Combined Effects of Tube Projection, Initial Tube-Tubesheet Clearance, and Tube Material Strain Hardening on Rolled Joint Strength

1

mwfERttop

ontme

i2R

J

Downloaded Fr

N. MerahDepartment of Mechanical Engineering,

King Fahd University of Petroleum & Minerals,Dhahran 31261, Saudi Arabiae-mail: [email protected]

A. Al-AboodiBuraydah College of Technology,

Buraidah, Al-Qassim 51432, Saudi Arabia

A. N. Shuaib

Y. Al-Nassar

Department of Mechanical Engineering,King Fahd University of Petroleum & Minerals,

Dhahran 31261, Saudi Arabia

S. S. Al-AniziDepartment of Consulting Services,

Saudi Arabian Oil Company,Dhahran 31311, Saudi Arabia

Combined Effects of TubeProjection, Initial Tube-TubesheetClearance, and Tube MaterialStrain Hardening on Rolled JointStrengthThe tube-to-tubesheet joint strength is measured in terms of interfacial pressure betweenthe tube’s outer surface and tubesheet bore. The strength of a rolled joint is influenced byseveral design parameters, including the type of tube and tubesheet materials, initial tubeprojection, and the initial radial clearance between the tube and tubesheet, among otherfactors. This paper uses finite element analysis (FEA) to evaluate the effect of severalparameters on the strength of rolled joints having large overtolerances, a situation thatapplies to used equipment. An axisymmetric finite element model based on the sleevediameter and rigid tube expanding roller concepts was used to analyze the effects of tubeprojection, initial tube-tubesheet clearance, and tube material strain-hardening propertyon the deformation behavior of the rolled tube and on the strength of the tube-tubesheetjoint. The FEA results show that for zero tube projection (flush) the initial clearanceeffect is dependent on the strain-hardening capability of the tube material. For lowstrain-hardening tube material the interfacial pressure remains constant well above theTubular Exchanger Manufacturer’s Association maximum overtolerance. A drastic reduc-tion in joint strength is observed at high values of radial clearances. The cut-off clear-ance (clearance at which the interfacial pressure starts to drop) is found to vary linearlywith the tube material hardening level, and the contact stress increases slightly formoderate strain-hardening tube materials but shows lower cut-off clearance levels. Fur-thermore, with flush tubes the maximum contact pressure occurs close to the secondaryface (at the end of rolling) while for joints with initial tube projection the contact pressureshows two maxima occurring near the primary and the secondary faces. This is attributedto the presence of two elbows in tube deformation near the primary and secondary faces.The average interfacial pressure increased with increasing projection length for all clear-ances. Tube material strain hardening enhances the interfacial pressure in a similarfashion for all initial tube projection lengths considered in the analysis.�DOI: 10.1115/1.3142387�

Keywords: tube-tubesheet, joint strength, projection, initial clearance, finite element

IntroductionDuring the rolling process the tube is projected from the pri-ary face of the tubesheet for many reasons, among them is toeld the edge of the tubesheet to the tube and to prevent the tube

rom shortening inside the tubesheet during expansion. Tubularxchanger Manufacturer’s Association �TEMA� �1� specifies inCB-7.513 that tubes shall be flush with or extend by no more

han one-half of a tube diameter beyond the face of eachubesheet. Yokell �2� suggested projecting the tube from the sec-ndary face of the tubesheet rather than the front to eliminate aotential source of corrosion and fatigue failure.

Simulation of rolling expansion process coupled with high levelf initial tube-tubesheet clearances and tube projection by the fi-ite element �FE� method is associated with a number of difficul-ies such as roller kinematics and the absence of loading axisym-

etry. In fact, the mechanical rolling process is actually anxample of periodical symmetry with respect to the load applica-

Contributed by the Pressure Vessel and Piping Division of ASME for publicationn the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received February 19,008; final manuscript received March 3, 2009; published online July 24, 2009.

ournal of Pressure Vessel Technology Copyright © 20

om: http://asmedigitalcollection.asme.org/ on 05/12/2014 Terms of Use: ht

tion. A number of researchers have shown that the complexity ofthe tube-to-tubesheet roller expansion can be simplified by reduc-ing it to an axisymmetric quasistatic problem. Aufaure �3� em-ployed this approach in which the roller profile is used to intro-duce a radial displacement to the inner surface of the tube.Displacements are applied in steps up to required expansion thenthe load is released such that the tube-to-tubesheet contact ensuresthe strength of the connection joint after transmitting a large radialstress to tube’s outer surface. Updike et al. �4� showed that theeffect of the mechanical roller expansion process can be ad-equately simulated with a two-dimensional axisymmetric math-ematical model. Subsequently, other researchers �5–10� haveadapted the use of axisymmetric FE model to simulate roller ex-pansion. Furthermore, Williams �5� showed that there was no ad-ditional gain in accuracy of predicting the residual stressesthrough the use of a three-dimensional finite element model.

Existing finite element analyses that deal with clearance effectson joint strength have mainly addressed hydraulic expansion oftubes into tubesheets. Allam et al. �6,9� and Merah et al. �7� usedFE to study the effect of initial clearance and material strain hard-ening on contact stress for hydraulic tube-to-tubesheet expansion.They found that the contact pressure decreases as the initial radial

OCTOBER 2009, Vol. 131 / 051201-109 by ASME

tp://asme.org/terms

iwsttv�

htssr

2

jjsepjertaum7iwmtTt1p

estmTast�m

atFs

Fi

0

Downloaded Fr

ed the effect of clearance, material strain hardening, and percentall reduction on rolled tube-tubesheet joint strength. They

howed that for each amount of percent wall reduction and type ofube material there exists a critical clearance value below whichhe joint strength is not affected. Their numerical results werealidated by the experimental results reported by Shuaib et al.10�.

The present paper presents results on the combined effects ofigh clearances, material strain hardening, and tube projection onhe deformation behavior of roller expanded tube and on the re-ulting contact pressure. The study was performed using an axi-ymmetric finite element model based on the sleeve diameter andigid roller concepts to simulate the rolled overexpanded joints.

Finite Element ModelFigure 1 shows a schematic representation of the tube-tubesheet

oint considered in the present study. To include ligament effect onoint strength, the equivalent sleeve diameter has been used in thistudy as suggested by a number of researchers �5–10�. Thequivalent sleeve is a single hole model that will produce contactressure, stress distribution, or deflection, depending on the ob-ective of the study, around the hole that is equivalent to the av-rage of those around the test hole on the real tubesheet configu-ation. Since this study concerns the same basic configuration ofhe stabilizer feed/bottom exchanger used in the work of Merah etl. �7� and Shuaib et al. �10�, the sleeve dimensions will remainnchanged. The geometry and dimensions of the axisymmetricodel are illustrated in Fig. 2. The tube inner and outer radii are

.425 mm and 9.525 mm, respectively, and the tubesheet bore’snner and outer radii are 9.525+c mm and 36 mm, respectively,here c is the radial clearance, which will be varied here from 0m to 0.5 mm to cover the range of clearance levels under inves-

igation. It should be mentioned that for this tube dimension theEMA allowable radial clearance is about 0.16 mm. The initial

ube projection beyond the primary face is varied between 0 and/2 the tube diameter �about 10 mm� to evaluate the effect of tuberojection.

The tube and tubesheet areas are meshed using the 2D quadraticlement defined by eight nodes having two degrees of freedom, ashown in Fig. 3. Because of the expected large deflections due tohe large overtolerances �clearances� used in this study the geo-

etric nonlinearities are included in the model. CONTA172 andARGE169 elements �11� are used to represent the 2D contactingnd deformable surfaces, respectively. These elements have theame geometric characteristics as the solid element face to whichhey are connected. Contact occurs when the elementCONTA172� surface penetrates one of the target segment ele-ents �TARGE169� on a specified target surface.The tube and tubesheet were constrained from translation in the

xial direction on the primary side of the tubesheet. The exactube expanding roller profile is represented by a rigid body line inig. 2. Loading during the rolling process is performed in three

ig. 1 Schematic representation of tube-tubesheet joint withnitial tube projection

teps. The first step displaces the roller radially outward in small

51201-2 / Vol. 131, OCTOBER 2009

om: http://asmedigitalcollection.asme.org/ on 05/12/2014 Terms of Use: ht

increments until contact of the tube with the tubesheet is estab-lished. The targeted percent wall reduction in the tube wall thick-ness is reached by performing 50 substeps in the second loadingstep. The third step simulates the retraction of the roller afterachieving the required tube wall thickness reduction. The ex-panded length of the tube, which is equal to the roller lengthshown in Fig. 2, was 47.25 mm �1.872 in.�; this represents about75% of the tubesheet thickness. The total radial displacement ofthe roller was obtained from the values of the required percentwall reduction %WR, tube thickness t, and initial clearance cusing the following equation:

Fig. 2 FE model geometry and dimensions in millimeters

Fig. 3 Meshed axisymmetric model

Transactions of the ASME

tp://asme.org/terms

Trt

rrat

�psteat

J

Downloaded Fr

ur = �%WRt

100� + c �1�

his radial displacement of the roller is used by industry duringoller expanding tube-to-tubesheet joints and the process is calledhe interference fit method.

The tube and tubesheet material elastic-plastic behavior is rep-esented by bilinear curves. Each of the tube and tubesheet mate-ial has a yield stress of 248 MPa, an elastic modulus of 207 GPa,nd Poisson’s ratio of 0.3. These properties were specified for theube and tubesheet materials in the finite element analysis.

Because of expected large plastic strains, the bilinear isotropicBISO� hardening option was used in the model. The curve in thelastic region was approximated by a linear relationship. Thelope of the approximated line �or lines� in the plastic region ofhe true stress-strain diagram defines the tangent modulus. Anlastic-perfectly-plastic material has a zero tangent modulus. Thepproximate value of the tangential modulus of plasticity Ett for

Fig. 4 Radial deformation profiles of the inin a joint with zero clearance

he tube was 733 MPa. However, to investigate the effect of tube

ournal of Pressure Vessel Technology

om: http://asmedigitalcollection.asme.org/ on 05/12/2014 Terms of Use: ht

and tubesheet material strain hardening on contact stresses, Ettvalues ranging from 0 GPa to 1.2 GPa are considered.

3 Effect of Clearance and Tube Projection on TubeDeformation

To evaluate the effect of projection on the strength of the rolledjoint, tube projection values ranging between 0 mm and 10 mmwere used in the investigation. These tube projection values fallwithin and beyond those specified by TEMA. The effect of vary-ing the radial clearance values between 0 mm and 0.5 mm and theeffect of varying the tube material strain-hardening parameter,represented by the tangent modulus Ett between 0 GPa and 1.2GPa, were also studied. The combined effects of projection, tan-gent modulus, and clearance on the tube deformation behavior andthe joint strength represented by the average contact stress arediscussed in the following.

Figure 4 shows the distributions of the residual radial displace-

r and outer surfaces of the tube expanded

ment of the inner and outer surfaces of the tube, after unloading

OCTOBER 2009, Vol. 131 / 051201-3

tp://asme.org/terms

thETtad4i

ofbscrqldaeetmfsl

m

0

Downloaded Fr

he expanding roller, along the expanded length of the tube thatas a tangential modulus of 800 MPa, which is a typical value oftt for steel tubes used in the stabilizer feed/bottom exchanger.he residual radial deflection of the inner and outer surfaces of the

ube in Fig. 4�a� is for a joint with flush tube �i.e., zero projection�nd with zero tube-tubesheet clearance, whereas the residual ra-ial deflection of the inner and outer surfaces of the tube in Fig.�b� is for a joint with a tube projection of 2 mm and with zeronitial tube-tubesheet clearance.

Figure 4�a� shows that for zero tube projection the deformationf the inner tube surface remains quasiuniform at about 0.07 mmrom the primary face of the tube until the transition zone �areaetween expanded and unexpanded tubes on the secondary faceide of the tubesheet�, where the inner surface deformation in-reases rapidly to a peak value of 0.097 mm, before it dropsapidly to 0.01 mm. The outer tube surface, however, exhibits auasiuniform deformation of about 0.055 mm along the deformedength of the tube until the transition zone where the deformationecays toward zero hence after; the outer surface does not shown abrupt change in geometry like the inner surface. The differ-nce in deformation between the inner and outer surfaces of thexpanded tube is what creates the residual radial �contact� stress athe interface between the tube and tubesheet. For the case of 2

m tube projection and zero initial clearance, the inner tube sur-ace radial deformation profile in Fig. 4�b� shows two humps; amall one at the primary face, due to the presence of a projected

Fig. 5 Radial deformation profilestube expanded in a joint with 0.127 m

ength of the tube, and a large one in the transition zone. The

51201-4 / Vol. 131, OCTOBER 2009

om: http://asmedigitalcollection.asme.org/ on 05/12/2014 Terms of Use: ht

deformation profile of the outer tube surface inside the tubesheetis similar to that of joint with zero projection shown in Fig. 4�a�.

Figure 5�a� shows the radial deformation profiles of the innerand outer surfaces of the tube for a joint with flush tube and atypical TEMA clearance of 0.127 mm. It is noticed that, althoughthe radial deformation of the tube is higher for the joint with 0.02mm clearance compared with that with zero initial tube-tubesheetclearance, the shape of the deformation profile is similar to that ofthe zero initial tube-tubesheet clearance. Figure 5�b� shows thatwhen the initial clearance is increased to 0.127 mm, the size of thehump near the primary surface is insignificant even for an initialtube projection of 4 mm. The presence of the initial clearance mayhave reduced the constraint on the outer tube wall and has thusreduced the effect of projection.

4 Combined Effects of Tube Projection, Initial Clear-ance, and Strain Hardening on Joint Strength

The effects of initial clearance and tube material strain harden-ing on the contact pressure for the case of a joint with a flush tubeare depicted in Fig. 6. For elastic-perfectly-plastic material �Ett

=0 GPa�, the increase in clearance produces a slight decrease incontact stress until the clearance reaches a critical value of 0.34mm �about twice TEMA clearance limit, represented by the dottedline in the figure�. The contact stress experiences a sudden dropafter the critical clearance value. On the other hand, for strain-

the inner and outer surfaces of theclearance

of

hardening materials, the contact stress increases with the increase

Transactions of the ASME

tp://asme.org/terms

icede

spar

Tl

Ttslm

li

Ff

J

Downloaded Fr

n radial clearance. As explained by Al-Aboodi et al. �8� the in-rease in interfacial stress is attributed to tube material strain hard-ning resisting tubesheet material spring back. The sudden drop isue to insufficient wall reduction as has been demonstrated inarlier work by the same researchers �8�.

The value of the cut-off �critical� clearance at which the jointtrength experiences a sudden drop has been found to be inverselyroportional to Ett �8�. The relationship between critical clearancend tangent modulus can be expressed by the following empiricalelation:

ccr = − 0.05Ett + 0.34 �2�he contact stress corresponding to the cut-off clearance is also

inearly related to Ett:

�cr = 9.766Ett + 53.633 �3�

he increase in contact stress with the increase in Ett is attributedo the tube material strain hardening resisting tubesheet materialpring back. Smaller cut-off clearances at higher Ett are due toarge strain difference upon spring back of strain-hardening tube

aterial.The contact pressure distribution profile shown in Fig. 7 fol-

ows a pattern similar to that of the tube surface deflection profilesn Figs. 4 and 5, with that of the joint with a tube projection case

ig. 6 Contact stress versus clearance for flush tube and dif-erent Ett with WR=5%

Fig. 7 Contact stress „in pascals… distribution

ournal of Pressure Vessel Technology

om: http://asmedigitalcollection.asme.org/ on 05/12/2014 Terms of Use: ht

having two maxima peaks �Fig. 7�b��, which are located near theprimary face and in the transition zone, resulting in higher averageinterfacial pressure.

The combined effects of tube material strain hardening and tubeprojection length for a radial clearance of 0.127 mm and 5% WRare illustrated in Fig. 8. These results show that the tube projectionlength has a similar effect on the contact pressure for all Ett valuesconsidered in this study. Again higher tube strain hardening resultsin stronger joint for all investigated values of tube projection. Thefigure shows that this strength is not affected by tube projectionlengths higher than 3.5 mm �about the 1/8 in. value prescribed byTEMA for the joint geometry under investigation�. The contactstress increased with tube projection length and reached a maxi-mum value at a projection length of approximately 1/4 of the tubediameter for all investigated levels of Ett and clearance. This in-crease in interfacial pressure is caused by the hump of the contactstress profile arising from the additional transition zone near theprimary face of the joint; this produced higher average contactstresses.

The combined effects of radial clearance and tube projection onresidual contact stress of the joint under investigation can be de-duced from Fig. 9 where the tube having Ett=0.8 GPa has beensubjected to 5% wall reduction during roller expansion. For the

Fig. 8 Combined effects of tube material strain hardening, Ett,and the length of tube projection for a joint with a clearance of0.127 mm and 5% tube wall reduction

s for flush tube and tube initial projection

OCTOBER 2009, Vol. 131 / 051201-5

tp://asme.org/terms

ls0mscfsbw

5

alabtpTraphtc

Fl

0

Downloaded Fr

evels of radial clearance shown in the figure, the contact stresshows gradual increase within the initial tube projection range ofmm and 3.5 mm and then stays at the same level beyond the 3.5m projection level. Figure 9 also shows that contact stress ver-

us projection curves are crowded together in the 0.1–0.3 mmlearance range. However, for 0.4 mm clearance the contact stressor a flush tube falls from an average of 61 MPa, which corre-ponds to the 0.1–0.3 mm clearance range, to 42 MPa. This isecause this clearance level exceeds the critical value for the 5%all reduction.

ConclusionAn axisymmetric finite element model based on the sleeve di-

meter and rigid tube expanding roller concepts was used to ana-yze the effects of tube projection, initial tube-tubesheet clearance,nd tube material strain-hardening property on the deformationehavior of the rolled tube and on the strength of the tube-ubesheet joint. The results showed that the presence of initial tuberojection introduced a second transition zone at the primary face.his transition zone is less important at larger clearances. This has

esulted in enhancing the average contact stress between the tubend tubesheet. The enhancement of joint strength is limited to arojection length of 1/4 of the tube diameter. Higher tube strain-ardening material resulted in higher contact stress for all projec-ion lengths. The effect of tube projection is independent of initiallearance below the critical clearance value.

ig. 9 Combined effects of clearance and tube projectionength for a plastic tangent modulus of 0.8 GPa and 5% WR

51201-6 / Vol. 131, OCTOBER 2009

om: http://asmedigitalcollection.asme.org/ on 05/12/2014 Terms of Use: ht

AcknowledgmentThe authors thankfully acknowledge the support of the King

Fahd University of Petroleum and Minerals �KFUPM� and SaudiArabian Oil Company. The support of Buraydah College of Tech-nology provided to A. A. Al-Aboodi. is also acknowledged.

Nomenclaturec � initial radial clearance between tube and

tubesheetccr � critical clearanceE � modulus of elasticity

Ett � tube material tangent modulust � tube thickness

ur � radial displacementWR � tube thickness wall reduction percentage�cr � contact stress corresponding to critical

clearance

References�1� 1988, Standard of the Tubular Exchanger Manufacturer Association, 7th ed.,

TEMA, New York.�2� Yokell, S., 1992, “Expanded, and Welded-and-Expanded Tube-to-Tubesheet

Joints,” ASME J. Pressure Vessel Technol., 114, pp. 157–165.�3� Aufaure, M., 1987, “Analysis of Residual Stresses Due to Roll-Expansion

Process: Finite Element Computation and Validation by Experimental Tests,”Transaction of the Ninth International Conference of SMIRT, pp. 499–503.

�4� Updike, D. P., Kalnins, A., and Caldwell, S. M., 1992, “Residual Stresses inTransition Zone of Heat Exchanger Tubes,” ASME J. Pressure Vessel Tech-nol., 114, pp. 149–156.

�5� Williams, D. K., 1997, “Prediction of Residual Stresses in the MechanicallyExpanded 0.750 Diameter Steam Generator Tube Plugs—Part 2: 3-D Solu-tion,” PVP �Am. Soc. Mech. Eng.�, 354, pp. 17–28.

�6� Allam, M., and Bazergui, A., 2002, “Axial Strength of Tube-to-TubesheetJoints: Finite Element and Experimental Evaluations,” ASME J. Pressure Ves-sel Technol., 124, pp. 22–31.

�7� Merah, N., Al-Zayer, A., Shuaib, A., and Arif, A., 2003, “Finite ElementEvaluation of Clearance Effect on Tube-to-Tubesheet Joint Strength,” Int. J.Pressure Vessels Piping, 80, pp. 879–885.

�8� Al-Aboodi, A., Merah, N., Shuaib, A. R., Al-Nassar, Y., and Al-Anizi, S. S.,2008, “Modeling the Effects of Initial Tube-Tubesheet Clearance, Wall Reduc-tion and Material Strain Hardening on Rolled Joint Strength,” ASME J. Pres-sure Vessel Technol., 130, p. 041204.

�9� Allam, M., Chaaban, A., and Bazergui, A., 1998, “Estimation of ResidualStresses in Hydraulically Expanded Tube-to-Tubesheet Joints,” ASME J. Pres-sure Vessel Technol., 120, pp. 129–137.

�10� Shuaib, A. N., Merah, N., Khraisheh, M. K., Allam, I. M., and Al-Anizi, S. S.,2003, “Experimental Investigation of Heat Exchanger Tubesheet Hole En-largement,” ASME J. Pressure Vessel Technol., 125, pp. 19–25.

�11� Swanson Analysis System, Inc., 2004, ANSYS, Version 9.0, Program and HelpDocumentations.

Transactions of the ASME

tp://asme.org/terms