3D FEM of Welding Process Using Element Birth & Element Movement Techniques

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Ihab F. Z. FanousMem. ASME

e-mail: [email protected]

Maher Y. A. YounanMem. ASME

Professor of Mechanics and Design,e-mail: [email protected]

Mechanical Engineering Department,American University in Cairo,

Cairo, Egypt

Abdalla S. WifiProfessor

e-mail: [email protected] Design and Production Department,

Cairo University,Cairo, Egypt

3-D Finite Element Modeling ofthe Welding Process UsingElement Birth and ElementMovement TechniquesThe modeling and simulation of the welding process has been of main concern for dent fields of applications. Most of the modeling of such a problem has been mainly informs that may also include many sorts of approximation and assumptions. This is dlimitations in the computational facilities as the analysis of 3-D problems consumesof time. With the evolution of new finite element tools and fast computer systemanalysis of such problems is becoming in hand. In this research, a simulation owelding process with and without metal deposition is developed. A new techniqumetal deposition using element movement is introduced. It helps in performing fulanalysis in a shorter time than other previously developed techniques such as the ebirth. @DOI: 10.1115/1.1564070#

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IntroductionMany models for the welding simulation have been develop

in the past few years. Most of the models had to include soapproximations in order to avoid long computing time and gmetrical nonlinearity. Also, most of them were intended for spcial applications in which reducing the model from 3-D to 2-for example, could be a valid assumption. On the other hasome 3-D models were developed in which approximations wapplied to the material behavior at elevated temperatures,without including the metal deposition.

Nguyen, Ohta, Matsuoka, Suzuki and Maeda@1# have devel-oped an analytical procedure for evaluating the transient tempture profile during the welding process. They used Goldak’s@2#formulation of the double-ellipsoidal heat source and compathe results with an experiment that he conducted. They assuthat there is no heat loss neither through convection nor radiafrom the surfaces of the plate, which lead to some discrepanctemperature predictions.

To calculate the residual stresses, Ueda and Yuan@3# and Mo-chizuki and Hattori@4# used the inherent strain method. It is bason the assumption that the inherent strain of a complicated westructure can be approximated by another of a similar simstructure. The inherent strain is affected by other parametersas the material of the base metal, the difference between theterial of the base metal and that of the filler, the welding speed,amount of heat input, etc. Hence, to use the inherent strain tnique, a database of the profile for different parameters shouldeveloped. However, for a complicated structure, the use of inent strain method becomes inaccurate.

Dong @5# has developed a model utilizing the element bitechnique to simulate the metal deposition that is valid incases with no thermal analysis of the sudden large temperavariation. This model is a combined two 2-D model with a smallowable variation in the results along the thickness. This conceliminates the effect of the heat transfer through the thicknesthe plate, which is of great effect in case of the thick plate weing. The technique used for developing a cross-sectional m

Contributed by the Pressure Vessels and Piping Division and presented aPressure Vessels and Piping Conference, Vancouver, BC, Canada, August 4–8,of THE AMERICAN SOCIETY OFMECHANICAL ENGINEERS. Manuscript received bythe PVP Division April 26, 2002; revised manuscript received February 5, 20Associate Editor: S. Y. Zamrik.

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applies only for a straightline welding. However, Dong’s tecnique could give a general overview of the residual stresses duwelding.

Hibbit and Marcal@6# have performed an advanced modelinprocedure for a complete 3-D simualtion of the welding proceThe loading of the welded structure due to operation conditiotemperature dependent material properties and phase transfotion were accounted for in their model.

Friedman @7# developed a comprehensive two-dimensionanalysis. Noting that the temperature profile does not vary wtime but moves at constant speed along the welding line, the plem size was reduced so as to evaluate the temperature profilesection perpendicular to the welding line.

Detailed analyses for 2-D and 3-D welding using the ADINsoftware were shown by Wilkening and Snow@8#. They consid-ered most of the non-linear aspects of the analysis includtemperature-dependent material properties and metal deposThe element birth technique was used to simulate the metal dsition. The moving heat source was modeled using a time cufor nodal heat flux.

In the present work, a new technique of element movemendeveloped for full 3-D simulation of the welding process. Tstandard commercial code ABAQUS is used to model this prlem as it has been used extensively in such a highly nonlinproblem in previous researches. In the first model considerethis research, the dimensions and thermal load values are acqfrom the research done by Friedman@7# for comparison and veri-fication. In this case, simple butt welding of two coplanar plawithout considering metal deposition is simulated. In the othtwo models that are considered in this research, larger thickneare assumed to include the effect of adding filler material inweld pool between the plates.

Finite Element ModelsIn developing a general purpose model for the welding proce

it is important to consider the moving heat source, heat lotemperature-dependent material properties and metal deposA moving heat source is modeled by setting a heat flux distrition that varies with time applied to the top surface of the wepool zone. Using ABAQUS, it is simulated by developing a usdefined subroutine to which time and position of interestpassed as parameters and returns the heat flux accordingly. Slarly, another subroutine is developed to simulate the heat

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from the top surface of the body. These subroutines are verifie‘‘Model 1’’ which simulates the welding process of two platewithout considering metal deposition, and compares to the resof Friedman@7#. Also, the material properties are entered to tmodel for different temperature values as described later inpaper. The verified subroutines of the heat load and heat lossmaterial data are then used to simulate another welding prothat includes the addition of filler material to the base plate. Itially, ‘‘Model 2’’ is developed to simulate the process utilizinthe element birth technique to simulate the metal deposition asbeen used in previous researches. This model shall be usedreference for verification of ‘‘Model 3’’ utilizing the elemenmovement technique that is developed in this research.

Verification Model „Model 1…. The model simulates basiarc welding of two coplanar plates along the parting line as illtrated in Fig. 1. The model is developed similar to that of@7# so asto be able to verify the subroutine of the heat source and heatin comparing the thermal history, and the structural boundary cditions in comparing the residual stresses.

Each plate has a length of 100 mm (x direction!, width of 50mm (y direction! and height of 2.5 mm. The welding speed ismm/s. The electric input is 24 V and 30 A, and the arc efficienis assumed to be 90%. The process is modeled using oneupon which symmetry loading and boundary conditions areplied. Parametric meshing is used in order to easily trackresults along a certain predefined path in any direction.

The element used is an 8-noded brick element that can pera coupled displacement-temperature analysis. For thermal symtry, the heat flux passing across the surface of symmetry showFig. 2 is assumed to be zero, and, for structural symmetry,translation in they direction of the same surface is also zerBesides, for structural stability of the model, fixture point 1constrained in thex and z directions, and fixture point 2 is constrained in thez direction.

The moving heat load is applied as distributed heat flux totop surface of the model, Fig. 3. The region within which the his applied has a circular shape assuming the heat source is apperpendicularly to the plate without any inclination. A user suroutine named DFLUX is developed in@9# using the FORTRANlanguage and included in the model to calculate the heat fluxcertain time and location within the surface of elements upwhich the load is applied according to Eq.~1!.

q~r !53Q

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Fig. 1 The diagram of the welding process of case 1

Fig. 2 General boundary conditions

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The total heat inputQ is evaluated according to the type of hesource. For example, in electric arc welding

Q5hVI (2)

This distribution, according to@7#, represents 95% of the total heaQ when applied within a circle with radiusr b . The distancer inEq. ~1! shown in Fig. 4 is the distance from the center point of theat source to the point for which the heat flux is being calculaand is given by

r 5A~x2xh!21y2 (3)

where

xh5~ t2t0!v (4)

The value oft0 is the time taken for the center point of the heatreach the first node along the welding line that has a value of zin Model 1. This way, as the time increases,xh increases simulat-ing the motion of the circle of the heat load zone as shown in F3. Therefore, when the value ofr is less than or equal tor b , theheat flux is calculated according to~1!. Otherwise, the heat load iset to zero.r b is set to 5 mm according to@7#.

The thermal boundary conditions include the radiation and cvection to the environment from all sides of the welded plaexcept the symmetry surface and the area upon which the heapplied. For all sides of the plate that lose heat, the heat loscalculated by

q5hconvection~Ti2Ta!1«emsbol~Ti42Ta

4! (5)

The connection coefficient is 8 W/m2°C, which is assumed to beconstant as it depends primarily on the ambient temperature,the emissivity is 0.5.

Another subroutine called FILM is developed in@9# in conjunc-tion with DFLUX to account for the variation of the heat loscoefficients with time for the top surface. In this code, the locatunder consideration is checked if it lies within the circle of appcation of the load using Eqs.~3! and~4!, and, if it is true, there isno heat loss. Otherwise, heat is lost by the same coefficients aother sides from the area of the top surface other than that of

Fig. 3 The moving heat source of Model 1

Fig. 4 Zones of heat load and heat loss

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heat load. The coefficient calculated in the FILM subroutine icombination of both the convection and radiation coefficiewhich is given by

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q5htotal~Ti2Ta! (7)

Element Birth Technique „Model 2…. To broaden the appli-cation of the modeling procedure, the problem of Model 2 simlates arc welding of two coplanar plates with the addition ofiller material between them. By developing several trial modeit was found that a length of 100 mm (x direction!, a width of 50mm (y direction! and a thickness of 5 mm (z direction! are ad-equate for a single pass welding process. The welding speeassumed to be 1 mm/s.

The metal deposition of the filler material is considered usthe element birth technique. This technique is based on deacting and reactivating the elements of the weld pool as the weldprogresses. The meshing of the base plate and the weld poolclear parting surface between them. That way, when the elemof the weld pool are deactivated, the remaining elements wohave the initial shape of the base plate with its modified edgeforms the cavity of the weld pool. The meshing in the weld poofine enough to account for the high temperature gradient calctions and that in the base plate has similar meshing characterdescribed in Model 1 with the elements near the fusion surfhaving a size close to the ones in the weld pool.

The elements defining the weld pool are grouped to form slicHaving the elements of the weld pool initially deactivated, eveslice is then reactivated as the heat sources moves along theing line as shown in Fig. 5. The nodes that appear due toreactivation of the elements have an initial temperature aboveliquidous temperature.

The structural boundary conditions described in Model 1not sufficient for the base plate since it is free to deform in thydirection. The welding process is assumed to be in a large stture that can allow for slight movement of the far surface in F6, but with no rotation about any axis which is simulatedforcing the displacement of all the nodes on the far surface tothe same. This is modeled by using a constraint equationcouples they component of the displacement of each two cosecutive nodes on the surface. Therefore, with reference to Fithe y displacement of node 1 is set to be equal to that of nodand that of node 2 is set to be equal node 3, etc...


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The heat source in this model is similar to that used in ModeHowever, it initially stays a while at the beginning of the weldinprocess for the filler material to start melting. Then the heat flstarts to gradually impose its effect as shown in Fig. 5. Note tthere is no heat load at the initial state. This effect is modeledusing the DFLUX and FILM subroutines as developed in Modehaving the initial timet0 greater than zero,

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At time zero,xh equals to2r b . This makes the heat source jusout of the model at the beginning of the analysis with the figroup of elements being active. As the heat source movesstarts to go out of the current active element slice, the next slicelements is activated, as illustrated in Fig. 5. The total heat inrate is 1300 W.

The analysis procedure is divided into several steps. In estep, a new group of elements is activated. This means that estep performs analysis over a time periodt i5xiv wherexi is thelength of the group of elements~along thex direction! to beactivated in that step. A step is added when all elements are avated to allow for heat loss only over a long period of time~40min! simulating cool down. Finally, an extra step is addedwhich the fixation of the far surface is released, as mentionbefore, to be able to check for the residual stresses at no loa

It is important to note that the automatically estimated timincrement in the analysis drops to a very small value due tovast difference in the temperatures of consecutive nodes inreactivated elements. This effect can be dramatic for small ement sizes of the weld pool at the fusion surface~the partingsurface!. In addition, the part of the heat passed to the base pis neglected in this model. Therefore, it is important to graduatransfer heat from the filler material to the base plate to smootthe contact between the two parts.

Element Movement Technique„Model 3…. The meshing inthis model is similar to that in Model 2. However, the elementsthe weld pool are separated from those of the base plate so abe free to move as shall be discussed in the next section. Pararic meshing is used in both parts in order to be able to hannodes along a certain path or on a certain plane within theparts. In order to impose the gradual heat transfer effect, theof the weld pool is shifted in thez direction a certain distancefrom the base plate as shown in Fig. 7. This way, the thermal

Fig. 6 General boundary conditions

Fig. 7 Gap clearance

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structural interaction between the two parts is made dependenthe distanced between them.

To avoid large skewing of the elements due to the moving osimulating metal deposition, the initial gap between the weld pand the base plate is set to be small compared to the elementin thez direction. The type of element used is the same as thathe previous models with structural and thermal degrees of frdom in order to perform coupled displacement-temperatanalysis.

Having the weld pool and the base plate parts separatedquired the introduction of gap thermal and structural interactbetween the two bodies. The gap links, named GAPUNITABAQUS, are used between the two parts to take care ofinteraction by joining adjacent nodes together. These linkstwo-noded elements and are modeled such that they allow hebe transmitted between nodes of the weld pool and the adjoinnodes of the base plate, which implies that the meshing ofadjoining surfaces must be the same in the horizontal and verdirections of the surfaces as illustrated in Fig. 7. The gap elemare assigned thermal conductivity, which is at the room tempeture. Its effective area which is the contact area that eachelement represents on the contact surfaces is shown in Fig. 8a).

To avoid heat to be transmitted from the weld pool to the baplate before any deposition, the thermal conductivity of the gelements are initially set to zero. However, since the base plaat room temperature and the weld pool is at the melting point,conductivity cannot be set to its maximum value just at the timecontact since there will be coincident points having temperatugreatly different. This may cause problems in the automatic incmenting process since a major parameter for calculating the tincrement is the maximum change in temperature per incremThis should not exceed a certain limit selected to be 200°C~largervalue of the temperature change limit may cause loss of accuand smaller value would lead to longer analysis time!. Therefore,the thermal conductivity of the gap elements gradually increafrom the initial value of zero at a certain gap clearance tomaximum value at zero clearance according to the values shin Fig. 8(b). This way, when the elements of the weld pool reathose of the base plate, the temperature of the two coincidnodes shall become approximately equal. This early interacaccounts for the heat lost from the molten metal to the base pwhile falling into the weld pool. Also, by increasing the valuethermal conductivity in the range before contact, the transferamount of heat can be increased and, thus, account for heat btransmitted from the heat source to the base plate directly. Thimportant in the model simulating arc welding where the heagenerated through the electric arc between the electrode~the fillermaterial! and the base plate. Also, in gas welding, there is soheat not subjected to the filler material and is applied directlythe base plate. However, it is necessary to keep the conductivizero clearance to be at a value similar to that of the base pmaterial so that the flow of heat across the gap element wouldequal to that through the material itself.

Due to the possible expansion of the base plate, elements o

Fig. 8 „a… The effective area, and „b… thermal conductivity ver-sus the gap clearance of the gap elements

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weld pool are allowed to penetrate the elements of the base p~a criteria know as over-closure in ABAQUS explained in@10#!when they are moved towards it.

When modeling the element movement, the nodes lying onsamey-z plane move together towards the base plate by applytranslational boundary condition equivalent to the initial gclearance. With reference to Fig. 9, the nodes that are yet to min the following steps are held in position in order not to alloany deformation in the remaining portion of the weld pool. In thcase, the elements formed by the nodes that moved towardsbase plate and the next group of nodes posses some strain. Tfore, the group of nodes that has just reached the base plate isin position until those of the next step follow them. This way, tstrain in the translated elements shall tend back to zero. Whensecond group of nodes is lowered, the first one is releasedeform freely without being affected with the strain previousgenerated in neighboring element. In order to reduce the stgenerated in the element, the nodes move only half of thedistance every step, which implies that the nodes reach theplate after two subsequent steps. The welding speed is the le


Fig. 9 The steps of the element movement technique

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of each element divided by the time of each step. When the noof the weld pool reach the base plate, a coupling equatioactivated between the coincident nodes of both parts to simuthe fusion process. These coupling equations force the defotion of the coincident nodes to be equal. Hence, the weld poolthe base plate act as one body at this point. A user subrouMPC is developed in@9# to activate the coupling between evegroup of nodes that come into contact at a specific time accorto the welding speed. In this subroutine, thex-coordinate of everygroup of nodes is checked if it is less than thex-coordinate of thecenter point of the heat source, and, if it is true, the couplequation is activated. Usually, the fusion at different pointstween the weld pool and the base plate depends on the peakperature and the time during which the coincident points staythe liquid state. However, this criterion is not included in tresearch and all coincident points on the contact surfaces arsumed to have full fusion because the model is designed to cfor the residual stresses.

The heat source has the same concept as that of Modelwhich the heat source must stay a while at the start of the weldprocess before it moves along the welding. However, when aping the DFLUX subroutine developed earlier, the value oft0 willbe different to match the deposition process. It is assumed thacenter point of the heat source should be at the first node ofwelding line just as the first group of nodes comes into con

Fig. 11 Zones of heat load and heat loss

Fig. 12 Temperature history

Table 1 Material properties versus temperature

Temperature (°C) 20 1550 1650 2000

Young’s modulus~GPa! 200 0.2 231025 231025

Poisson ratio 0.25 0.25 0.25 0.25Yield strength~MPa! 290 1 0.01 0.01Yield strength at strain 1.0~MPa! 314 1 0.01 0.01Thermal expansion (1/°C31026) 10 15 15 15Thermal conductivity (W/m.°C) 50 30 30 30Specific heat (J/kg.°C) 450 400 400 400Latent heat~J/kg! 260,000

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with the base plate. In other words, since the first group of noreaches the base plate in two consecutive steps, the valuet0shall be twice the time taken for each step, which is 2 s for themodel in hand. Figure 10 shows the motion of the heat load whcenter~the darkest point! reaches the first node of the weldingtime54 s.

Finally, the thermal heat loss is modeled such that heat isfrom all sides of the plate and the weld pool except those surfathat are in contact. Just as it is mentioned in the previous caseheat from the top surface is modeled using the previously deoped FILM subroutine with the value oft0 identical to that justcalculated for DFLUX. However, since the topmost elementsthe weld pool that are yet to be deposited are considered pathe top surface, they must not be considered in the heat lossTherefore, the FILM subroutine is slightly modified so that ements withx-coordinate larger than that of the center point of theat source must have a heat loss coefficient of zero. Figurshows the heat load and heat loss regions in Model 3 accordinthe modifications in the FILM subroutine.

The analysis steps in this case are similar to that of Modewith two extra steps added to the procedure in order to accounthe depositing groups of nodes, and that the deposition of egroup is done in two steps

Fig. 13 Stress distribution along the midsection

Fig. 14 Temperature history at the top and bottom surfaces ofModels 2 and 3

Table 2 Comparison of analysis steps

Elementbirth

Elementmovement

Min. time increment 0.000002872 0.00011No. of increments 1753 966No. of iterations 4758 3471Total analysis time ;48 h ;24 h



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Fig. 15 Comparison between the element birth and element movement techniques for „a… sx „longitudinal stress … and „b…sy „transverse stress … history at the monitoring points, „c… sx and „d… sy distribution along the midsection, „e… sx and „f …sy distribution along the welding line, and „g… and „h… along the fusion line

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Material Properties. The material used in Model 1 is InconeAlloy 600 that is used by Friedman@7#. The material propertiesused with metal deposition in Model 2 and Model 3 were acquifrom Brown @11# whose properties are shown in Table 1. Tlatent heat indicated is included by ABAQUS in the specific hvariation with temperature between the liquidous and solidlevels.

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Results and Discussion

Verification Study. Good agreement appeared betweenthermal and structural results of Model 1 and those of Friedm@7#. Figure 12 shows the temperature history at 3 monitorpoints indicated in Fig. 2 along the mid transverse line on theand bottom surface. Figure 13 shows the history of the varia

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of the longitudinal stress along the transverse direction (y direc-tion! along the top of the midsection.

Element Birth Versus Element Movement Technique. Theresults of the element movement technique~Model 3! had a veryclose match with those of the element birth~Model 2!. Figure 14shows a comparison of the temperature history at the monitopoint near the fusion surface shown in Fig. 6. The slight reducin the peak temperature predicted using the element movemedue to the gradual flow of heat from the weld pool to the baBesides, due to the difference in the node arrangement betwthe two techniques in having two separate bodies in Modeinstead of one in Model 2, there is a difference in the arrangemof the integration points representing similar nodes. This causdifference in the temperature of the monitoring points due tohigh temperature gradient. In addition, it can be observed thatemperature of the monitoring point at the top is lower than thathe bottom since the distance of the former from the welding lis larger than that of latter.

Table 2 shows a comparison between the two techniques inanalysis steps and timing. This illustrates the huge reduction intime spent to perform the simulation using the element movemtechnique.

Figure 15 illustrates a detailed comparison of the longitudi(sx) and transverse (sy) stresses between the two models. A veclose match in the history of the stress components at the mtoring point ~Fig. 6! is shown in Fig. 15(a) and (b). The midsection~Fig. 6! was selected for monitoring since it gives an oveview of the behavior of the whole welded structure. A very clomatch can be observed between the two techniques in the dbution of the residual stresses along the mid section’s topbottom paths as illustrated in Fig. 15(c) and (d). Finally, thewelding line, being the hottest part, and the fusion line, whergreat variation in the residual stress distribution is expectedoccur, were also selected for monitoring. The variation ofresidual stresses along these paths of Model 2 compared wellthose of Model 3 as shown in Fig. 15(e) – (h).

ConclusionIn the verification model, the results of the 3-D model simul

ing the welding process compared well with that of@7#. The sub-routines in that model can be used confidently to simulate mosthe moving heat source used in the welding processes. It cafurther developed to simulate inclined heat sources to covewider range of applications.

In comparing the element movement technique versus thement birth technique, it can be observed that the former showe

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Nomenclature

q(r ) 5 heat flux at distancer from center of heat source(W/m2)

Q 5 total heat input rate~W!r b 5 radius at which total heat input is 95% of actual

value ~m!hconvection5 convection coefficient (W/m2 °C)

«em 5 emissivitysbol 5 Stefan-Boltzman constant (5.66931028 W/m2K)

Ti 5 expected temperature for current increment~K!Ta 5 ambient temperature~K!t i 5 time of stepi (s)v 5 welding speed~m/s!

References@1# Nguyen, N. T., Ohta, A., Matsuoka, K., Suzuki, N., and Maeda, Y., 19

‘‘Analytical Solutions for Transient Temperature of Semi-Infinite Body Sujected to 3-D Moving Heat Sources,’’ Weld. J.~Miami!, Aug., pp. 265–274.

@2# Goldak, J., 1990, ‘‘Keynote Address: Modeling Thermal Stresses and Distions in Welds,’’ Recent trends in welding science and technology, ASM Innational.

@3# Ueda, Y., and Yuan, M. G., 1993, ‘‘Prediction of Residual Stresses in BWelded Plates Using Inherent Strains,’’ ASME J. Eng. Mater. Technol.,115,Oct., pp. 417–423;116, July 1994, pp. 285.

@4# Mochizuki, H., and Hattori, H., 1999, ‘‘Residual Stress Analysis by SimplifiInherent at Welded Pipe Junctures in a Pressure Vessel,’’ ASME J. PresVessel Technol.,121, Nov., pp. 353–357.

@5# Dong, P., 2001, ‘‘Residual Stress Analyses Multi-Pass Birth Weld: 3-D SpeShell versus Axisymmetric Models,’’ ASME J. Pressure Vessel Technol.,123,May, pp. 207–213.

@6# Hibbit, Hugh D., and Marcal, Pedro V., 1973, ‘‘A Numerical, ThermoMechanical Model for the Welding and Subsequent Loading of a FabricaStructure,’’ Comput. Struct.,3, pp. 1145–1174.

@7# Friedman, E., 1975, ‘‘Thermomechanical Analysis of the Welding Processing the Finite Element Method,’’ ASME J. Pressure Vessel Technol.,97, Aug.,pp. 206–213.

@8# Wilkening, W. W., and Snow, J. L., 1993, ‘‘Analysis of Welding-Induced Rsidual Stresses With The Adina System,’’ Comput. Struct.,47~4/5!, pp. 767–786.

@9# Fanous, I. F. Z., ‘‘3D Modeling of the Welding Process Using Finite Elments,’’ M.Sc. thesis, The American University in Cairo, February 2002.

@10# Hibbitt, Karlsson, and Sorensen, ‘‘ABAQUS/Standard User’s Manual,’’ 62001.

@11# Brown, S., and Song, H., 1992, ‘‘Finite Element Simulation of Welding LarStructures,’’ ASME J. Eng. Ind.,114, Nov., pp. 441–451.



3D FEM of Welding Process Using Element Birth & Element Movement Techniques

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