APPLICATION OF FEM ANALYSIS METHODS TO A CYLINDER-CYLINDER INTERSECTION STRUCTURE

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1 18th Iteratial Cferece Structural Mechaics i Reactr echlgy (SMiR 18) Beijig, Chia, August 7-12, 25 SMiR18-F7-4 APPLICAION OF FEM ANALYSIS MEHODS O A CYLINDER-CYLINDER INERSECION SRUCURE Lipig XUE G.E.O. WIDERA Ceter fr Jiig ad Maufacturig Ceter fr Jiig ad Maufacturig Assembly Assembly Marquette Uiversity Marquette Uiversity Milwaukee, WI 53233, USA Milwaukee, WI 53233, USA Phe: Phe: ,Fax: lipig.xue@mu.edu ge.widera@mu.edu Zhifu SANG Departmet f Mechaical ad Pwer Egieerig Najig Uiversity f echlgy Najig, Jiagsu 219, Chia Phe: zfsag@jut.edu.c ABSRAC he bjective f this paper is t study a particular cylidrical shell itersecti (d/d=.526) by use f bth liear elastic ad elastic-plastic stress aalyses via the fiite elemet methd usig the FEA sftware ANSYS. he frmer maily fcuses the calculati f the stress ccetrati ad flexibility factrs i the itersecti area befre the structure experieces plastic behavir. Whe a elastic-plastic aalysis methd is emplyed, the limit lad ad burst pressure eed t be determied. I this study, tw differet methds, the duble elastic-slpe methd ad the taget itersecti methd are bth emplyed t determie the limit pressure. predict the burst pressure ad failure lcati, the arc-legth methd i ANSYS is used t slve the liear prblem. Fially, the FEA results are cmpared t experimetal data ad the agreemet is shw t be gd. Keywrds: Stress ccetrati factr, flexibility factr, limit pressure, burst pressure 1. INRODUCION Cylidrical shell itersectis are structural cfiguratis cmmly used i may idustries. he acti f varius lads leads t high lcal stresses i the itersecti regi resultig i stress ccetratis there. I additi, due t difficulties that may arise durig weldig ad the resultig defects, the itersecti regi the becmes the weakest pit ad failure surce f the whle structure. hus, it is very imprtat t be able t accurately btai the magitude ad lcati f stresses ad strais s as t allw e t examie the failure mdes f these structures. Stress aalysis methds fr cylidrical shell itersectis fall it tw areas: liear elastic aalysis ad elastic-plastic aalyses. As far as the liear elastic aalysis is ccered, the stress itesity ad flexibility 1329

2 factrs are tw imprtat factrs which eed t be determied. Whe elastic-plastic aalysis is csidered, limit lad ad burst pressure aalyses are tw f the phemea that ca be ivestigated. Extesive ivestigatis f stress itesificati ad flexibility factrs fr cylidrical shell itersectis ad similar cfiguratis have bee perfrmed by Fujimt ad Sh (1988), Willias ad Clark (1996), Wais et al. (1999) ad s. he Pressure Vessel Research Cucil (PVRC) has spsred several prjects t determie limit lads s as t be able t refie the desig criteria fr pressure vessels ad pipe cectis. he particular studies which were cducted t btai the limit lads fr iteral pressure ad exteral lads the zzle by use f liear fiite elemet aalyses have icluded Break (199) ad Juker (1982). N similar bdy f kwledge is available fr burst pressure predicti f cylidrical shell itersectis by use f FEA. 2. EXPERIMENAL SUDY 2.1 Descripti f est Vessel Structure ad Dimesi A test vessel was desiged ad fabricated fr the experimetal study. It csists f a mai vessel, a zzle, tw elliptical heads, fillig ad vetig cectis, etc. It shuld be ted that the dimesis f the test vessel were determied by a Pressure Vessel Research Cucil (PVRC) versight cmmittee. able 1 illustrates the cfigurati ad gemetric dimesis f the test vessel. able 1 Gemetric Dimesis f est Vessel Scheme f est Vessel Dimesi D i d t Lv L mm mm mm mm mm mm d/d t/ D/ D i : iside diameter f vessel : thickess f vessel D: mea diameter f vessel t: thickess f zzle d: utside diameter f zzle Lv: legth f vessel d: mea diameter f zzle L: legth f zzle Material Prperties he material f the mai vessel ad zzle is Q235-A (lw carb steel, similar t A36-77). A typical egieerig stress-strai curve up t the ultimate stregth is shw i Fig.1. his plt idicates a elastic tesile mdulus f 2.1x1 5 MPa which is used thrughut the aalysis. Average values f the yield stregth σ y ad ultimate stregth σ u fr material Q235-A are ad 472 MPa, respectively. 133

3 Fig.1 ypical Egieerig Stress-Strai Diagram fr Q235-A Fabricati f est Vessel Sigle V-grve butt jits, Fig.2 (a), were used fr bth the lgitudial ad circumferetial welds used i the maufacture f the test vessel. A sigle bevel grve fillet weld, Fig.2 (b), was emplyed fr the vessel-zzle crer jit. he details f the welds are shw i Fig.2. ugste-iert gas arc weldig (rt f welds) ad maual electric-arc weldig (depsit f weld rd material) were used fr all welds. (a) (b) Fig.2 Welds fr est Vessel Experimetal Prcedure he test was perfrmed usig electrical resistace gages t btai the lad versus strai plts fr bth the elastic ad plastic regis. he strai gages were istalled i the lgitudial ad circumferetial sectis the utside surface f the vessel ad zzle, as dictated by the PVRC versight cmmittee. he strai gage rsettes attached t the vessel ad zzle eed t be lcated as clse as pssible t the weld i the itersecti area. he lcati ad distributi f the strai gages thrughut the vessel are shw i Fig.3. he test vessel was pressurized with a hydraulic test pump. he test was cducted by icreasig the pressure gradually i icremets f abut.25 MPa ad strai gage readigs were recrded durig each lad step. 2.2 Experimetal Results Elastic Aalysis he maximum elastic stress i the itersecti uder iteral pressure f 1. MPa ccurs at strai gage N.1, which lcated the utside surface f the mai vessel i the lgitudial plae. he value is 242.3MPa. he stress ccetrati factr (SCF) ca be btaied by divided the maximum stress by the mial hp stress i the vessel σ. 1331

4 PD σ = = = 5.5 (1) σ max SCF = = = 4.8 (2) σ Fig.3 Lcati ad Distributi f Strai Gages Limit Pressure he experimetal limit pressures, P φ ad L P Lt, are btaied by use f tw methds frm the pressure-hp strai curve f the critical gages lcated ear the jucti f the vessel ad zzle (see Fig.4). Here, P φ represets the duble elastic-slpe methd (itersecti f the pressure-strai curve with a lie thrugh L the rigi havig duble the slpe f the elastic prti f the curve). Further, P is the limit pressure usig the taget itersecti methd (itersecti f the tagets draw t the curve i the elastic ad plastic regis). Lt 1332

5 P (MPa) PL φ = 2.85MPa 3. 5 PLt = 3.MPa Hp St r ai (a) Strai Gage N.1 P (MPa) PL φ = 3.14MPa 3.5 PLt = 3.15MPa Hp Strai (b) Strai Gage N.7 Fig.4 Pressure-Strai Curves ad Limit Pressures Burst Pressure he test vessel was pressurized i small icremets t burst. he burst pressure is 7.4 MPa. he iitiati f the fracture ccurred ff the lgitudial plae at the jucti betwee the vessel ad zzle. Figure 5 shws the rupture f the test vessel. 1333

6 Fig.5 Rupture f est Vessel 3. FINIE ELEMEN ANALYSIS 3.1 Fiite Elemet Mdel A fiite elemet aalysis f the test vessel is perfrmed usig ANSYS cde (23). hree-dimesial 2 de structural slid elemets are used t geerate the fiite elemet mdel mesh. Fr iteral pressure lad case, a quarter symmetric fiite elemet mdel (see Fig.6) is used due t the symmetry f structure ad ladig. Guidelies fr FEA mdelig f cylider-t-cylider itersectis established i WRC Bulleti 493 (24) are emplyed t create the mdel. his led t a fiite elemet mdel havig twety-fur elemets i the circumferetial directi f the zzle, tw elemets thrugh the thickess, sixtee elemets i the axial directi f the vessel ad zzle prir t reachig the decay distace ( 3. R ad 3. rt ). he maximum aspect rati at the itersecti area is less tha 5. determie flexibility factrs due t i-plae ad ut-f plae mmets at the ed f zzle, half fiite elemet mdels are emplyed istead (see Fig.7). hree fiite elemet mdels, lger (Lv=7D, L=7D), medium (Lv=4D, L=2.5D) ad shrter (Lv=2D, L=D) are emplyed t determie the flexibility factrs, respectively. he reas why a lger mdel is als emplyed is due t the effect f legths f the vessel ad zzle the flexibility factrs (See Referece (22) fr detailed ifrmati). 1334

7 Fig.6 Fiite Elemet Mdel fr Iteral Pressure Lad Case Fig.7 Fiite Elemet Mdel fr Exteral Lad Case 3.2 Budary ad Ladig Cditis Fr the iteral pressure lad case, symmetry budary cditis are emplyed the tw symmetry plaes. simulate the ctaied pressure, equivalet axial stresses are impsed as budary cditis at the eds f the vessel ad zzle. A i-plae mmet the zzle represets symmetric ladig abut the X-Z plae (see Fig.7), while the ut-f-plae mmet represets a atisymmetric ladig abut the X-Z plae. herefre, symmetry budary cditis are impsed all des at the X-Z plae fr i-plae mmet, while atisymmetry budary cditis are impsed all des at the X-Z plae fr ut-f-plae mmet lad case. Further, the left ed f the vessel is fixed while the right ed f the vessel ad the ed f the zzle are free. I rder t cmpare the results f fiite elemet aalysis with thse f experimetal study, the true stress true strai curve f material Q235-A described by 8 pits as shw i Fig.8 are emplyed fr the FEA material prperties iput. he material is assumed t be istrpic. Piss s rati is take as.3 fr the elastic strais. 1335

8 6 5 rue stress (MPa) rue strai Fig.8 Multiliear Material Mde Curve 3.3 Results Elastic Aalysis Stress Ccetrati Factr he maximum elastic stress frm FEA ccurs at the ier crtch crer. he stress ccetrati factr fr this particular structure, which equals t 5.11, ca be btaied by divided the maximum stress by the mial hp stress i the vessel σ (see Eq. 1). Decck (1975) devised a empirical SCF fr pressure ladig based his cllecti f 156 experimetal results frm steel ad araldite mdels f brach juctis. His prpsed equati fr predictig the SCF at the ier crtch crer was as fllws: SCF 2 2 ( d D) 3 ( t ) ( d D)( D ) 1+ ( t ) 3 2 ( d D) = (3) 1 2 Substitutig D/, d/d ad t/ f the test vessel it the abve equati gives: SCF=5.43. able 2 Cmpariss f SCF s Experimet FEA Eq. 3 SCF able 2 shws the cmpariss f SCF s determied frm experimet, FEA ad Eq.3, respectively. Althugh Eq.3 yields a mre cservative SCF, (csiderig the lcati where the experimetal SCF was determied), e ca see that the SCF s agrees quite well with each ther Flexibility Factrs he flexibility factrs k f cylidrical shell itersectis are defied by the virtual sprig f rtati: ( beam ) EI k = (4) Md where 1336

9 = rtati at the tp f zzle by FEA beam = mial rtati at the tp f a zzle by beam thery E = Yug s Mdulus I = mmet f iertia f zzle I v M d = mmet f iertia f vessel = i-plae r ut-f-plae mmet at the tp f zzle = utside diameter f zzle determie the i-plae ad ut-f-plae flexibility factrs beam will be substitute it Eq.4. Fr i-plae mmet ladig M i = Y beam M i L 1. L = + E I Iv v k, k frm the umerical results, i ad (5) (6) Fr ut-f-plae mmet ladig M = X (7) Where X, Y beam M L 1. 3L = + E I Iv v = rtatis at the tp f zzle (frm FEA) Fujimt (1988) develped empirical frmulas fr the flexibility factrs by fixig bth eds f vessel. he legths f the vessel ad zzle are Lv=2.89D ad L=3.5D, respectively. Wais (1999) als develped crrelati equatis based average flexibility factrs f e vessel ed fixed ad bth vessel eds fixed. he legths f the vessel ad zzle are Lv=2D ad L=1.5D, respectively. able 3 shws the preset i-plae ad ut-f-plae flexibility factrs fr shrter, medium, lger legth mdels as well as flexibility factrs frm empirical frmulas frm Fujimt ad Wais. Frm able 3, it is see that the agreemet fr k is quite gd. I additi, the results shw that the legths f the vessel ad zzle i d affect the flexibility factrs, especially fr k. It is wrthwhile t te that there is cservative value i evaluatig flexibility factrs i pipig systems. herefre, it is desirable that the vessel ad zzle be lg eugh t elimiate their effect flexibility factrs prir t perfrmig a parametric fiite elemet aalysis. able 3 Cmparis f Flexibility Factrs Preset Shrter Mdel Preset medium Mdel Preset Lger Mdel Fujimt (1988) Wais (1999) Lv=2D, L=D Lv=4D, L=2.5D Lv=7D, L=7D Lv=2.89D, L=3.5D Lv=2D,L=1.5D k i k Limit Pressure Figure 9 depicts the pressure-strai curves uder the iteral pressure at the same lcatis as thse f the experimetal study (i.e., at the lcatis where the strai gages were istalled). Usig the duble elastic-slpe (8) 1337

10 ad taget itersecti methds, the limit pressure at the lcatis metied abve fr the test vessel are als illustrated i Fig.9. P (MPa) FEM PL φ = 2.75MPa 5 FEM PLt = 2.88MPa Hp Strai (a) Strai Gage N P P FEM Lφ FEM Lt = 2.8MPa = 3.5MPa P (MPa) Hp Strai (b) Strai Gage N.7 Fig.9 Limit Pressure by FEM able 4 shws the cmparis f limit pressure frm FEA with thse frm experimet. Frm able 4, it is see that the umerically determied limit pressures agree reasably well with the experimetal results. I additi, the duble elastic-slpe methd yields mre cservative limit pressure. Further, the limit pressures at stai gage N.1 are lwer that thse at strai gage N.7. It ca thus be ccluded that the failure f the structure is mre likely t ccur the vessel rather tha 1338

11 able 4 Cmparis f Limit Pressure Strai Gage N.1 Strai Gage N.7 Experimet FEA PL φ P Lt FEM PL φ FEM P Lt Burst Pressure predict the burst pressure, a failure criteri is ecessary. I referece (1999), failure is defied as the pressure fr which the structure apprached dimesial istability, i.e., ubuded displacemet fr a small icremet i pressure. his cditi is symptmatic f a ill-cditied budary prblem caused by the cmbied chages i gemetry ad material stiffess leadig t a physical istability. he failure lcati is determied based the maximum average equivalet plastic strai acrss the thickess f the specime. Figure 1 shws the pressure versus equivalet plastic strai curve at the critical de where the maximum equivalet plastic strai ccurs. Frm Fig.1, it is see that whe the pressure reaches 8.6 MPa, the equivalet plastic strai icreases sigificatly with little chage f pressure, i.e., the slpe f the pressure-equivalet plastic strai curve becmes vaishigly small. Based the criteria metied abve, the ttal pressure (8.6 MPa) that causes this cditi is the icipiet failure pressure. herefre, the pressure (ear zer lad-strai slpe) ca be deemed as the burst pressure. Cmpared with the experimetal burst pressure 7.4 MPa, the predicted burst pressure is 16% higher. Fr this cylidrical shell itersecti, the maximum average equivalet plastic strai acrss the thickess ccurs abut 26 degrees ff the lgitudial plae at the jucture the vessel. he failure lcati cicides with the experimetal result (See Fig.5) Pressure (MPa) % 1% 2% 3% 4% 5% 6% Equivalet plastic strai Fig.1 Pressure versus Equivalet Plastic Strai curve 1339

12 4. CONCLUSIONS he elastic ad plastic behavirs f a thi-walled cylidrical shell itersecti with a large diameter ( D / 1 ) have bee discussed by use f fiite elemet aalysis. Frm a cmparis f the FEA results with the experimetal data, the fllwig cclusis ca be reached: 1. Frm the pit f view f stress ccetrati, limit pressure ad burst pressure, the weakest lcati ccurs at the itersecti area f vessel. 2. he legths f the vessel ad zzle d affect the flexibility factrs. I rder t elimiate the effect f this factr the flexibility factrs, the legths f the fial FE mdels shuld be ascertaied prir t perfrmig ay fiite elemet aalysis. 3. he limit desig methd circumvets the cmplicated stress categries, ad is a simple ad advaced desig techique. he key pit f this methd is t determie the limit lad f the vessel. he duble elastic-slpe methd fr determiig the limit lad is cservative. 4. he burst pressure ad failure lcati f a cylidrical shell itersecti ca be predicted by emplyig a defrmati based failure criteri. 5. Fiite elemet simulatis ca be emplyed with sufficiet accuracy t study the varius failure mdes assciated with cylidrical shell itersecti structures. 5. REFERENCES Swas Aalysis System Ic., (23), Aalysis Egieerig Aalysis Systems User s Maual. Break, E. G. ad Gerdee, J.C., (199), Jural f Pressure Vessel echlgy, Vl.112, pp.138. Decck, J., (1975),Rep. N. M14, Cetre de Recherches Scietifiques et echiques de L Idustrie des Fabricatis Metalliques. Fujimt,. ad Sh,., (1988), Jural f Pressure Vessel echlgy, Vl.11, pp.374. Jes, D. P., Hlliday, J. E. ad Lars, L. D., (1999), Jural f Pressure Vessel echlgy, Vl.121, pp.149. Juker, A.., (1982), America Sciety f Mechaical Egieers Paper, 82-PVP-1. Wais, E. A., Rdabaugh, E C. ad Carter, R., (1999), America Sciety f Mechaical Egieers, Pressure Vessels & Pipig Divisi (Publicati), Vl.383, pp.159. Williams, D. K. ad Clark, J. R., (1996), Pressure Vessels ad Pipig Desig, Aalysis, ad Severe Accidets, ASME, Vl.331, pp.55. Xue, L. ad Widera, G. E. O., (22), Parametric Fiite Elemet Aalysis f Large Diameter Rati Shell Itersectis Subjected t Exteral Ladigs: Flexibility Factrs fr Exteral Mmets Nzzle, PVRC Reprt. Xue, L. ad Widera, G. E. O., (24), Weldig Research Cucil Bulleti