Fatigue and Creep-Fatigue Testing of Bellows at Elevated Temperature

Transcription

1 S. Yamamoto K. Isobe S. Ohte Mehanial Engineering Laboratory, Researh and Development Center. N. Tanaka S. Ozaki Nulear Engineering Laboratory, Nulear Energy Group. K. Kimura Advaned Reator Engineering Department, Nulear Energy Group. Fatigue and Creep-Fatigue Testing of Bellows at Elevated Temperature Fatigue and reep-fatigue tests at elevated temperature were onduted on two different-sized bellows, <f> 1100 mm and <t> 300 mm in nominal inner diameter, to investigate the fatigue life and the reep-fatigue interation in a bellows, and also to provide test data for developing a life predition method and design-by-analysis rules for bellows in elevated temperature servie. A series of tests onsisted of strain behavior and fatigue tests at room temperature, and fatigue and reep-fatigue tests at elevated temperature. Also, inelasti finite element analyses were performed on a bellows under internal pressure and yli axial defletions. Analytial results were ompared with the measured data obtained in the room temperature testing to verify the strain predition method. Toshiba Corporation, Kawasaki, Japan Introdution ASME Code Case N-290 [1], whih is the only ode overing the design of bellows expansion joints in Class 1 systems, requires life testing to demonstrate fatigue integrity for the bellows in elevated temperature servie, sine design rules to evaluate the fatigue and reep-fatigue damage are urrently under onsideration. The EJMA standard [2], whih is most ommonly used in the bellows design, is not appliable in the temperature range, where reep effets are introdued. Therefore, design-by-analysis rules for the fatigue and reepfatigue evaluations are desired to redue design ost and to enable onstrution of reliable bellows expansion joints. Only a limited amount of test data [4-6], whih is neessary to develop the design rule for the fatigue and reep-fatigue evaluation for a bellows, is urrently available on deformation responses and fatigue and reep-fatigue life of bellows at elevated temperature. Partiularly, no test data on a largesized bellows and/or yli angular rotations is found in the open literature. Bellows size effets on the fatigue and reep-fatigue life are signifiant onerns sine the forming proedure may affet life differently, depending on the bellows size. In the EJMA standard, maximum axial defletions resulting from imposed angular rotations are taken as the equivalent axial defletions for the fatigue evaluation. This method has to be to verified by test data at elevated temperature. Contributed by the Pressure Vessels and Piping Division for publiation in the JOURNAL or PRESSURE VESSEL TECHNOLOGY. Manusript reeived by the PVP Division, April 19, For the aforementioned reasons, fatigue and reep-fatigue tests at elevated temperature were onduted on two differentsized bellows, 4> 1100 mm and 4> 300 mm in nominal inner diameter, to investigate the fatigue life and the reep-fatigue interation in a bellows, and also to provide test data for developing a life predition method and design-by-analysis rules for bellows in elevated temperature servie. A series of tests onsisted of strain behavior and fatigue tests at room temperature, and fatigue and reep-fatigue tests at elevated temperature. Cyli axial defletions or angular rotations, whih simulated bellows movements in hinged or gimbal expansion joints, were applied to a test bellows in eah test. Also inelasti finite element analyses were performed on a bellows under internal pressure and yli axial defletions. Analytial results were ompared with the measured data obtained in the room temperature testing to verify the strain predition method. A simplified fatigue life evaluation method has been developed based on the experimental data and is reported separately in referene [10]. Bellows Test Assemblies Speifiations for bellows tested in this study are shown in Table 1. Two different sizes of bellows, <f> 300 mm and 4> 1100 mm nominal inner diameter, were seleted to evaluate bellows size effets on the fatigue and reep-fatigue strength. Therefore, the material and the forming proedure used for both bellows are idential, as shown in Table 1. Both bellows, Journal of Pressure Vessel Tehnology AUGUST 1988, Vol. 110/301 Copyright 1988 by ASME

2 Table 1 Bellows speifiations Identifiation Material 316 Stainless Steel 316 Stainless Steel Type of Bellows U Shape Formed Bellows U Shape Formed Bellows Number of Plies 1 1 Nominal Inner Diameter 300 mm 1100 mm Thikness 1.5 mm 2.0 mm Number of Convolutions 7 7 Convolution Height 18 mm 60 mm Convolution Pith 16 mm 60 mm Bellows Length 112 mm 420 mm " 300 B 11o,"s Table 2 Test parameters Test Desription Test Conditions 11'300 11'1100 Temperature 'C R.T R.T Strain Behavior and Inner Pressure MPa OJ47 Fatigue Test at Loading Profile...f\IVy.../\N'v Room Temperoture Number of Axiai Tests I 1 (3) Number of Angular Tests - 1 (3) Temoerature 'C I 550 Fatigue Test at Elevated Temperature Creep- Fatigue Test at Elevated Temperature Inner Pressure MPa Loading Profil...IV\Iv...IV\Iv Number of Axia I Tests 4 I 5 4 T 4 Number of AngUlar Tests - I Temperature 'C Inner Pressure MPa Loading Profile...f"'\I\..f\.j\ Hold Time min Number of Axial Tests I 1 I 1 Number of Angular Tests Testing Proedures Fig E E "" t- 230mm N-290 Basi Tolerane For Crown Thikness ;;:JWvvv- 1.7'b!='1.71mm2!;===j;3==C4!===!:'5=6==C7!:"'==' Convolution Number Bellows ross setion thikness (ti> 1100 bellows) whih onsist of seven single-ply U-shaped onvolutions, were made of type 316 stainless steel and fored into shape by hydrauli forming from welded ylinders having a longitudinal seam. Solution heat treatment was performed after forming. Figure 1 shows test assemblies for the 300 and 1100 bellows. The bellows were attahed to the test rigs by full penetration irumferential welds, whih met the requirements in ASME Code Case N-290. Liquid penetrant examinations and radiographi examinations for all longitudinal and irumferential weld joints were performed and ensured no initial defets in the weld joints. The bellows profile data, suh as onvolution height, thikness, pith, diameter, so on, whih are speified in the ode ase, were preisely measured prior to the tests and ompared with the toleranes in the ode ase, beause they are most signifiant fators whih govern the fatigue and reepfatigue life for bellows. As a result, all of 1100 bellows and most of the 300 bellows satisfied the profile toleranes required in the ode ase. Figure 2 shows.a typial variation in ross setion thikness in a 1100 bellows, measured by an ultrasoni devie, and the thikness toleranes required in the ode ase. Test Parameters. Test parameters for eah type of test are shown in Table 2. Using some bellows for elevated temperature fatigue and reep-fatigue tests, strain measurements were performed prior to the elevated temperature tests, as shown in Table 2. Testing Mahines. Figures 3 and 4 show fatigue testing mahines for the 300 and 1100 bellows, respetively. Both testingmahines were espeiallydesigned for testing bellows at elevated temperature and an apply axial defletions or angular rotations to the test bellows. Strain Behavior and Fatigue Testing at Room Temperature. Detailed strain distributions on a bellows surfae under yli defletions were measured with strain gages at room temperature. The tests onsisted of elasti strain measurements and inelasti strain measurements, whih were followed by fatigue testings. Fatigue and Creep-fatigue Testing at Elevated Temperature. In elevated temperature fatigue tests, the bellows were set in the testing mahines and heated up to the test temperature before being pressurized by air. Then, yli axial defletions or angular rotations were applied to the test bellows at 4 yles per min in the fatigue testing. In reep-fatigue tests, test proedures were idential to those for fatigue tests, exept for the holding time at the maximum tensile points. Failure was deteted by pressure redutions in the bellows due to air leakage through fatigue raks. When this redution ourred, test mahines were automatially stopped. Test Results Strain Behavior and Fatigue Testing at Room Temperature. Test results obtained from a 1100 bellows are desribed in this setion as typial harateristis of the bellows strain behavior. In the tests, small axial defletions in 302/VoI.110, AUGUST 1988 Transations of the ASME

3 2.5..-t 'e 1.0 Vi ) Fig. 3 Fatigue testing mahine for the Q 300 bellows '----' ,L----L-- Fig. 5 Bellows axial defletion versus meridional strain on outer sur fae at the first root 2.5 0f I--'e 1.0 f Vi a 1) mm Fig. 6 Bellows axial defletion versus meridional strain on outer sur fae at the seond rown Fig. <I Fatigue testlng mahine for the q, 1100 bellows 2 80mm the elasti range were ylily applied to the bellows, whih was pressurized at MPa. Then yli axial defletions were inreased to ± 50 mm. After three yles of ± 50 mm defletions, ± 80 mm axial yli defletions were applied until the bellows failed. In the elasti range, bellows deformation was almost uniform and no strain onentrations were observed. Figures 5 and 6 show meridional strain responses at the first root and the seond rown under ± 50 mm and ± 80 mm yli axial defletions, respetively. Strain ranges at all roots and rowns, whih were obtained from data similar to that shown in Figs. 5 and 6, are plotted in Fig. 7. From these results, strain response harateristis for the bellows are summarized as follows: Strain response under yli defletions reahed steady state onditions after 2 or 3 yles. Strain ranges ourring at roots were larger than at rowns under axial defletions. As the inelasti strain responses, highly loal strain onentration was observed in the first root region. The deformation in the bellows was nonuniform, even though the test bellows satisfied tight profile toleranes in the ode ase. / 50mm a L !;2--± ,5':----!67:.:..:.:..:..:. Convolution Number Fig. 7 Meridional strain range on bellows outer surfae due to yli axial defletion Figure 8 shows variations of meridional strain range at onvolution roots, due to the inelasti strain onentration. This figure inludes data from various P 1100 bellows, whih were measured similarly to the testing desribed in the foregoing prior to elevated temperature testing. Also, the data under yli angular rotations is inluded. In angular rotation tests, maximum axial extensions or ompressions at outer diameter at 0 and 180-deg phase resulting from imposed angular rotations were taken as the equivalent axial defletions. The strain range satters more as the defletion range inreases in the figure. This implies the loalized inelasti strain onentration progresses more and strain ranges at different Journal of Pressure Vessel Tehnology AUGUST 1988, Vol. 110/303

4 3.0 Axial Angular oase' 0 o ase 13 a> ase' 7 I2l ase e ase 11,. ase;.. ase 12 '"g> 1.5 'e Vito E o 0.5 L 2.0 Maximum Strain Range Io II / 1/ /1 " " B / Ii " bilil,," /EJMA(E<+l) Defletion Range mm Fig. 8 Meridional strain range on root outer surfae versus bellows ax ial defletion range 0 Fig. 10 Cross setion of a fatigue rak in <> 1100 bellows tested at elevated temperature Estimated O L..02=--L-J.-L..JL.L..lJW1O-=3---..l--L---Ll...u..L.Ll. 1 O-'-4--L--'--L...L.LLLU1Q5 Fig. 9 Cyles to Failure Nf Bellows fatigue test results at elevated temperature onvolutions are not equalized as the defletion inreases. Another signifiant point, whih this figure implies, is the similarity in data from different bellows and different motions (axial and angular). Thus maximum strain ranges under various defletion ranges an be predited by the urve shown in Fig. 8. Thebellows failed at 1121 yles under ± 80 mm yli axial defletions at room temperature. The failure ourred at the bottom of the first root, beause of the high strain onentration. Five irumferential fatigue raks, ranging from 20 mm to 50 mm in length, were observed. Fatigue Testing at Elevated Temperature. Fatigue test results, obtained from both rf> 300 and rf> 1100 bellows, are shown in Fig. 9, whih inludes axial defletion ases and angular rotation ases. In this figure, strain range E r EJMA means apparent elasti strain range alulated from axial defletion range Or with the equation in the EJMA standard t2d 5t..Jd/(d+W») Or E - ( + - (1) r,ejma- 2w3(d+w)Cj 3W 2 C d N where t is thikness, d is bellows root outer diameter, W is onvolution height, N is the number of onvolutions, C j, Cd are onstants speified in the EJMA standard. From the results, signifiant findings were obtained as follows: 1 Fatigue life dereased as temperature inreased. 2 No signifiant fatigue life differenes were observed be- 304/VoI.110,AUGUST ,um Fig. 11 Fratograph of frature surfae in <> 1100 bellows tested at elevated temperature tween rf> 300 bellows and rf> 1100 bellows; in other words, no size effets were observed. 3 Test results at both 400 C and 550 C orrelated weii with fatigue life estimations by the EJMA standard. 4 The fatigue life under yli angular rotations agreed well with that under yli axial defletions. The seond finding implies that bellows size effets need not be taken into aount in bellows designs, as long as the beiiows size is in the range between rf> 300 mm and rf> 1100 mm in diameter. Based on the third finding, the fatigue life estimation equation in the EJMA standard is appliable up to 550 C under the fatigue onditions in whih reep effets an be ignored. From the fourth finding, it is onluded that, in the design, the fatigue life under angular rotations an be evaluated, based on the fatigue data under axial defletions. Figures 10 and 11 show a typial ross setion and a fratograph, respetively, for a fatigue rak in a rf> 1100 bellows. Almost aii the fatigue raks in rf> 300 and rf> 1100 bellows were irumferential raks at the bottom of the root, with a ouple of exeptions involving raks at the rown apex. No failure ourred near the weld. In the rf> 300 bellows, the rak initiated on the outer surfae grew through the thikness, while inthe rf> 1100 bellows, raks initiated onboth sides ofthe surfae onneted eah other in the middle of the ross setion, as shown in Fig. 10. Clear striations and transgranular rakings were observed in the fratograph (Fig. 11). Creep-Fatigue Testing at Elevated Temperature. Creepfatigue tests results are shown in Fig. 12. Hold time effets on the bellows fatigue life were learly observed. Fatigure life was signifiantly redued, as the hold time beame longer. Transations of the ASME

5 ij..: w <ll 0> 0.5 0:: 'E ti 0 txl l 0 l:1p'j Bellows f300 dl100 Pressure MFa Q Hold Time mlo AxIal Test 0 JJ n p 0 p ):( AnQular Iii1 " - '" Estimated by EJMA 0... OJ 0 '- UJ <11 en ::: 0 0::: ::: '5 L..... l/) 5 2 Sellows Temp. 'C 400 I 550 R.T.I 400 I 550 AXial Te.t () I 0 I til I 0 Angular Te.t - -I - 1@1 NRIM Test Data R.T. 4OO' 5SO C Fig. 12 Cyles to Failure N f Creep fatigue test results at 550'C O. 5L..."--l---L-l-LLL1..ll...,,.---'--l.-L...LL.L.L.l..L..,---L:...l.---'---'.l.J...LJ:J Cyles to Failure Nt Fig. 14 Maximum strain range versus yles to failure (omparisons between bellows fatigue test results and Type 316 stainless steel fatigue data) eyl i AXial Defletion Fig.15 I't )'t' I' Inner Pressure Finite element model for q, 1100 bellows Fig.13 Fratograph of frature surfae In 1100 bellows tested under GO min hold time Failure modes were idential to those in the fatigue testing, exept for the fratograph. Figure 13 shows a fratograph of the frature surfae in a 1100 bellows, whih was tested with 60 minute hold time. Combinations of striations due to the fatigue and intergranular frature surfae due to the reep were observed. In addition, no bellows size effets on the reep-fatigue strength were observed. Test data in axial and angular defletion ases were in good agreement with eah other, the same as for the fatigue testing results. Analyses and Disussions Fatigue Failure Mehanism in Bellows. Highly loal strain onentration in a weak onvolution was observed in the strain measurements at room temperature. As the bellows is essentially a series of springs, strain onentration in a weak onvolution an not be prevented, even though the bellows meet tight profile toleranes in the ode ase. In the room temperature fatigue tests, the bellows failed at the bottom of the first root, where the high strain onentration ourred. A relation between the maximum strain range measured at the bottom of the first root under ± 80 mm yli defletions and yles to failure is ompared with the material fatigue data [8] for type 316 stainless steel at room temperature in Fig. 14. Agreement between them is shown to be good. Sine strains were not measured in elevated temperature tests, the maximum strain range for eah test ase is predited from the urve shown in Fig. 8, assuming that the maximum strain range at elevated temperature is same as at room temperature. This assumption is approximately appliable, as the tests were onduted by defletion ontrol. FEM analyses, whih were performed to verify the assumption, predited a differene in the strain range at root outer surfae between 550 C and at room temperature was about 5 perent. Relations between the maximum strain range obtained in the foregoing and yle to failure were also plotted and ompared with material fatigue data at elevated temperature in Fig. 14. Correlations between the bellows fatigue data and material fatigue data are good in the figure. Consequently, it is onluded that the bellows fatigue life is governed by material fatigue strength and the maximum strain range ourring at the weakest onvolution in a bellows. Inelasti Finite Element Analyses. It has been shown, in the previous setion that the inelasti strain onentrations in a weak onvolution under yli loading governs the bellows fatigue life. Therefore, the inelasti strain response, inluding the strain onentration, has to be aurately analyzed to predit the bellows fatigue life. In referene [7], Beht et al. onlude that the finite element analysis an predit stresses in bellows with reasonable auray, if the preditions are based on atual geometry and resultant strain onentrations. So, analyses using the finite element model developed by Beht were performed to verify the analytial method, and to haraterize the inelasti strain response, espeially strain onentrations, in bellows. The 1100 bellows under internal pressure and yli axial defletions was analyzed using the MARC finite element program [9]. Analytial results were ompared with the measured data obtained in the room temperature testing. The finite element model for the bellows onsisted of three and a half onvolutions and an end tangent, as shown in Fig. 15. Thikness variations shown in Fig. 2 were modeled preisely. Ludwik-type material model shown in the forthoming Journal of Pressure Vessel Tehnology AUGUST 1988, Vol. 110/305

6 CALCULATED o MERIDIONAL STRAIN (OUT) i MEASURED A CIRCUMFERENTIAL STRAIN (OUT) I f\ f\ fl f 2 O Meridional Strain I Cirumferential Strain (Measured)_JMJ Convolution Number I 2 Ar Length Fig. 16 Elasti surfae strains in the <s 1100 bellows under MPa inner pressure and 5 mm axial extension Inner Surfae \ Outer Surfae (\ '/\ V /^,.\ / /\ D /\ n -1.0 I O Ar Length Fig. 17 Inelasti surfae strain in the <j> 1100 bellows under MPa inner pressure and 50-mm axial ompression / o I was employed, as it was onsidered to be most appropriate for 316 stainless steel, espeially for simulating initial yielding behavior of the material. 1.0 a /a o v \ l (2) 0.5,* de n (3) where e is total strain, e p is plasti strain, a is stress, a y is yield stress (proportional limit), E is Young's modulus, H' is hardening oeffiient, m and K are material onstants. Material onstants were obtained in separate tensile testings at room temperature as follows: E = v = Oy = m = K = 1.94 x10 s MPa (Poisson's ratio) 206 MPa MPa Figure 16 shows omparisons between predited and measured surfae strains in the bellows under MPa inner pressure and 5 mm axial defletion. In this ase, the bellows strains stay in the elasti range and agreement between them is exellent. In Fig. 17, the predited surfae strains at the 50 mm defletion point in the first yle are ompared with the measured data. Figure 18 shows the surfae strain response at the first root predited in the ±50 mm yli axial defletion ase. The meridional strain at the first root is predited 13 perent larger than that at the other roots, due to the thikness variations, shown in Fig. 2. However, the finite element analysis underestimates the strain onentrations at the first root by a fator of about 2. The analytial model has to be improved for quantitative agreements with the measurements. Geometri variations in onvolution height, pith, et., and the elastiplasti material onstitutive equations for yli loadings are remaining onerns in the analytial model. Inelasti analyses, inluded onsideration of reep, relaxation and kinemati plasti hardening, were performed separately and results were disussed in referene [10]. Conlusions and Reommendations The fatigue failure mehanism in the bellows under yli defletions has been larified by the testing and analyses on- 306/Vol. 110, AUGUST O Axial Defletion Fig. 18 Meridional strain response on outer surfae at the first root (inelasti analysis) duted in this study. Loal strain onentration in a weak onvolution ours due to deviations from nominal geometry in the bellows, even though the bellows satisfies tight profile toleranes in ASME Code Case N-290. Maximum strain, resulting from loal strain onentration, governs the bellows fatigue life. So, if strain an be predited, the bellows fatigue life is preditable, based on the material fatigue data. Thus, development of a strain predition method for the bellows is a key task to establish design-by-analysis rules. Detailed finite element analyses ould qualitatively simulate strain behavior in a bellows, however underestimated the onentrated strain. For design-by-analysis approah, bounding strain onentration effets, using nominal geometry, are reommended to be a pratial method and disussed separately in referene [10]. Other signifiant onlusions and reommendations obtained from the testing are summarized as follows: No bellows size effets exist as long as the bellows size is in the range between <j> 300 mm and </> 1100 mm in nominal inner diameter. So, bellows size effets need not be taken into aount in the bellows design. Taking maximum axial defletions resulting from imposed angular rotations as equivalent axial defletions, fatigue life of the bellows under angular rotations is preditable, based on the fatigue data under yle axial defletions. The fatigue life of the bellows is signifiantly redued due to the hold time effets, so that the reep-fatigue interation has to be taken into aount in the design rule. mm Transations of the ASME

7 Aknowledgment The authors wish to express their appreiation to Dr. Fujita, an emeritus professor of The University of Tokyo, for his valuable suggestions during the ourse of this study. Referenes 1 ASME Code Case N-290, "Expansion Joints in Class 1, Liquid Metal Piping," Setion HI, Division 1. 2 Standard of the Expansion Joint Manufaturers Assoiation, In., ASME Code Case N-47-22, "Class I Components in Elevated Temperature Servie," Setion III, Divsion 1. 4 "Analysis of Stresses in Bellows, Part 1, Design Criteria and Test Results," NAA-SR Kobatake, K., et al., "Fatigue Life Predition of Bellows Joints at Elevated Temperatures," PVP-51, MCoy, Jr., H. E., "Testing of Bellows for Engineering Systems," PVP Vol-51, Beht, C, et al., "Stress Analysis of Bellows," PVP Vol-51, NRIM Fatigue Data Sheet No. 15, National Researh Institute for Metals, MARC General Purpose Finite Element Program, MARC Analysis Researh Corporation, Palo Alto, Calif., Kobatake, K., et al., "Simplified Fatigue Life Evaluation Method of Bellows Expansion Joints at Elevated Temperature," PVP Vol-103, Journal of Pressure Vessel Tehnology AUGUST 1988, Vol. 110/307