimen was a 2¦ schedule 10, 90° long radius, SS304L, seamless, butt welding elbow, with segments of straight pipes
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
Fig. 5. Engineering stress strain curves for Pipe-1. Fig. 7. Load – displacement curves for Pipe-1.
Fig. 6. Engineering stress strain curves for Pipe-2.
Fig. 8. Load – displacement curve for Pipe-2.
217
218
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
welded to both ends, as illustrated in Fig. 3. The length of each straight tangent portion was approximately five times the outside diameter of the elbow. This length was selected so that the end constraints would have negligible effect on the elbow behavior (Yu, 1998). Actual geometrical dimensions and pipe wall thicknesses were measured before the test. Five cross-sections along the pipe bend radius, labeled P-1 to P-5 in Fig. 4(a), were selected as planes for which measurements were taken. In each plane, the
Fig. 11. SG01 strain responses for Pipe-1 (taken from figure 24 in Greenstreet, 1978). Fig. 9. Local mesh for strain gage location for SG01, Pipe-1.
wall thicknesses at extrados, intrados and flanks were measured as shown in Fig. 4(b). The measured data are given in Table 1 and the average wall thicknesses and average outside diameters are provided in Table 2.
4. Finite element analysis In this study, ANSYS (1999) version 5.6, ABAQUS (2000) version 6.1 were used. Two types of FEA models, one using shell elements and the other using elbow elements, were tried. For the FEA shell models, ANSYS SHELL43, SHELL181 and ABAQUS S8R5 were utilized. For the FEA elbow element models, ABAQUS ELOW31 was used. In all cases, large deformation and stress stiffness effects were taken into account.
4.1. Material models
Fig. 10. SG00 strain responses for Pipe-1 (taken from Figure 24 in Greenstreet, 1978).
FEA requires the non-linear stress–strain curves, but none were available for any of the specimens tested. However, the values of the three material
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
219
Fig. 12. Strain gage locations for Pipe-2. (a) SG01 to SG05 locations (Load coming out of paper); (b) SG01 to SG03 photograph (Load going in paper).
parameters (E, Sy and Su) were provided in Greenstreet (1978) for Pipe-1 and in the manufacturer’s report for Pipe-2, as shown in Tables 3 and 4, respectively. In the current study, the procedure described in Tan and Matzen (2002) was used to construct the specimen stress– strain curves based on these three parameters and available measured stress– strain curves of the same type of material. Briefly, this procedure is one in which a stress–strain curve is constructed such that its yield stress, ultimate stress and modulus of elasticity are the same as a specified set (e.g. handbook value for E and the manufacturer’s specifications for Sy and Su) and the shape of the curve is similar to one obtained from a test on a similar material. For Pipe-1, a uniaxial tensile test stress–strain curve for SA 106 Grade B carbon steel, published in Gosselin and Wais (1999) and shown here in Fig. 5 (after being converted to engineering stress and strain), was used as the base curve and it is assumed that the engineering ultimate strain corresponding to the ultimate
stress was 20%.1 For Pipe-2, an ASTM type tensile test was performed on a coupon specimen cut from a piece of straight pipe, which is the same product batch as the straight pipes used in the NCSU specimens. The experimental engineering stress-engineering strain data are shown in Fig. 6 as open circles, and labeled as ‘2¦Sch10 Coupon’. The measured stress–strain data show close agreements with the manufacturer’s report, as given in Table 4. Since the manufacturer’s test report gave different properties for the elbow and straight tangent pipes, two separate non-linear stress–strain curves were needed in the FEA model—one for the straight tangent pieces and one for the elbow. For the straight tangent portions, the stress–strain curve of 2¦Sch10 Coupon was used directly. For the elbow portion, a new 1 It is recognized that this process, which was developed for modifying curves for stainless steel, is not exact and may distort a stress – strain curve for Carbon Steel. However, the process is thought to be sufficiently accurately for the intended purpose here.
220
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
stress–strain curve was constructed as illustrated by the line labeled ‘Linearly Scaled Elbow Curve’ in Fig. 6, using the data of the 2¦Sch10 Coupon as the base curve. Since the weld bead of Pipe-2 specimen was ground off before the test, it was assumed to be negligible in the FEA model.
4.2. Correlation of global beha6ior For Pipe-1, experimental load– displacement curves from in Greenstreet (1978) were digitized and are replotted here in Fig. 7. The circular marks show the test data of load vs. displacement at Dial Gage 1(labeled as Test D1) and the rectangles are for Dial Gage 2 (Test D2.) FEA results are shown in Fig. 7 for three shell element models (SHELL43 and SHELL181 from ANSYS and
S8R5 from ABAQUS) and one elbow element model (ELBOW31 from ABAQUS.) All of the FEA results are remarkably similar to each other and they match the test results very well, although there is a slight over prediction of the D2 data as the elbow yields. As seen in Fig. 8, the FEA results for Pipe-2 also matched the measured displacement data very well. A close inspection of the curves will show that the curve for SHELL43 ends at 4¦ (10.2 cm) and the curve for SHELL181 ends at 4.5¦ (11.4 cm). At these points in the analyzes, convergence difficulties caused the program to terminate. For elbow model, no convergence problems were encountered. The reason for this lack of convergence with the shell analyzes is not yet fully understood.
Fig. 13. Local mesh for strain gage locations for Pipe-2. (a) Gage sizes, locations, orientations and FEA local mesh for SG01, SG02 and SG03; (b) gage sizes, locations, orientations and FEA local mesh for SG04 and SG05.
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
221
Fig. 14. Strain responses for Pipe-2. (a) SG01 Longtitudinal strain; (b) SG01 Hoop strain; (c) SG02 Longtitudinal strain; (d) SG02 Hoop strain; (e) SG03 Longtitudinal strain; (f) SG03 Hoop strain; (g) SG04 Longitudinal strain; (h) SG04 Hoop strain; (i) SG05 Longitudinal strain; (j) SG05 Hoop strain.
4.3. Correlation of strains In
Greenstreet
(1978),
measured
response
curves were given for two strain gages, designated SG00 and SG01. Gages SG00 and SG01 were located 33 and 48°, respectively, around the el-
222
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
bow, measuring from the flank to the intrados. Gage SG00 was 36° along the bend angle from the elbow-straight pipe weld while gage SG01 was 41° along the bend angle. To simulate these strains a shell model using ANSYS SHELL181 was
created with the mesh refined locally at the strain gages locations, as illustrated in Fig. 9. The digitized curves from Greenstreet (1978) are shown in Figs. 10 and 11 along with the FEA results. It is seen that the FEA responses followed the experi-
Fig. 14. (Continued)
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
223
Fig. 14. (Continued)
mental results closely for SG01, while there is some deviation between FEA and test data for a portion of the SG00 load– strain curve. The reason for the deviation is not clear. For Pipe-2, five tee-rosette strain gages (MicroMeasurements Division, Measurements Group, Inc., Raleigh, NC. Gage type: EA-06-062TT-120), called SG01 to SG05 hereafter, were mounted on the specimen, as illustrated in Fig. 12(a) and (b). These positions were in the high-strain regions given by FEA predictions and were selected in order to verify the FEA procedure. For each gage, longitudinal and hoop strains were recorded. The gage elements were aligned with the local coordinate axes of the shell elements in the gage areas. A model using ANSYS SHELL181 was created similar to the one used for the Pipe-1 specimen to simulate these responses. The local mesh at the strain gage region was refined, as shown in Fig. 13. The FEA results plotted together with the measured experimental data are shown in Fig. 14. In general, the FEA predictions match all the
experimental responses very well. The discrepancies, which are reasonably small, are likely a result of the interpolation of the strain data from the FEA postprocessor. In this study, the FEA results were the average element strains at the gage regions. The discrepancy between the actual gage areas and those defined in FEA will unavoidably introduce some error.
5. Conclusions This paper presents two experiments for out-ofplane monotonic loading of piping elbows and the non-linear FEA procedures used to simulate them. FEA shell models and elbow models were used and they all give excellent results compared with measured load– displacement responses and the shell models produced strain responses that matched test data quite well. When only the global behavior is required, the ABAQUS elbow element would appear to be preferable to ABAQUS or ANSYS shell elements.
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
224
Acknowledgements The authors would like to acknowledge the support of the Center for Nuclear Power Plant Structures, Equipment and Piping and North Carolina State University, the PVRC Subcommittee on Flexibility Models and Stress Intensification Factors (Grant 98-PNV-6) and the North Carolina Supercomputing Center.
Appendix A. Nomenclature Do E eu ey Sy Su T
outside diameter of pipe Young’s modulus uniaxial engineering ultimate strain uniaxial engineering yield strain yield stress ultimate stress wall thickness
References ABAQUS, Version 4.8, Hibbitt, Karlsson and Sorensen, Inc., 1989. ABAQUS Version 6.1, 2000. Hibbitt, Karlsson & Sorensen, Inc. ANSYS Engineering Analysis System User’s manual for ANSYS Revision 4.4, May 1, 1989, Houston, Pennsylvania. ANSYS Version 5.6, 1999. ANSYS Inc. Basavaraju, C., Lee, R.L., 1993. Stress distribution in elbow due to external moments using finite-element methodology. PVP, ASME 249, 103 –112. Beskin, L., 1945. Bending of thin curved tubes. J. Appl. Mech. Trans. ASME 67, A-1 –A-7. Fujimoto, T., Soh, T., 1988. Flexibility factors and stress indices for piping components with D/T\ = 100 subjected to in-plane or out-of-plane moment. J. Press. Vessel Technol. 110, 374 – 386. Gosselin, S.R., Wais, E.A., 1999. A case study comparison of ASME section III appendix F and proposed code case N-584 criteria in carbon steel and stainless steel pipes. PVP-vol. 383, ASME, 13 –22 Greenstreet, W.L., 1978. Experimental study of plastic responses of pipe elbows. ORNL/NUREG-24, 1– 51. Hilsenkopf, P., Boneh, B., Sollogoub, P., 1988. Experimental study of behavior and functional capability of ferritic steel elbows and austenitic stainless steel thin-walled elbows. Int. J. Pres. Vessel Piping, 0308-0161/88, 111 –128. Hovgaard, W., 1930. Bending of Curved Pipes. Proc. of the
3rd International Congress for Applied Mechanics, Stockholm, Sweden, vol. 2, pp. 331 – 341. Imazu, A., Sakakibara, Y., Nagata, T., Hashimoto, T., 1979. Plastic instability test of elbows under in-plane and outof-plane bending. Trans. of the 5th SMiRT Conference, Berlin, Germany, E6/5. Kussmaul, K., Diem, H.K., Uhlmann, D., Kobes, E., 1995. Pipe bend behavior at load levels beyond design. 13th SMiRT Conference, Brazil, pp. 187 – 198. Machida, H., Kamishima, Y., Ueta, M., Dozaki, K., 1995. Stress index of 45 and 90 degree elbow subjected to inplane and out-of-plane moment. Transactions of the 13th International Conference on Structural Mechanics in Reactor Technology (SMiRT 13), Brazil, pp. 377 – 382. Mourad, H.M., Younan, M.Y.A., 2000. Nonlinear analysis of pipe bends subjected to out-of-plane moment loading and internal pressure. PVP-vol. 399, Design and Analysis of Pressure Vessels and Piping, ASME, 123 – 129. Mourad, H.M., Younan, M.Y.A., 2000. The effect of modeling parameters on the predicted limit loads for pipe bends subjected to out-of-plane moment loading and internal pressure. PVP-vol. 399, Design and Analysis of Pressure Vessels and Piping, ASME, 131 – 148. Natarajan, R., Mirza, S., 1981. Stress analysis of curved pipes with end restraints subjected to out-of-plane moments. Proceedings of the 6th SMiRT Conference, Paris, F2/8, pp. 1 – 9. Prost, J.P., Taupin, Ph., Delidais, M., 1983. Experimental study of austenitic stainless steel pipes and elbows under pressure and moment loadings. 7th SMiRT Conference, Chicago, G/F 5/5. Smith, R.T., 1967. Theoretical analysis of the stresses in pipe bends subjected to out-of-plane bending. J. Mech. Eng. Sci. 9 (2), 115 – 123. Smith, R.T., Ford, H., 1967. Experiments on pipelines and pipe bends subjected to three-dimensional loading. J. Mech. Eng. Sci. 9 (2), 124 – 137. Tan, Y., Matzen, V.C., 2002. Correlation of test and FEA results for thin-walled piping elbows considering welds (accepted for publication in Nuclear Engineering and Design). Tan, Y., Matzen, V.C., Yu, L., 2002. Correlation of test and FEA results for the nonlinear behavior of elbows (accepted for publication in the ASME J. Pres. Vessel Technol.). Turner, C.E., Ford, H., 1957. Examination of the theories for calculating the stresses in pipe bends subjected to in-plane bending. Proc. Instn. Mech. Engrs. von Karman, T., 1911. U8 ber die Forma¨ nderung du¨ nnwandiger Rohre, insbesondere federnder Ausgleichrohre. Zeitschrift des Vereines deutscher Ingenieure 55, 1889 – 1895. Wilkins, K., Tan, Y., Matzen, V.C., 2001. Monotonic out-ofplane tests on 2-inch, schedule 10 elbows. Data developed at the Center for Nuclear Power Plant Structures, Equipment and Piping, NCSU, Raleigh, NC. Yu, L., 1998. Elbow stress indices using finite element analysis. Ph.D. dissertation, December, NCSU, Raleigh, NC.
Correlation of test and FEA results for elbows subjected to out-of-plane loading Ying Tan, Kevin Wilkins, Vernon Matzen * Center for Nuclear Power Plant Structures, Equipment and Piping, North Carolina State Uni6ersity, Raleigh, NC 27695 -7908, USA Received 10 October 2001; received in revised form 1 February 2002; accepted 8 March 2002
Abstract The objective of this study is to validate a finite element analysis (FEA) simulation methodology to predict the out-of-plane behavior of piping elbows. Two out-of-plane elbow experiments and the corresponding FEA shell and elbow element models are presented. For load–displacements results, all the FEA predictions showed excellent agreement with measured experimental results, and for load– strain behavior, the shell FEA model results correlated quite well with the experimental results. © 2002 Elsevier Science B.V. All rights reserved.
1. Introduction
2. Background
In previous publications (Tan et al., 2002; Tan and Matzen, 2002), finite element analysis (FEA) procedures were developed and used to successfully simulate the behavior of eight physical tests: two four-point-bending tests on straight pipes, four in-plane closing bending tests and two inplane opening bending tests on 90° long-radius stainless steel (SS) elbows. The purpose of this study is to determine if out-of-plane behavior can be equally well simulated.
The study of pipe bends began with von Karman (1911). Since then Hovgaard (1930), Turner and Ford (1957) developed comprehensive theories for curved tubes under in-plane bending. Beskin (1945) extended von Karman’s theory and Smith (1967) adapted Turner and Ford’s analysis to deal with out-of-plane bending. All the studies above were based on elastic and small-deflection assumptions. In addition to theoretical studies, extensive experimental investigations have been performed. Smith and Ford (1967) carried out an experimental investigation on three individual pipe bends subjected to three-dimensional loading, one for in-plane bending, one for out-of-plane bending and one for combined in-plane and out-of-plane bending. Deflections, cross-sectional distortions and strains were measured. In 1978, results from
* Corresponding author. Tel.: +1-919-515-7736; fax: + 1919-515-5301. E-mail address: [email protected] (V. Matzen).
0029-5493/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 9 - 5 4 9 3 ( 0 2 ) 0 0 1 3 2 - 2
214
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
20 elbow tests were presented by Greenstreet (1978), of which five were out-of-plane tests, some with internal pressure and some without. Imazu et al. (1979) tested a thin-walled 304SS elbow at 600 °C using out-of-plane bending. In Prost et al.’s (1983) experimental study, three out-of-plane elbow tests were conducted at room temperature with and without internal pressure and one at elevated temperature (340 °C). Hilsenkopf et al. (1988) presented the results of two series of tests performed on 90° large-radius elbows, among which six were out-of-plane tests. Each series consisted of three tests. One was out-of-plane bending at room temperature without internal pressure, one was without internal pressure but at 120 °C, and one was at room temperature but with internal pressure. The moment– rotation relationships and the ovalization modes were recorded and illustrated. All of the work cited above was based on experiments— FEA simulation was not involved. Natarajan and Mirza (1981) described a finite element procedure for the analysis of a piping system subjected to out-of-plane moments. Basavaraju and Lee (1993) utilized ANSYS (1989) to study stress intensification factors and the C2 stress index for in-plane and out-of-plane moment, in which linear elastic analysis was used. To determine the stress for an elbow which has a stiffener closer than one pipe radius from the
Fig. 2. Test setup for Pipe-2. (a) Schematic; (b) Photograph.
Fig. 1. Test setup for Pipe-1 (from Figure 2 of Greenstreet, 1978).
elbow, Machida et al. (1995) carried out elastic stress analyzes using FEA for a 90° elbow subjected to out-of-plane moment. Mourad and Younan (2000a) using ABAQUS (1989) and taking geometric and material non-linearities into account, performed non-linear analyzes of elbows subjected to out-of-plane moment and internal pressure. All the works above focused exclusively on FEA study and the computed results were not confirmed by experimental data. Some reconciliation work has been conducted to bridge the experimental and FEA investiga-
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
215
data by 13–21% for out-of-plane forces and they attributed the discrepancies to ‘the geometric irregularities of the test models’. Kussmaul et al. (1995) reported a 90° elbow subjected to out-ofplane bending without internal pressure, and a FEA using ABAQUS ELBOW31 to simulate the test. Their computed forces differed by up to 15–20% compared with experimental results. They attributed the discrepancies to inaccurate material properties. Mourad and Younan (2000b), in a second 2000 paper, concentrated on the effect of FEA modeling parameters for pipe bends subjected to out-of-plane moment and internal pressure. They verified their FEA models by comparing their computed results to measured test data reported by Greenstreet (1978). Their correlations are quite good. Curiously, the Greenstreet data they present vary by 8–9% from what Greenstreet has in his report, although this deviation would appear to have little effect on the correlation assessment. The strain correlation for what they call their ‘connected model’ is also quite good, but they display the results in a moment –strain graph whereas Greenstreet gave his results in load–strain coordinates and so it is difficult for a casual observer to correlate their results directly with the original Greenstreet curve. They conclude that using the ‘closest in properties to a real elastic-plastic strain-hardening material’ (Mourad and Younan, 2000a) is very important for correlations between FEA and tests. As described above, even though much research has been performed on elbows subjected to outof-plane bending, the problem of simulating test
Fig. 3. Specimen dimensions for Pipe-2.
Fig. 4. Measured cross-sections. (a) Cross-section location; (b) pipe cross-section.
tions. Fujimoto and Soh (1988) analyzed very thin-walled pipe bends under in-plane and out-ofplane moments and compared their FEA stress distributions with experimental measurements. The experimental values are less than their FEA Table 1 Measured outside diameters and wall thicknesses for Pipe-2 Plane no.
P-1
P-2
P-3
P-4
P-5
Average
Unit
(in)
(cm)
(in)
(cm)
(in)
(cm)
(in)
(cm)
(in)
(cm)
(in)
(cm)
Do Flank–Flank t-Flank t-Flank Do Intra–Extra t-Intrados t-Extrados
2.380 0.132 0.135 2.375 0.131 0.119
6.045 0.335 0.343 6.033 0.333 0.302
2.385 0.130 0.131 2.365 0.141 0.120
6.058 0.330 0.333 6.007 0.358 0.305
2.376 0.130 0.135 2.370 0.139 0.117
6.035 0.330 0.343 6.020 0.353 0.297
2.382 0.130 0.138 2.377 0.141 0.119
6.050 0.330 0.351 6.038 0.358 0.302
2.380 0.132 0.142 2.377 0.128 0.120
6.045 0.335 0.361 6.038 0.325 0.305
2.381 0.131 0.136 2.373 0.136 0.119
6.047 0.332 0.345 6.027 0.345 0.302
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
216
Table 2 Average outside diameters and wall thicknesses for Pipe-2 Do Segments of test specimens
Elbow Straight pipe
Average t
(in) (cm) (in) (cm)
Average
0.133 0.338 0.110 0.279
Do/t
Extrados–Intrados
Flank–Flank
Average
2.373 6.027 – –
2.381 6.047 – –
2.377 6.038 2.375 6.033
17.9 21.6
Table 3 Material properties of Pipe-1 Carbon steel SA106 Grade B
Sy
Pipe-1 (Greenstreet, 1978, Table 1) Base curve (ANSYS, 1999, Table 3)
Su
E
(ksi)
(MPa)
(ksi)
(MPa)
(ksi)
(GPa)
50.0 42.5
345 293
73.6 69.7
507 480
30,100 42,922
208 296
ey (%)
eu (%)
N/A 0.2
N/A 20
Table 4 Material properties of Pipe-2 Stainless steel 304
Sy
Segments of test specimens
(ksi)
(Mpa)
(ksi)
(MPa)
(ksi)
(GPa)
35.4 39.5 38.4
244 272 265
81.0 82.2 85.8
558 567 592
N/A N/A 29,000
N/A N/A 200
Manufacturer’s report NCSU ASTM test
Elbow Straight pipe Straight pipe
and FEA results accurately has not been fully solved. This paper describes an investigation into this problem and a resolution to it.
Su
E
3. Experiments
to as Pipe-1 in this paper). The test information is illustrated in Fig. 1. Measured specimen dimensions were not presented and only the following nominal dimensions were reported in Greenstreet (1978): Do = 6.625 in (16.83 cm) and t=0.280 in (0.711 cm) for a Do/t ratio of 23.7.
3.1. Pipe-1
3.2. Pipe-2
The first set of data used to verify the FEA procedure described in Tan et al. (2002), Tan and Matzen (2002) is from an out-of-plane bending test on 6¦ schedule 40 long radius carbon steel elbow, reported by Greenstreet (1978), (called Test No. PE-3 in Greenstreet (1978), and referred
At North Carolina State University (NCSU), an elbow specimen, designated Pipe-2, was tested (Wilkins et al., 2001) under out-of-plane loading, as shown in Fig. 2. The specimen was a 2¦ schedule 10, 90° long radius, SS304L, seamless, butt welding elbow, with segments of straight pipes
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
Fig. 5. Engineering stress strain curves for Pipe-1. Fig. 7. Load – displacement curves for Pipe-1.
Fig. 6. Engineering stress strain curves for Pipe-2.
Fig. 8. Load – displacement curve for Pipe-2.
217
218
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
welded to both ends, as illustrated in Fig. 3. The length of each straight tangent portion was approximately five times the outside diameter of the elbow. This length was selected so that the end constraints would have negligible effect on the elbow behavior (Yu, 1998). Actual geometrical dimensions and pipe wall thicknesses were measured before the test. Five cross-sections along the pipe bend radius, labeled P-1 to P-5 in Fig. 4(a), were selected as planes for which measurements were taken. In each plane, the
Fig. 11. SG01 strain responses for Pipe-1 (taken from figure 24 in Greenstreet, 1978). Fig. 9. Local mesh for strain gage location for SG01, Pipe-1.
wall thicknesses at extrados, intrados and flanks were measured as shown in Fig. 4(b). The measured data are given in Table 1 and the average wall thicknesses and average outside diameters are provided in Table 2.
4. Finite element analysis In this study, ANSYS (1999) version 5.6, ABAQUS (2000) version 6.1 were used. Two types of FEA models, one using shell elements and the other using elbow elements, were tried. For the FEA shell models, ANSYS SHELL43, SHELL181 and ABAQUS S8R5 were utilized. For the FEA elbow element models, ABAQUS ELOW31 was used. In all cases, large deformation and stress stiffness effects were taken into account.
4.1. Material models
Fig. 10. SG00 strain responses for Pipe-1 (taken from Figure 24 in Greenstreet, 1978).
FEA requires the non-linear stress–strain curves, but none were available for any of the specimens tested. However, the values of the three material
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
219
Fig. 12. Strain gage locations for Pipe-2. (a) SG01 to SG05 locations (Load coming out of paper); (b) SG01 to SG03 photograph (Load going in paper).
parameters (E, Sy and Su) were provided in Greenstreet (1978) for Pipe-1 and in the manufacturer’s report for Pipe-2, as shown in Tables 3 and 4, respectively. In the current study, the procedure described in Tan and Matzen (2002) was used to construct the specimen stress– strain curves based on these three parameters and available measured stress– strain curves of the same type of material. Briefly, this procedure is one in which a stress–strain curve is constructed such that its yield stress, ultimate stress and modulus of elasticity are the same as a specified set (e.g. handbook value for E and the manufacturer’s specifications for Sy and Su) and the shape of the curve is similar to one obtained from a test on a similar material. For Pipe-1, a uniaxial tensile test stress–strain curve for SA 106 Grade B carbon steel, published in Gosselin and Wais (1999) and shown here in Fig. 5 (after being converted to engineering stress and strain), was used as the base curve and it is assumed that the engineering ultimate strain corresponding to the ultimate
stress was 20%.1 For Pipe-2, an ASTM type tensile test was performed on a coupon specimen cut from a piece of straight pipe, which is the same product batch as the straight pipes used in the NCSU specimens. The experimental engineering stress-engineering strain data are shown in Fig. 6 as open circles, and labeled as ‘2¦Sch10 Coupon’. The measured stress–strain data show close agreements with the manufacturer’s report, as given in Table 4. Since the manufacturer’s test report gave different properties for the elbow and straight tangent pipes, two separate non-linear stress–strain curves were needed in the FEA model—one for the straight tangent pieces and one for the elbow. For the straight tangent portions, the stress–strain curve of 2¦Sch10 Coupon was used directly. For the elbow portion, a new 1 It is recognized that this process, which was developed for modifying curves for stainless steel, is not exact and may distort a stress – strain curve for Carbon Steel. However, the process is thought to be sufficiently accurately for the intended purpose here.
220
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
stress–strain curve was constructed as illustrated by the line labeled ‘Linearly Scaled Elbow Curve’ in Fig. 6, using the data of the 2¦Sch10 Coupon as the base curve. Since the weld bead of Pipe-2 specimen was ground off before the test, it was assumed to be negligible in the FEA model.
4.2. Correlation of global beha6ior For Pipe-1, experimental load– displacement curves from in Greenstreet (1978) were digitized and are replotted here in Fig. 7. The circular marks show the test data of load vs. displacement at Dial Gage 1(labeled as Test D1) and the rectangles are for Dial Gage 2 (Test D2.) FEA results are shown in Fig. 7 for three shell element models (SHELL43 and SHELL181 from ANSYS and
S8R5 from ABAQUS) and one elbow element model (ELBOW31 from ABAQUS.) All of the FEA results are remarkably similar to each other and they match the test results very well, although there is a slight over prediction of the D2 data as the elbow yields. As seen in Fig. 8, the FEA results for Pipe-2 also matched the measured displacement data very well. A close inspection of the curves will show that the curve for SHELL43 ends at 4¦ (10.2 cm) and the curve for SHELL181 ends at 4.5¦ (11.4 cm). At these points in the analyzes, convergence difficulties caused the program to terminate. For elbow model, no convergence problems were encountered. The reason for this lack of convergence with the shell analyzes is not yet fully understood.
Fig. 13. Local mesh for strain gage locations for Pipe-2. (a) Gage sizes, locations, orientations and FEA local mesh for SG01, SG02 and SG03; (b) gage sizes, locations, orientations and FEA local mesh for SG04 and SG05.
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
221
Fig. 14. Strain responses for Pipe-2. (a) SG01 Longtitudinal strain; (b) SG01 Hoop strain; (c) SG02 Longtitudinal strain; (d) SG02 Hoop strain; (e) SG03 Longtitudinal strain; (f) SG03 Hoop strain; (g) SG04 Longitudinal strain; (h) SG04 Hoop strain; (i) SG05 Longitudinal strain; (j) SG05 Hoop strain.
4.3. Correlation of strains In
Greenstreet
(1978),
measured
response
curves were given for two strain gages, designated SG00 and SG01. Gages SG00 and SG01 were located 33 and 48°, respectively, around the el-
222
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
bow, measuring from the flank to the intrados. Gage SG00 was 36° along the bend angle from the elbow-straight pipe weld while gage SG01 was 41° along the bend angle. To simulate these strains a shell model using ANSYS SHELL181 was
created with the mesh refined locally at the strain gages locations, as illustrated in Fig. 9. The digitized curves from Greenstreet (1978) are shown in Figs. 10 and 11 along with the FEA results. It is seen that the FEA responses followed the experi-
Fig. 14. (Continued)
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
223
Fig. 14. (Continued)
mental results closely for SG01, while there is some deviation between FEA and test data for a portion of the SG00 load– strain curve. The reason for the deviation is not clear. For Pipe-2, five tee-rosette strain gages (MicroMeasurements Division, Measurements Group, Inc., Raleigh, NC. Gage type: EA-06-062TT-120), called SG01 to SG05 hereafter, were mounted on the specimen, as illustrated in Fig. 12(a) and (b). These positions were in the high-strain regions given by FEA predictions and were selected in order to verify the FEA procedure. For each gage, longitudinal and hoop strains were recorded. The gage elements were aligned with the local coordinate axes of the shell elements in the gage areas. A model using ANSYS SHELL181 was created similar to the one used for the Pipe-1 specimen to simulate these responses. The local mesh at the strain gage region was refined, as shown in Fig. 13. The FEA results plotted together with the measured experimental data are shown in Fig. 14. In general, the FEA predictions match all the
experimental responses very well. The discrepancies, which are reasonably small, are likely a result of the interpolation of the strain data from the FEA postprocessor. In this study, the FEA results were the average element strains at the gage regions. The discrepancy between the actual gage areas and those defined in FEA will unavoidably introduce some error.
5. Conclusions This paper presents two experiments for out-ofplane monotonic loading of piping elbows and the non-linear FEA procedures used to simulate them. FEA shell models and elbow models were used and they all give excellent results compared with measured load– displacement responses and the shell models produced strain responses that matched test data quite well. When only the global behavior is required, the ABAQUS elbow element would appear to be preferable to ABAQUS or ANSYS shell elements.
Y. Tan et al. / Nuclear Engineering and Design 217 (2002) 213–224
224
Acknowledgements The authors would like to acknowledge the support of the Center for Nuclear Power Plant Structures, Equipment and Piping and North Carolina State University, the PVRC Subcommittee on Flexibility Models and Stress Intensification Factors (Grant 98-PNV-6) and the North Carolina Supercomputing Center.
Appendix A. Nomenclature Do E eu ey Sy Su T
outside diameter of pipe Young’s modulus uniaxial engineering ultimate strain uniaxial engineering yield strain yield stress ultimate stress wall thickness
References ABAQUS, Version 4.8, Hibbitt, Karlsson and Sorensen, Inc., 1989. ABAQUS Version 6.1, 2000. Hibbitt, Karlsson & Sorensen, Inc. ANSYS Engineering Analysis System User’s manual for ANSYS Revision 4.4, May 1, 1989, Houston, Pennsylvania. ANSYS Version 5.6, 1999. ANSYS Inc. Basavaraju, C., Lee, R.L., 1993. Stress distribution in elbow due to external moments using finite-element methodology. PVP, ASME 249, 103 –112. Beskin, L., 1945. Bending of thin curved tubes. J. Appl. Mech. Trans. ASME 67, A-1 –A-7. Fujimoto, T., Soh, T., 1988. Flexibility factors and stress indices for piping components with D/T\ = 100 subjected to in-plane or out-of-plane moment. J. Press. Vessel Technol. 110, 374 – 386. Gosselin, S.R., Wais, E.A., 1999. A case study comparison of ASME section III appendix F and proposed code case N-584 criteria in carbon steel and stainless steel pipes. PVP-vol. 383, ASME, 13 –22 Greenstreet, W.L., 1978. Experimental study of plastic responses of pipe elbows. ORNL/NUREG-24, 1– 51. Hilsenkopf, P., Boneh, B., Sollogoub, P., 1988. Experimental study of behavior and functional capability of ferritic steel elbows and austenitic stainless steel thin-walled elbows. Int. J. Pres. Vessel Piping, 0308-0161/88, 111 –128. Hovgaard, W., 1930. Bending of Curved Pipes. Proc. of the
3rd International Congress for Applied Mechanics, Stockholm, Sweden, vol. 2, pp. 331 – 341. Imazu, A., Sakakibara, Y., Nagata, T., Hashimoto, T., 1979. Plastic instability test of elbows under in-plane and outof-plane bending. Trans. of the 5th SMiRT Conference, Berlin, Germany, E6/5. Kussmaul, K., Diem, H.K., Uhlmann, D., Kobes, E., 1995. Pipe bend behavior at load levels beyond design. 13th SMiRT Conference, Brazil, pp. 187 – 198. Machida, H., Kamishima, Y., Ueta, M., Dozaki, K., 1995. Stress index of 45 and 90 degree elbow subjected to inplane and out-of-plane moment. Transactions of the 13th International Conference on Structural Mechanics in Reactor Technology (SMiRT 13), Brazil, pp. 377 – 382. Mourad, H.M., Younan, M.Y.A., 2000. Nonlinear analysis of pipe bends subjected to out-of-plane moment loading and internal pressure. PVP-vol. 399, Design and Analysis of Pressure Vessels and Piping, ASME, 123 – 129. Mourad, H.M., Younan, M.Y.A., 2000. The effect of modeling parameters on the predicted limit loads for pipe bends subjected to out-of-plane moment loading and internal pressure. PVP-vol. 399, Design and Analysis of Pressure Vessels and Piping, ASME, 131 – 148. Natarajan, R., Mirza, S., 1981. Stress analysis of curved pipes with end restraints subjected to out-of-plane moments. Proceedings of the 6th SMiRT Conference, Paris, F2/8, pp. 1 – 9. Prost, J.P., Taupin, Ph., Delidais, M., 1983. Experimental study of austenitic stainless steel pipes and elbows under pressure and moment loadings. 7th SMiRT Conference, Chicago, G/F 5/5. Smith, R.T., 1967. Theoretical analysis of the stresses in pipe bends subjected to out-of-plane bending. J. Mech. Eng. Sci. 9 (2), 115 – 123. Smith, R.T., Ford, H., 1967. Experiments on pipelines and pipe bends subjected to three-dimensional loading. J. Mech. Eng. Sci. 9 (2), 124 – 137. Tan, Y., Matzen, V.C., 2002. Correlation of test and FEA results for thin-walled piping elbows considering welds (accepted for publication in Nuclear Engineering and Design). Tan, Y., Matzen, V.C., Yu, L., 2002. Correlation of test and FEA results for the nonlinear behavior of elbows (accepted for publication in the ASME J. Pres. Vessel Technol.). Turner, C.E., Ford, H., 1957. Examination of the theories for calculating the stresses in pipe bends subjected to in-plane bending. Proc. Instn. Mech. Engrs. von Karman, T., 1911. U8 ber die Forma¨ nderung du¨ nnwandiger Rohre, insbesondere federnder Ausgleichrohre. Zeitschrift des Vereines deutscher Ingenieure 55, 1889 – 1895. Wilkins, K., Tan, Y., Matzen, V.C., 2001. Monotonic out-ofplane tests on 2-inch, schedule 10 elbows. Data developed at the Center for Nuclear Power Plant Structures, Equipment and Piping, NCSU, Raleigh, NC. Yu, L., 1998. Elbow stress indices using finite element analysis. Ph.D. dissertation, December, NCSU, Raleigh, NC.