Analysis Of Leakage In Bolted-Flanged Joints Using Contact .
DJournal of Mechanics Engineering and Automation 5 (2015) 135-142doi: sis of Leakage in Bolted-Flanged Joints UsingContact Finite Element AnalysisHector EstradaDepartment of Civil Engineering, University of the Pacific, Stockton 95211, USAReceived: September 09, 2014 / Accepted: November 18, 2014 / Published: March 25, 2015.Abstract: The evolution of leakage is studied using detailed contact finite element analysis. The distribution of stress at the gasket isanalyzed using a contact condition based on slide-line elements using ABAQUS, a commercial finite element code. Slide-lineelements also take into account pressure penetration as contact that is lost between flange and gasket. Results are presented for aparticular flange, a raised face flange sealed by a mild steel gasket. A comparison of the results from the gasket contact analysis andthe contact conditions specified by the ASME Boiler and Pressure Vessel Code, Sections VIII, Division 1 shows that the conditionsspecified in the ASME Code predict leakage relatively accurately.Key words: Flanged joints, contact finite element analysis, design codes.1. Introduction In the piping industry, there are several problemsthat continue to receive a considerable amount ofresearch attention, particularly in the area ofbolted-flanged joint design. Two problems that arecritical in bolted flanged joint design are strength ofthe joint and leakage. The first problem has beenstudied since the 1920s for metallic joints with ageneral consensus on the available solution wellestablished [1]. The second problem has been studiedfor almost an equally long period yet leakage analysiscontinues to be the subject of much study, as evidentby the number of articles published in the past quartercentury [2-4].Here, an analysis is presented that can be used indesign formulations for the detection of leaks for aspecified pressure. There are many parameters thatinfluence joint leakage (bolt load, internal pressure,gasket material, flange stiffness, flange geometry,contained medium, etc.); of these parameters, boltCorresponding author: Hector Estrada, Ph.D., professor,research fields: bolted joints, applications of :hestrada@pacific.edu.load, flange stiffness, internal pressure, and gasketmaterial appear to be most critical.Half of a typical raised face bolted flange isdepicted in Fig. 1. This is one of the symmetries thatcan be exploited in modeling bolted flanged joints.There is another symmetry that can be used to reducethe size of the model, the wedge model shown in Fig.1. Also, leakage can be analyzed using anaxisymmetric model, taking into account properboundary conditions, without loss of practicalaccuracy.The gasket pressure distribution in the hoopdirection has been shown to be uniform for a standardbolt spacing using three-dimensional finite elementanalyses [5]. However, the axisymmetric model iscomputationally more efficient than the wedge model.Also, a very important option needed to properlymodel the leakage is not supported inthree-dimensional elements, namely, the pressurepenetration option in ABAQUS, which is the reasonwhy the emphasis is placed on axisymmetric modeling.This is also the procedure used in the strengthanalytical model, the Taylor-Forge method [1].
136Fig. 1Analysis of Leakage in Bolted-Flanged Joints Using Contact Finite Element AnalysisTypical bolted-flanged joint and wedge model.A sequence of load steps depicting the loadinghistory of a joint and leakage development is shown inFig. 2. Contact area between the gasket and the flangeis lost as the internal pressure is increased. Thiscontact loss between the gasket and the flange is dueto flange rotation. The rotation is caused by the boltload, the hydrostatic end load and the fluid penetratingthe space where the contact is lost. In the first step,only the bolt load is applied. In this case, the gasketpressure (or contact pressure) is the largest near thebolt and decreases away from the bolt. Since the boltsencircle the gasket, the gasket pressure decreasestoward the inside of the pipe in the radial direction. Inthe circumferential direction, the gasket pressure is thegreatest close to the bolt and decreases toward thepoint between two bolts. In the second step, the loss ofcontact area has allowed fluid to penetrate. Thisprocess continues until the contact area recedestoward the outer edge of the gasket; at the point wherecontact is lost, leakage occurs.Some attempts to address this problem have beenreported in the literature. In Ref. [6], a semi-empiricalapproach was used to study the loss of contact. Asingle bolt plastic model, consisting of two circularplastic washers clamped by a bolt, was used tomeasure the loss of contact between the two plasticplates using potentiometric gauges. After loading, theremaining contact area was determined from theinterfacial pattern (i.e., Newton rings) of lightreflected from the separated surfaces. This result wasused in an axisymmetric finite element model of thesingle bolt system to establish the stress distribution(a) Bolt load onlyFig. 2(b) Loading(c) LeakageContact area at three load increments.near the bolt. This was then extended to study the boltspacing in a flanged-joint connection model. Effect ofthe pipe/hub, gasket, or internal pressure was notincluded in the model. Later, the same researchers [7]revisited, and extended their model to include effectsof pipe/hub and internal pressure using a dimensionalanalysis. Nishioka et al. [8, 9] used finite elementanalysis to investigate the loss of contact in aflanged-joint. They formulated the problem asdescribed above; however, due to limits on availablecomputational techniques at the time, they were onlyable to use an iterative procedure to determine the lossof contact. A constant strain triangle axisymmetricelement was used to model the flange and gasket.Also, it was assumed that the gasket yielded when thenormal stress reached the gasket yield stress. Theauthors investigated the effect of hub taper and thenumber of bolts on the gasket contact stresses. Sawa etal. [10] investigated the contact stresses analyticallyusing an axisymmetric elasticity formulation andconducted experimental analysis of leakage.The problem of leakage is further complicatedwhen the gasket material is loaded past its elastic limitpoint, so that it fills up the irregularities on the flangeface. Also, as the rotation increases, the bolt load isrelaxed; the relaxation is assumed negligible since amechanic typically retightens the bolts in order tomaintain a uniform bolt load over the life of the joint.In this paper, we study the evolution of leakageusing detailed contact finite element analysis. Theleakage analysis results compared well values obtained
137Analysis of Leakage in Bolted-Flanged Joints Using Contact Finite Element Analysisusing contact conditions specified by the ASME Boilerand Pressure Vessel Code, Sections VIII, Division 1(referred to as the ASME code hereafter) [11]. Thepaper is organized as follows: Section 2 gives adescription of the flange; Section 3 gives a descriptionof the loading; Section 4 provides a discussion of thefinite element model; Section 5 presents results anddiscussions; finally, Sections gives the conclusions.2. Flange DescriptionThe flange geometry and dimensions used in theanalysis were extracted from Ref. [9] and are shown inFig. 3. The characteristics of the gasket and number ofbolts are also from Ref. [9], all of which aresummarized in Table 1. The flange is a raised faceflange typically used in high pressure applications.The flange face nearest the bolt holes is raised 3 mm,which allows rotation of the flange. The flange isconstructed of steel with Young’s modulus of 200GPa and Poisson’s ratio of 0.3. The ASME codeassumes flange failure when the material yields. Whenthe stresses in the flange exceed the yield point of theflange material, the flexibility increases and thelikelihood of leakage also increases. The gasket isfabricated of mild steel and is allowed to be stressedbeyond its yield point so as to fill any imperfectionson the surface of the flange face. The stress-straindiagram of the gasket is assumed to be trilinear asshown in Fig. 4 [12]. This assumption requiresmaterial nonlinearity in the contact analysis.3. Flange LoadingThe loading is depicted in Fig. 5. As explainedabove, there are two loading steps: (1) the gasketseating step in which only the bolt load is applied, (2)the operating step in which both bolt load and internalpressure are resisted by the flange. The internalpressure is determined from the fluid containmentrequirements; the bolt load is computed based ongasket properties and internal pressure to maintain asealed joint.Fig. 3Flange geometry and dimensions.Stress (MPa)Epl 2 GPaEel 2 GPaStrain (%)Fig. 4Table 1Gasket stress-strain diagram.Bolt and gasket characteristics.CharacteristicNominal flange size (mm)Gasket material typeGasket width (mm)Inside diameter of the gasket (mm)Effective gasket width (mm)Gasket factor mGasket yield factor, y (Pa)Number of boltsSize of boltsValue300Soft flat mild steel153156.95.5124,10016M48The initial gasket pre-stress is provided by thepre-load in the bolts during the gasket seating loadstep. In this state, the gasket deforms filling theirregularities on the flange face, insuring full contactover the entire surface. The internal pressure is thenapplied during the operating condition and the gasket
138Analysis of Leakage in Bolted-Flanged Joints Using Contact Finite Element AnalysisInternal pressure 9.81 PaEnd pressure 16.38 PaBolt load 18.87 Panumerical analysis are taken from the ASME code andare shown in Table 1. These gasket parameters weredetermined experimentally and from industrialexperience as noted in the ASME code.The bolt load required to prevent leakage is given inthe ASME code for the gasket seating, Wm2 andoperating, Wm1 conditions. The seating bolt load, Wm2,is given in Eq. (1):Wm2 goπGy(1)where, go is the pipe thickness and G (diameter) is thelocation of the gasket stress force resultant and isdefined by the ASME code for various types of gasketsand flange face geometries. For the flange investigatedhere, G is the mean diameter of the gasket.The operating bolt load Wm1 is given in Eq. (2):Wm1 pB2/4 p(G2 - B2)/4 2πbGmp(2)where, p is the internal pressure, B is the pipe borediameter, and b is the effective gasket width, whichfor the flange investigated here is defined by theASME code as half the gasket width. That is, fluidpenetration is assumed to occur up to the middle ofthe gasket. Also, the diameter of the gasket stressresultant, G, remains unchanged after pressurization.The values for G and b are not theoretically exact;however, they are simple to calculate and aresufficiently accurate for practical purposes. The factorof 2 in the last term of Eq. (2) is an additional safetyfactor.The bolting is proportioned using Wm1 and Wm2. Thefollowing criterion is used to determine the minimumFig. 5Axisymmetric finite element mesh.pre-stress decreases. The ASME code specifies twodistinct loading conditions for analysis, based on twogasket parameters: the yield factor, y, defined as theminimum gasket stress that causes the gasket materialto conform to the flange face irregularities, and thegasket factor, m, defined as the ratio of the minimumgasket stress needed to hold a seal under internalpressure to the internal pressure. These factors dependon the material properties of the gasket and its sealingperformance. Values of these parameters used in thisrequired bolt area to prevent leakage:(3)Am max (Wm1/Sb, Wm2/Sa)where, Sa is the allowable bolt stress at ambienttemperature and Sb is the allowable bolt stress atdesign temperature. These allowable stresses can befound in the ASME code for different materials.The ASME code specifies the bolt load, W, to bethe average of the computed minimum, Am, and theactual bolt area, Ab, times the allowable stress Sa.W ½(Ab Am)Sa(4)The reason for the lower bolt load requirement is
Analysis of Leakage in Bolted-Flanged Joints Using Contact Finite Element Analysis139that in some cases the actual bolt area is much higherthan the theoretical minimum. This is a compromisebetween economy and safety. However, when theASME code recommends an additional safety factorfor assembly abuse, the flange may be designed usingthe actual bolt area, Am, as opposed to the lower valuespecified in Eq. (4). Once the minimum required boltarea is known, the bolting system can be designed: bolttype, number of bolts, bolt circle C, and bolt spacing.This formulation has been criticized over the years.The concern being that the calculated bolt load, W, istoo low to prevent leakage. However, the primarycontributing factor to leakage is joint assembly wherebolt tightening is completed one bolt at a time. Theprocedure leads to elastic interaction between bolts.That is, after tightening the first bolt, subsequenttightening of the remaining bolts will affect thepre-loads in the previously tightened bolts;consequently, bolt pre-load decreases. Even undercontrolled conditions in the laboratory, attaining auniform pre-load in all the bolts remains a challenge[13]. A uniform pre-load produces a uniformcompression on the gasket along the entirecircumference of the joint. Bickford [13] states thatbolt elastic interaction is one of the reasons joints aregenerally overdesigned to function properly. The twomost successful ways to get a uniform pre-load in allthe bolts are: (1) applying the total torque in multipleequal increments and (2) simultaneously tightening allthe bolts. As many as 10 increments are needed toestablish a uniform pre-load, in the field, it is usuallydone in one increment [13]. This is a serious problemand many industries have gone to simultaneouslytightening all bolts, e.g., heads in car engines.4.1 Gasket Contact4. Finite Element Modelbolt hole area: Er Ez 120 GPa, Eθ 0.12 MPa, νrz 0.3, νzθ νrθ 0, Grz 46.1 GPa, and Grθ Gzθ 0.06 MPa. These elasticity moduli and Poison’srations are specified for the bolt hole part of the mesh.The material properties for the gasket and the rest ofthe flange are shown in Table 1.We used PATRAN [14] to create the finite elementmesh depicted in Fig. 5, and ABAQUS [15] toperform the analysis. Second order axisymmetricelements, CAX8 are used throughout the mesh of theflange and gasket.Contact between the gasket and the flange face ismodeled using ISL22A elements on the gasket and asideline that is attached to the flange face. Also, sincethe gasket is not rigidly attached to the flange, it canbe blown out by the internal pressure (this can happenin cases where softer gaskets are used and flange facesare very smooth). To model this, we use a standardCoulomb friction model. We assume a coefficient ofstatic friction of 0.8, a very rough surface.4.2 Bolt HolesThe flange material is not homogeneous because ofthe presence of the bolt holes, the shaded area in Fig.5. This is handled by smearing the material propertiesused in the bolt hole area of the mesh. That is, usingmaterial properties corresponding to a weaker materialin the bolt hole area. Guidelines for determiningeffective material properties for perforated plates canbe found in the ASME code. For the model presentedhere, the effective material properties are calculatedusing an elasticity moduli reduction factor. This factoris equal to one minus the ratio of the volume of thebolt holes to the volume swept by the bolt diameteralong the entire circumference of the flange along thebolt circle diameter. Hence, the reduction factor is 0.6.The effective in-plane moduli of elasticity areobtained by multiplying the reduction factor times theflange modulus. The in-plane Poison’s ration is leftunchanged. The modulus in the hoop direction shouldbe very small and the hoop Poison’s ration should bezero. The effective shear modulus is computed fromits respective modulus of elasticity and Poison’s ratio.These lead to the following material properties for the
Analysis of Leakage in Bolted-Flanged Joints Using Contact Finite Element Analysis4.3 Boundary ConditionsWe specify axisymmetric boundary conditions onthe symmetric plane of the gasket. That is, the axialdisplacement in the middle of the gasket is zero (Fig. 5).4.4 Bolt LoadThe bolt load computed using Eq. (4) is smearedover the bolt hole upper surface as a normal pressure,as shown in Fig. 5. This is the load applied at thebeginning of the analysis, the seating condition. In thiscase, there should be no contact loss during theloading and the reacting gasket pressure should belarger than the minimum effective seating pressure, y.4.5 Internal PressureThe internal pressure loading is divided into threeloads: (1) the internal pressure, which acts on theinternal surface of the vessel; (2) the hydrostatic endload, which is the membrane stress acting far from thejoint in the pipe due to the internal pressure and iscomputed using the first term of Eq. (2); (3) thepenetrating pressure as the contact between the flangeface and the gasket is lost. The PPENn sub-option ofthe distributed load option is used to simulate pressurepenetration between surfaces in contact. This fluidpressure will penetrate into the mating surfaceinterface until some area of the surfaces is reachedwhere the contact area pressure between the abuttingsurfaces exceeds the fluid pressure, cutting off furtherpenetration. The pressure penetration loads start fromthe inside of the vessel, left side in Fig. 5, andpenetrate between the surfaces continuously from thisside. The pressure penetration path can be specified inABAQUS. The pressure penetration option inABAQUS is only supported in plane stress andaxisymmetric elements, not 3-D, which is the reasonwhy we solved the problem using an axisymmetricmodel.analyses. The nonlinearities in the problem are due tothe contact conditions and the gasket material inelasticbehavior. We use an automatic time increment sizecontrol because this approach is usually more efficientthan a user incrementation control.Fig. 6 shows the results for the seating condition;the gasket contact stress and the deformedconfiguration after the bolt load is applied, which isdone in the first load step over nine load increments.This bolt load must be sufficient to deform the gasketinto the flange face irregularities so as to closepotential leak paths. The ASME code specifies aminimum seating gasket contact stress y, which isplotted as 124 MPa in Fig. 6. The average of theABAQUS results is 102 MPa as shown in Fig. 6. Notethat the average of the ABAQUS results is lower thany; however, approximately one third of the surfacearea is loaded past this point; i.e., the area that remainsin contact throughout the loading history.Fig. 7 shows the deformed configuration after theinternal pressure is applied, operation condition. Inthis loading step, the gasket and flange begin toseparate and fluid begins to penetrate, which starts atincrement 7, which is shown in Fig. 8. At the end ofthe step, increment 9, the contact is lost up to themiddle part of the third element along the pressurepenetration path. This is depicted in Fig. 7, thedeformed configuration near the gasket, and also inthe contact pressure plot in Fig. 8.y 124 MPa (ASME code)ABAQUS resultsAverage ABAQUS results 102 MPaNormal stress on gasket face (MPa)1405. Results and DiscussionsLength along gasket face (mm)All analyses are performed as large displacementFig. 6Gasket seating contact stress, step 1, increment 9.
141Analysis of Leakage in Bolted-Flanged Joints Using Contact Finite Element Analysismp 53.9 MPa (ASME code)ABAQUS results, 9 incrementsAverage ABAQUS results 75.0 MPaNormal stress on gasket face (MPa)Internal pressure, p 9.8 MPaIncrement 1Pressure has penetrated upto this point for increment 9Increment 9Length alon
analyzed using a contact condition based on slide-line elements using ABAQUS, a commercial finite element code. Slide-line elements also take into account pressure penetration as contact that is lost between flange and gasket. Results are presented for a particular flange, a raised face flange sealed by a mild steel gasket. A comparison of the results from the gasket contact analysis and the .
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