FATIGUE MECHANISM OF BOLTED JOINTS UNDER MULTI-AXIAL VIBRATION

Transcription

1 Proceedings of the 5th Interntionl Conference on Integrity-Relibility-Filure, Porto/Portugl July 2016 Editors J.F. Silv Gomes nd S.A. Meguid Publ. INEGI/FEUP (2016) PAPER REF: 6299 FATIGUE MECHANISM OF BOLTED JOINTS UNDER MULTI-AXIAL VIBRATION Shinji Hshimur 1(*), Tomotk Tnk 2, Tkefumi Otsu 3 1 Deprtment of Engineering Science nd Mechnics, Shibur Institute of Technology, Tokyo, Jpn 2 Dep. Mechnicl Engineering, Grdute School of Ngok University of Technology, Ngok, Jpn 3 Deprtment of Mechnicl Engineering, Kurume Ntionl College of Technology, Fukuok, Jpn (*) Emil: hsimur@shibur-it.c.jp ABSTRACT Mny bolted joints nd bolt/nut ssemblies re used in vrious fields. However it is lso undenible tht there re mny ccidents cused by bolts filure. Mny ftigue tests of bolted joints which re subjected to xil vibrtion hve been conducted. Ftigue tests of bolted joints which re subjected to trnsverse vibrtion hve been lso conducted in recent yers. However the ctul bolted joints re subjected to complex vibrtion. In this study, ftigue tests of bolted joints which ws simultneously subjected to xil vibrtion nd trnsverse vibrtion were performed to revel ftigue phenomenon of bolted joint subjected to complex vibrtions. In the experiments, the mplitude of xil vibrtion force ws constnt nd the mplitude of trnsverse vibrtion force ws only chnged. The experiments for the bolted joint subjected to only trnsverse vibrtion were lso conducted to compre. The results showed tht the pprent trnsverse ftigue limits, the highest mplitude of trnsverse vibrtion which the bolted joint did not fil due to ftigue, were different ccording to the phse difference of superposition of vibrtions. If the two vibrtions were superposed with the sme phse, the pprent trnsverse ftigue limit decresed becuse principl stress t the first thred root becme the highest. Keywords: Bolted joint, ftigue mechnism, xil vibrtion, trnsverse vibrtion. INTRODUCTION Mny Bolted joints nd threded fsteners re used for ssembling mchines nd structures. But it is lso undenible tht there re mny ccidents cused by bolts filure (Ministry of Lnd, 2013). A lot of reserches bout ftigue of bolted joints hve been investigted so fr. Especilly, ftigue chrcteristics nd mechnisms for the bolted joints subjected to xil vibrtion hd been reveled (Stephens, 2007) (Yoshimoto, 1984) (Ohshi, 1985) (Ohshi, 1994) (Alexnder, 2000). In recent yers, investigtion of ftigue nd self-loosening of bolted joints which re subjected to trnsverse vibrtion hve been lso conducted (Jing, 2003) (Jing, 2002) (Hshimur, 2006) (Hshimur, 2007). In the most cses, ftigue crcks occurs t root of the first thred, which externl threds begin to engge internl threds. A nominl stress t the root of the first thred cn be esily clculted from the xil vibrtion force nd the effective section re if the bolted joint ws subjected to xil vibrtion. A method to clculte nominl stress t the root of the first thred occurred by trnsverse force hd lso been proposed if the bolted joint ws subjected to only trnsverse vibrtion (Hshimur, 2010). However clcultion method of the stress t the root of the first thred of bolted joints, which ws simultneously subjected to xil vibrtion nd trnsverse vibrtion, hve

2 Symposium_17: Mechnicl Connections not been proposed yet. Jing et l. investigted n influence of loding direction on selfloosening of bolted joint (Zhng, 2006). In their experiments, ngles of cyclic lods pplied to the bolted joints were 30 degree, 15 degree nd 0 degree from pure shering direction. The results sid tht the ngle of the cyclic lod from pure shering direction resulted in n increse in self-loosening resistnce. In their experiments, reltive displcement of the two clmped prts ws controlling prmeter, nd xil vibrtion nd trnsverse vibrtion hd not been seprtely controlled. They hve focused not on ftigue but on self-loosening. As mentioned bove, the ftigue investigtions of bolted joints subjected to either xil vibrtion or trnsverse vibrtion hve been performed. However the ctul bolted joints re subjected to xil vibrtion nd trnsverse vibrtion simultneously. Ftigue tests of bolted joint subjected to xil vibrtion nd trnsverse vibrtion hve been conducted in this study to revel the bolt ftigue mechnisms in detil. In the ftigue tests, the mplitude of xil vibrtion force ws constnt nd the mplitude of trnsverse vibrtion force ws only chnged in ech experiment. In the ftigue tests, xil vibrtion nd trnsverse vibrtion were pplied to the bolted joint with the sme phse nd the different phse. The ftigue tests for the bolted joint subjected to only trnsverse vibrtion were lso conducted to compre. The ftigue chrcteristics were evluted with n pprent trnsverse ftigue limit, the highest mplitude of trnsverse vibrtion tht the bolt does not brek due to ftigue. EXPERIMENTAL APPARATUS AND PROCEDURES Figure 1() shows test bolt nd Fig. 1(b) shows tightening sitution of tightened test bolt sitution subjected to trnsverse vibrtion nd xil vibrtion. The test bolt ws commercil hexgon hed bolt M10, thred pitch 1.5mm, nominl length l=45mm, property clss 8.8. The corners of the bering surfce under the bolt hed were mchined to ignore n influence of the scrtch due to corners of the bering surfce during ftigue test. A new test bolt ws used in ech experiment. Fig. 1 - A test bolt nd tightening sitution In the experiments, grip length l g of the bolted joint ws 35 mm nd engging thred length l e ws 10 mm. After the test bolt ws tightened with the initil clmping force F i into the internl thred s shown in Fig. 1(b), xil vibrtion ws pplied to the upper clmped prt nd trnsverse vibrtion ws pplied to the lower clmped prt. Consequently the test bolt received xil vibrtion nd trnsverse vibrtion simultneously

3 Proceedings of the 5th Interntionl Conference on Integrity-Relibility-Filure Figure 2 shows schemtic illustrtion of n experimentl pprtus for the multi-xil ftigue tests. The pprtus ws designed to simulte two-plte structure without nut. The test bolt ws tightened into the internl thred dpter through the upper clmped prt nd lod cell to mesure clmping force F in the center of the pprtus. The upper clmped prt ws supported by bll retiner to move in only xil direction. The contct surfces round the upper clmped prt were hrdened to reduce the friction. Frictionl losses were mesured to be less thn 1% of the xil vibrtion force were neglected in this study. The upper clmped prt ws lso supported by disk spring in xil direction to increse the lod fctor of the bolt. Fig. 2 - An experimentl pprtus The lower clmped prt ws supported by four liner rollers to move in only trnsverse direction. The internl thred dptor ws ttched to the lower clmped prt. Since the contct surfces round the lower clmped prt were hrdened to reduce the friction, frictionl losses round the lower clmped prt were lso were neglected. The displcement of vibrted clmped prt ws mesured by non-contct lser displcement trnsducer. Axil vibrtion ws pplied using n eccentric cm nd severl disk springs. The mplitude of xil vibrtion force ws ( P/2)=2.3 kn constnt nd the stress rtio R ws R=0. The xil vibrtion force P ws mesured by lod cell ttched on the upper clmped prt. Trnsverse vibrtion ws lso pplied using n eccentric cm nd lef springs. The mplitude of trnsverse vibrtion force ws ( Pt/2) controlled chnging number of lef springs. The stress rtio Rt ws Rt=-1. The trnsverse vibrtion force Pt ws mesured by lod cell ttched on the right side of the lower clmped prt. The rottions of the eccentric cms for xil vibrtion nd for trnsverse vibrtion were synchronized by timing belts. If phses between the xil vibrtion nd the trnsverse vibrtion were different, it is considered tht the ftigue chrcteristics might vry depending on the phses. The combintion of the two phses come down to two cses pproximtely s shown in Fig.2(b). The first cse ws sme phse, nd we defined the cse s phse A. The second cse ws phse gp 90 degree, nd we defined

4 Symposium_17: Mechnicl Connections the cse s phse B. Incidentlly, if the phse gp is 180 degree, the phse gp equls to phse A. In this cse, the point, t which the mximum stress generted, chnge to the opposite root of threds. The internl thred dptor plte prt ws mde of chromium-molybdenum steel JIS SCM435 nd mnufctured by tpping. The tp ws inserted into the internl threds to check the deformtion of the internl threds before ech experiment. If n bnormlity of the internl thred were detected, the dptor would be replced with new one. Otherwise, the dptor ws repetedly used in the experiments. The upper clmped prt nd the lower clmped prt were lso mde of chromium-molybdenum steel JIS SCM435 nd hole dimeter D h in the bering surfce prt ws 11mm. The ftigue tests were strted fter the test bolt ws tightened by wrench with F i =15kN nd device to pply the xil vibrtion ws ttched on the upper clmped prt. To revel influences of n interction between two vibrtions on bolted joint ftigue, the ftigue tests were conducted in three conditions. In the first condition, the bolted joints were pplied the two vibrtions with phse A. In the second condition, the bolted joints were pplied the two vibrtions with phse B. The third condition ws the ftigue tests under only trnsverse vibrtion. The mplitude of xil vibrtion force ws fixed with constnt ( P /2)=2.3 kn, nd the mplitude of trnsverse vibrtion force ws chnged from ( P t /2)=0.7 kn to 0.27 kn in ech experiment to revel ftigue limits. The ftigue tests were stopped when the clmping 7 force F reched zero or the loding cycle exceeded 1 10 cycles. In ll ftigue tests, the thred surfce nd bering surfce were lubricted by MoS 2 grese. In this study, we defined the highest mplitude of trnsverse vibrtion tht the bolt does not brek due to ftigue s n pprent trnsverse ftigue limit ( P t /2) w when the bolt received only trnsverse force. When the test bolt received the xil vibrtion in ddition to the trnsverse vibrtion in phse A, the pprent trnsverse ftigue limit ws denoted by ( P t /2) w-a. When the test bolt received the xil vibrtion in ddition to the trnsverse vibrtion in phse B, the pprent trnsverse ftigue limit ws lso denoted by ( P t /2) w-b. The ftigue chrcteristics were evluted by these pprent trnsverse ftigue limits lthough the xil vibrtion ws pplied to the test bolt. RESULTS OF MULTI-AXIAL FATIGUE TESTS Figure 3 shows the results of ftigue tests. The ordinte is the mplitude of trnsverse force ( P t /2), nd bsciss is the number of cycles to filure N f. In Fig. 3, blck circulr symbols indicte the ftigue lives N f of the test bolts subjected to trnsverse vibrtion only. And white circulr symbols show the results tht the test bolts did not brek due to ftigue. The pprent ftigue limit due to trnsverse vibrtion only ws ( P t /2) w =0.43 kn. Blck rhombus symbols indicte the ftigue lives N f of the bolts subjected to xil vibrtion with phse A in ddition to trnsverse vibrtion. And white rhombus symbol shows the results tht the test bolts did not brek. The pprent ftigue limit of phse A ws ( P t /2) w-a =0.27 kn. Blck squre symbols indicte the ftigue lives N f of phse B. A white squre symbol shows the results tht the test bolts did not brek. The pprent ftigue limit of phse B ws ( P t /2) w-b =0.34 kn. It cn be seen in Fig. 3 tht the ftigue limits for ech loding condition were different. As mtter of course, the pprent ftigue limit ( P t /2) w by only trnsverse vibrtion were the highest in ll conditions becuse the bolted joint in phse A nd phse B ws subjected to the xil vibrtion in ddition to the trnsverse vibrtion. The number of cycles to filure N f,

5 Proceedings of the 5th Interntionl Conference on Integrity-Relibility-Filure which the bolted joint ws subjected to the trnsverse vibrtion only, were lso longer thn the other conditions. Frcture crcks occurred t the root of the first thred in most cses. Fig. 3 - Reltionships between mplitude of trnsverse vibrtion force P t /2 nd number of cycles to filure N f. It cn be lso seen tht the pprent ftigue limit ( P t /2) w-b of phse B ws bout 25 % higher thn the pprent ftigue limit ( P t /2) w-a of phse A lthough the sme xil vibrtion ws pplied to the bolted joint. The difference of these conditions ws the phse gp of vibrtions only. The results indicte tht the stresses t the root of the first thred were different in ech loding condition even if the mplitude of xil vibrtion force nd the mplitude of trnsverse vibrtion were the sme. Therefore we hve to understnd reltionships between the stresses t the root of the first thred nd the mplitudes of ech vibrtion force. Incidentlly, the difference between ( P t /2) w nd ( P t /2) w-a ws 0.16 kn lthough the xil vibrtion ws pplied to the bolted joint in ddition to trnsverse vibrtion in the experiments of phse A. The difference between ( P t /2) w nd ( P t /2) w-b ws lso 0.09 kn. These two differences were very smll. It is seen from the results tht trnsverse vibrtion hs gret influence on the bolt ftigue in comprison with xil vibrtion. In our experimentl pprtus, there were liner rollers between clmped prts. Hence it is considered tht the ctul pprent ftigue limits re lrger thn the results in this study becuse the ctul pprent ftigue limits must be included friction force between bering surfces. However the ctul pprent trnsverse ftigue limits re not so strong even if the friction force between clmped prts ws included. Therefore we hve to py enough ttention to trnsverse vibrtion of bolted joints. STRESS AT A ROOT OF THE FIRST THREAD To revel n influence of the phse gp on the ftigue strengths, we mesured the stresses t the root of the first thred pplied by xil vibrtion nd trnsverse vibrtion using strin gges. And then we hve lso proposed method to clculte the stresses t the root of the first thred by xil vibrtion nd trnsverse vibrtion nlyticlly

6 Symposium_17: Mechnicl Connections At first we clculted the reltionship between xil force P nd the stress σ t the root of the first thred. When the bolted joint received xil force P, the dditionl xil force Q of the bolt becomes following eqution. Q =Φ (1) P where Φ is lod fctor of the bolted joint nd expressed by Eq.(2). Φ = Cb C + C b c where C b is spring constnt of the bolt nd C c is spring constnt of the clmped prt. Let S be the lod to the clmped prt due to xil force P, Φ is expressed s Φ = Q P P S = P The nominl stress σ cused by xil force P is expressed by following eqution. P σ = Φ A s P S = A s where A s is n effective section re of the bolt thred portion. In the experimentl pprtus, xil force P ws mesured by the lod cell for xil force nd the lod S to the clmped prt ws mesured by the lod cell for clmping force. As result of preliminry experiments, lod fctor Φ of the pprtus ws Φ=0.68. Next, the reltionship between the trnsverse force nd the stress t the root of the first thred is clculted. Fig. 4 shows schemtic illustrtion of deformed bolt which is subjected to trnsverse vibrtion only. In Fig.4, point O is point under the bolt hed, point A is border point between the shnk nd threded portion. Point B is the first bolt thred which begins to engging the internl thred. When the bolt receives trnsverse force P t, the bolt deforms S-shpe s shown in Fig.4 becuse the engged bolt threds re constrined by the internl threds. At this time, the bolt hed hs n inclintion ϕ o t point O. The thred surfce slips t point B in the trnsverse direction, δ s-slip. The threded portion simultneously inclines t point B, ϕ B, nd the bending moment M B t point B is generted. The right side of Fig.4 shows bending moment digrm of the bolt subjected to trnsverse force P t. The bending moment M on the bolt is expressed by following eqution by bem theory. (2) (3) (4) M ( lg x) M B = P (5) t + Where where l g is grip length of the bolted joint. The bending moment M B is expressed s M B = C P t l g (6) where C is coefficient of the bending moment. If ϕ B =0 nd ϕ o =0, the coefficient C becomes 0.5. However the coefficient C does not become zero becuse ϕ B nd ϕ o re existing ctully. Hence it is not esily to determine the coefficient C becuse C depends on the inclintion ϕ B t point B nd the slippge δ s-slip between thred surfces

7 Proceedings of the 5th Interntionl Conference on Integrity-Relibility-Filure Fig. 4 - A schemtic illustrtion of deformed bolt due to trnsverse force If the coefficient C is known, the reltionship between the trnsverse force P t nd the nominl stress σ t t the root of the first thred cn be expressed s follow. M B d C P l 3 t g d3 σ t = = (7) I 2 I 2 b b where d 3 is the root dimeter of bolt thred nd I b is the moment of inerti of effective section re of the bolt thred. If we could know either the bending moment M B or coefficient C, the nominl stress σ t t the root of the first thred cn be clculted from trnsverse force P t. Then we mesured the bending moment M B t point B using test bolt ttched strin gges. Fig.5 shows test bolt to mesure the bending moment M B nd bending moment digrm. The thred portion, which did not engge with the internl threds, ws removed by lthe. Six strin gges were ttched to the both opposite sides on the bolt shnk s shown in n illustrtion in Fig.5. The outputs of the strin gges were clibrted pplying bending moment to the test bolt in dvnce. A grph in Fig.5 shows bending moment digrm when trnsverse vibrtion ( P t /2) ws pplied to the bolted joint. The bending moment digrms were drwn for three mplitudes of trnsverse vibrtion, ( P t /2)=0.29 kn, ( P t /2)=0.46 kn nd ( P t /2)=0.55 kn. As cn be seen in Fig.5, ll bending moment digrms were liner ginst the bolt position in xil direction. It cn be lso seen in Fig.5 tht the bolt deformed like S-shpe. The bending moment M B t point B ws clculted by extrpoltion. Coefficient C becme C=0.37 substituting M B for Eq.(6). And this coefficient C ws lmost the sme for the ll mplitudes of trnsverse vibrtion. The stress (σ +σ t ) t the root of the first thred due to xil vibrtion P nd trnsverse vibrtion P t were clculted substituting ( P /2) nd ( P t /2) for Eq.(4) nd Eq.(7)

8 Symposium_17: Mechnicl Connections Fig. 5 - A test bolt ttched strin gges nd bending moment digrms of the test bolt Figure 6 shows the mesured stress σn-exp nd the clculted stress (σ+σt)n-cl by Eq.(4) nd Eq.(7) when the test bolt ws subjected to ( Pt/2)=0.46 kn nd ( P/2)=2.3 kn in phse A. The mesured stress σn-exp ws mesured from the output of M1, B1, M2 nd B2 by extrpoltion. In Fig.6, the ordinte is the nominl stress σn t the root of the first thred nd the bsciss is time. The blck wide solid line nd the gry wide solid line show the stress t the left side root of the first thred, T1. The blck thin solid line nd the gry thin solid line show the stress t the right side root of the first thred, T2. The blck lines show the results of n experiment using the test bolt ttched the strin gges. The gry lines show the clculted stress (σ+σt)n-cl. In the bolt sitution of Fig.6, when the bolt pulled with the mximum xil force such s wide rrow, the lower clmped prt received the mximum trnsverse force in left direction. Hence the mplitude of the stress t T1 ws higher thn tht t T2. Fig. 6 - Comprisons of the stresses which were mesured by the strin gges nd the stresses which were clculted using the xil vibrtion nd the trnsverse vibrtion

9 Proceedings of the 5th Interntionl Conference on Integrity-Relibility-Filure It cn be seen in Fig.6 tht the experimentl stress σn-exp nd the clculted stress (σ+σt)ncl were lmost the sme lthough the experimentl stress hd included electricl noise little. Consequently, the vlidity of superposition of the stresses clculted using Eq.(4) nd Eq.(7) were confirmed. The results indicte tht there is lmost no interction between xil vibrtion nd trnsverse vibrtion. Nmely it is considered tht xil vibrtion hs lmost no influence on the slippge between thred surfces occurred by trnsverse vibrtion. In Fig.6, the mplitude of stress σn t S1 determines the ftigue life of the bolt becuse the mplitude of σn t S1 ws lrger thn tht of σn t S2. Bsed on these results, the mximum mplitudes of stress t the root of the first thred were clculted for ech experimentl condition, nd the experimentl results in Fig.3 were re-drwn by the mximum mplitudes of stress t the root of the first thred. Figure 7 shows the experimentl results which were drwn by the mximum mplitudes of stress (σ +σ t ) n-cl t the root of the first thred. In Fig.7, circulr symbols indicte the ftigue chrcteristic of the bolts subjected to trnsverse vibrtion only. Its ftigue limit ws σ tw =97 MP. Rhombus symbols indicte the ftigue chrcteristic of phse A. Its ftigue limit ws (σ t +σ ) w-a =88 MP. Squre symbols indicte the ftigue chrcteristic of phse B. The ftigue limit ws (σ t + σ ) w-b =81 MP. It cn be seen tht the true ftigue limits in Fig.7 re lmost the sme lthough the pprent ftigue limits re different in Fig.3. The finite ftigue lives N f becme lso lmost the sme. The results show tht the true ftigue limits never chnge by the loding conditions lthough the pprent ftigue limits chnge depending on the loding conditions. Fig. 7 - Reltionships between nominl stresses t the root of the first thred nd number of cycles to filure CONCLUSIONS In this study, we conducted the ftigue tests of bolted joints simultneously subjected to xil vibrtion nd trnsverse vibrtion of which phses were controlled. The min conclusions obtined in this study re summrized s follows. 1. The pprent trnsverse ftigue limit, the highest mplitude of trnsverse vibrtion tht the bolt does not brek due to ftigue, chnges depending on phse difference between xil vibrtion nd trnsverse vibrtion

10 Symposium_17: Mechnicl Connections 2. The true ftigue limits do not chnge depending on phse difference between xil vibrtion nd trnsverse vibrtion. 3. The nominl stress t the root of the first thred, which is frcture point, cn clculte by superposition of the stresses due to xil vibrtion nd trnsverse vibrtion. REFERENCES [1]-Ministry of Lnd, Infrstructure nd Trnsport, Press relese report, The number of ccidents tht wheels fllen off by wheel bolt filure in 2010 is 24., (ccessed on 30 November, 2013) (in Jpnese). [2]-Stephens, I., Brdley, J., Horn, J., Arkem, M. nd Grdmn, J., Influence of cold rolling threds before or fter het tretment on the ftigue resistnce of high strength corse thred bolts for multiple prelod conditions, ASTM Specil Technicl Publiction Vol.1487 STP, 2007, Pges [3]-Yoshimoto, I., Mruym, K. nd Ymd, Y., Prediction of Ftigue Strength of Bolt-nut Joints Bsed on Residul Stress, Trnsctions of the Jpn Society of Mechnicl Engineers, Series A, Vol.50, No.452 (1984), pp (in Jpnese). [4]-Ohshi, N., Hgiwr, M., nd Yoshimoto, I., Chrcteristics of Bolted Joint in Plstic Region Tightening Dispersion of Tightening Axil Force nd Sfety ginst Ftigue -, Bull. Jpn. Soc. Precis. Eng., Vol. 51, No. 7, 1985, pp (in Jpnese). [5]-Ohshi, N., Ksno, H., nd Yoshimoto, I., Reserch on Ftigue Testing of Bolts for Qulit y Assurnce, Trnsctions of the Jpn Society of Mechnicl Engineers, Series C, Vol.60, No.576 (1994), pp (in Jpnese). [6]-Alexnder, D.F., Skochko, G.W., Andrews, W.R., Briody, R.S., Ftigue testing of lowlloy steel fsteners subjected to simultneous bending nd xil lods, ASTM Specil Technicl Publiction Issue 1391, 2000, pp [7]-Jing, Y., Zhng, M., Prk, T.-W. nd Lee, C.-H., An Experimentl Investigtion on Self-loosening of Bolted Joints, ASME Pressure Vessel nd Piping Conf., July 20-24, 2003, Clevelmd, OH, PVP-Vol.457, Anlysis of Bolted Joints, PVP , 2003, pp [8]-Jing, Y., Zhng, M., nd Lee, C.-H., A Study of Erly Stge Self-loosening of Bolted Joints, ASME Journl of Mechnicl Design, Vol. 125, 2003, pp [9]-Hshimur, S. nd Drrell F. Socie, A Study of Loosening nd Ftigue of Bolted Joints under Trnsverse Vibrtion,SAE 2005 Trnsctions, Journl of Mterils nd Mnufcturing, Section 5 (2006), pp [10]-Hshimur, S., Influences of Vrious Fctors of Bolt Tightening on Loosening-Ftigue Filure under Trnsverse Vibrtion, SAE 2007 Trnsctions, Journl of Mterils nd Mnufcturing, Section 5, 2007, pp [11]-Hshimur, S. nd Kurkke, Y., A Study to Predict Ftigue Limits of Bolted Joints under Trnsverse Vibrtion, Proceedings of the 2010 SAE World Congress, Detroit, Michign, April 14-16, Technicl Pper No [12]-Zhng, M., Jing, Y., nd Lee, C.-H., An Experimentl Investigtion of the Effects of Clmped Length nd Loding Direction on Self-Loosening of Bolted Joints, Trnsction of ASME, Journl of Pressure vessel Technology, Vol. 128, 2006, pp