Welding Simulation of Ship Structures Using Coupled Shell and Sol

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Lehigh University

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Teses and Dissertations

1-1-2003

Welding simulation of ship structures usingcoupled shell and solid volume nite elements

Dongjin KimLehigh University

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Recommended CitationKim, Dongjin, "Welding simulation of ship structures using coupled shell and solid volume nite elements" (2003).Teses andDissertations. Paper 816.
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Dongjinof ShipUsingShell and

VolumeElements

2004


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Welding Simulation of Ship Structures Using Coupled Shelland Solid Volume Finite Elements

byDongjin Kim

A. ThesisPresented to the Graduate and Research Committee

ofLehigh Universityin Candidacy for the Degree of

Master of Science

inDepartment of Mechanical Engineering and Mechanics

Lehigh UniversityDecember, 2003


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Abstract

Table of Contents

12245

Chapter 1 - Introduction1.1 Introduction to Welding Distortion1.2 Introduction to Welding Heat Sources1.3 Introduction to Simulation of Welding1.4 Application of Research (Introduction to Research concerning ship hull

construction) 91.5 The objectives of present research 11

Chapter 2 -Comparison -between the coupled modelwith shell elementsand the 3D volume model of a fillet welded T-beam 12

2.1 Properties ofmaterial (AL-6XN) 122.1.1 Thermal properties 122.1.2 Mechanical properties 14

2.2 Model generation 162.3 Thermal Model (thermal source modeling) 19 -2.4 Mechanical Model 212.5 Thermal Results 232.6 Mechanical Results 292.7 Conclusion about Comparison of both models 43

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Chapter 3 - Comparison of coupled elements models with different boundaryconditions 45

3.1 Properties ofmaterial 453.2 Model generation 453.3 Thermal Model 463.4 Mechanical Model 463.5 Thermal Results 483.6 Mechanical Results 48

Chapter 4 - Welding simulation of a practical problem (the hull of ship) 664.1 Model generation 664.2 Thermal and Mechanical Model 674.3 Thermal Results 684.4 Mechanical Results 70

Chapter 5 - Conclusions 775.1 Future work 775.2 Conclusions 78

Appendix 79HEAT.DAT 79MECH1.DAT 83

Reference 87

Vita 89IV


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Abstract

The objective of this research is to develop an efficient approach to determine theglobal deformations in ship structures resulting from thermal effects from the weldingprocess by using coupled shell and solid finite elements. The finite element method hasemerged as one of the most attractive approaches for computing residual stresses inwelded joints, but its application to practical analysis and design problems has beenhampered by computational difficulties that occur due to the enormous computationalsize ofany practical problem. These difficulties arose primarily in situations with three-dimensional (3D) modeling of a welding process. Although two-dimensional (2D)modeling has been used widely in residual stress problems, current studies have shownthat 2D analysis cannot render accurate residual stresses in many specific weldingproblems. Therefore, it is most effective to use shell elements in conjunction with solidelements. In the zone close to the heat affected zone, 3D modeling is repeated. However,use of shell elements away from this region will decrease significantly the number ofelements in the welding model, reducing the computational size for the overall 3D model.This study investigates the temperature, distortion and residual stress in afillet welded T-joint, comparing those computed by the coupled elements of both volume and shellelements, with those computed by volume elements only. In addition, the displacements inwelded T-joints with different constraints were compared. The practical problem of awelded box beam used in ship hull design was simulated by using a coupled model ofshell and solid elements.

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Chapter 1 - Introduction

1.1 Introduction to welding distortionResidual deformations and stresses will be generated in a structure as a

consequence of the local plastic deformations introduced by the local temperature historyassociated with welding, Le., rapid heating and subsequent cooling.

K. Masubuchi discussed the various types of welding-induced distortion andresidual stresses. This research resulted in a number of empirical relations and focusedentirely on welding distortion that remains after the completion of the weld and ignoringthe intermediate states. [1]

In a general welding problem, residual stresses are produced by plastic strains dueto tremendous thermal gradients, by material dilation during solid phase transformations,and by plastic deformations caused by plastic strains and solid phase transformations. [2]Near the weld pool, the temperature change due to welding is extremely rapid and thetemperature distribution uneven. In the region of the weld, the molten metal supports noload and no strength of the solid, but high-temperature metal around the weld isdrastically reduced. As the temperature far from the weld is relatively low, the expansionof metal near the weld is constrained and forced into high compression. Regions far fromthe weld are forced into tension to balance the compressive stresses close to the weld.When the part c


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distortion, the part often contracts uniformly along the weld. (See Figure I) The secondis longitudinal shrinkage parallel to the weld line, and the final category is angulardistortion about the weld line. With thin-walled structures, buckling is also an importantproblem. [1]

----_ ...._--_ ........

10) TRAmVERSE SHRINKAGE

---------

Ie) ROTATIONAl OISTORTION

10) LOIHIITUDINAL BENDINGDISTORTION

(bl ANGULAR CHAt/GE

hI) LONGIT\JDINAL SHRINKAGE

(I ) BUCKLING DISTORTION

Figure 1 - Distortions in WeldingUntil recently, most researches of weld distortion relations were empirical

because the analytical solution of welding distortion was too difficult to be practical.While empirical relations based on experiments are useful for estimating distortion inparts similar to those used for deriving the relations, these solutions are available only forsimple geometries. [3] All experimental methods have at least two disadvantages. First,their application usually requires special equipment and personnel that are not usually

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associated with welding research. Second, residual stresses can most often be measured atdiscrete locations on a weld, usually close to the weld surface. A complete picture of theresidual stress distribution in a general weldment is practically impossible to obtain byexperimental techniques. [4]

1.2 Introduction to welding heat sourcesRosenthal had developed a solution for conduction from a moving heat source in

the late 1930s. This has been the most popular analytical method for calculating thethermal history of welds. [5] However, as these models assume a point source andtherefore infinite temperature at the source, the model breaks down close to the weldpool. One additional limitation of the Rosenthal solution, when applied to direct metaldeposition, is that it does not include any mass addition to the weld pool. [6]

To overcome most of these limitations, Pavelic et al [7] suggested a heat sourcemodeled with a Gaussian distribution of flux deposited on the surface of the workpiece in1969. With this model, the concentration of the heat source can be varied by changing aparameter called the concentration coefficient. Friedmen, Krutz, and Segerlind [8-9]developed a variation of Pavelic's model that is expressed in coordinates that move withthe heat source. While these models are a significant improvement over Rosenthal's

model, it has been suggested that heat should be distributed to the molten zone to reflectmore accurately the digging action of arc. These models do not account for the rapidtransfer of heat throughout the fusion zone. To better represent high power densitysources, a hemispherical Gaussian distribution was developed. Unfortunately, this modelwas still ill suited to deal with deep penetration welds that are not spherically symmetric.

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[5] To account for this problem, Goldak, Chakravarti, and Bibby [10] proposed anonaxisymmetric three-dimensional heat source model. This model accommodatesshallow welds, deep welds, symmetrical welds, and asymmetrical welds, all of whichlead to more accurate models of the welding process. Thermal models of weldingprocesses have also improved, taking into account parameters such as weld torch width,non-linearities due to variation of thermo-mechanical properties of material withtemperature, radiation heat transfer from the weld pool, temperature-dependentconvective heat transfer coefficients, and more. [2]

For the simulation of the arc welding process, a double ellipsoidal geometry of theheat source is used in this research. This approach is numerically more stable and moreaccurate than a point or line source, especially in the temperature range above 600C.

1.3 Introduction to simulation ofweldingInterest in developing adequate analytical models ofwelding processes dates from

the late 1930s and 1940s. [11-12] To be sure, from the perspective of continuummechanics, the welding process can be viewed as transient boundary value problem. Theconstitutive equations in this problem take into account the physics of heat transfer andthe mechanics of thermal dilatation, as well as the processes of change in materialmicrostructure and phase transformation. The boundary conditions model the weldingheat input, the surface heat losses, the mechanical restraints, and, most importantly, thecontact between the welded parts and the filler metal deposited. At a minimum, atemperature-dependent elastic-plastic material model should be incorporated. Practicalsolution of such a complex boundary value problem became possible only in the 1960s,

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with the computer implementation of powerful numerical techniques, among which thefinite element method emerged as the most powerful. [13]

The computational demands of fully 3D welding models are so prohibitive that allFE investigations of residual stresses in welds before the late 1980s were performed onsimplified two-dimensional (2D) models. In 2D models, only a plane perpendicular to thedirection of the weld is considered. The behavior out of plane can be taken as plane stress(assuming zero out-of-plane stresses), plane strain (assuming zero out-of-plane strains),generalized plane strain (assuming constant strain normal to the model plane), oraxisymmetric. [5] Argyris et. al. [14] computed the thermo-mechanical response using2D models in a staggered solution strategy to combine and integrate the thermal andmechanical computational steps. Rybicki et. al. [15] performed thermo-elasto-plasticanalysis on a 2D axisymmetric finite element model for a two-pass girth-butt welded pipeproblem, and verified the numerical results with the experimentally obtained temperaturehistory and residual stress distributions. Papaxoglu and Masubuchi [16] solved themultipass GMAW process problem by performing uncoupled 2D heat transfer and stressstrain analyses, incorporating the phase transformation strains.

Since investigators tried to avoid modeling in 3D, the computed residual stresseswere verified by comparison with experimental measurements. Certain discrepanciesbetween computed and experimentally measured residual stresses were reported. This ledto the belief that 2D models in certain situations are inadequate to quantify the residualstresses accurately in a welded joint. [4] 2D models, as mentioned above, have beenparticularly useful with their high efficiency and accuracy in determining the solution in

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the analysis plane and reduced computational requirements. However, for weldingpractices where tack welding or fixturing allow out-of-plane movement 2D analyses maynot be accurate. This seems to be particularly for distortion predictions. Furthermore,longitudinal heat transfer, instability aspects and end effects (Le. due to initiation andtermination of the heat source) cannot be realized in two dimensional formulations. [17]3D modeling of welds was first attempted by Tekriwal and Mazumder [18-19] and,independently, by Karlsson and Josefson. [20] Their analyses confirmed the 3D nature ofthe temperature and stress fields developed during welding, but at the same timedemonstrated the restrictions of the 3D calculations. The investigators were limited torelatively coarse FE meshes to accommodate the analysis in the computer facilitiesavailable to them. [4]

Most of the currently performed welding simulations, both 2D and 3D, are basedon small deformation theory and are limited to simpler structures and weld geometries orfocus only on the heat affected zone, ignoring the surrounding structure. [17]

Brown and Song [21] show that the interaction between the weld zone and thestructure can have a dramatic effect on the accumulated distortion in many cases, thecontribution of the structure dominates the state of distortion and stress, a state that ismuch different from the on e predicted by a simulation of the weld zone alone.

As a full three-dimensional model is computationally expensive and unnecessaryIn many temperature and stress calculations, Daniewicz [22] developed a hybrid(experimental-numerical) approach that the weld joints are represented by "weldelements" to simulate the shrinkage caused by welding, which is determined

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experimentally. This approach does not deliver the desired accuracy due to the difficultyin measuring weld shrinkage.

Michaleris et al developed a two-step numerical analysis technique for predictingwelding-induced distortion and assessing the structural integrity of large and complexstructures, that combines two-dimensional welding simulations with three-dimensionalstructural analysis in a decoupled approach. [3-23] First, a two-dimensional weldingsimulation is performed to determine the residual stress distribution. The model limited toa portion of the structure that represented the mechanical restraints that were used. Then athree dimensional structural (elastic) analysis performed using the stress distribution ofthe welding simulations as. loading to determine if the structure would buckle and thecorresponding mode and/or magnitude of deformation. The advantage of a decoupledapproach is computational simplicity and efficiency. Complex 3D welding simulationswere not performed. It should be pointed out that Michaleris' approach has the difficultyof applying the accurate weld load, obtained from 2D model. The difficulty is due to thedifferent mesh size, the limited region applied weld load to 3D model and the assumptionthat residual stress distributions are generated by imposing a strain as load. Although thismethod delivers reasonable results by using limited computer resources, a criticalbuckling load can be only predicted using decoupled 2D welding simulation and 3Deigenvalue buckling analyses. The effects of temperatures and distortions per time stepcannot be calculated over predicted and the temperatures around the weld pool, since thetwo-dimensional model neglects conduction in the weld direction.

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1.4 Application ofResearch (Introduction to Research concerning ship hullconstruction)

Many ships of current construction are of the conventional hull type, i.e., basically

a single skin of steel plating stiffened orthogonally by stiffeners and transverse members.The double hull is a relatively new development in the evolution of ship structuralsystems. The fundamental difference from the conventional hull is that its twin skins ofsteel plate are separated from each other by longitudinal girders that span betweentransverse bulkheads along the length of the ship. The double hull offers some advantagesover conventional hulls, such as improved combat and collision resistance, fewer areas ofdiscontinuities and complex welded details, possibilities for automated fabricationtechniques, and simplified distribution systems.

Recent advances in steel making have resulted in the development of new steelswith improved material properties such as high yield strength, good weldability, goodductility and high corrosion resistance. Application of AL-6XN non-magneticsuperaustenitic stainless steel in double hull ship structure could be essential for thedevelopment of future double hull construction because of the characteristics that thisalloy begins to deform inelastically under relatively low stress level, but have more workhardening capability and higher ultimate strength than many plain carbon steels. [24]

Most solutions concerned with ship hull fabrication are numerical, i.e., basedupon the finite element method. Because the determination of the ultimate limit state ofthe overall hull girder is a complex problem involving large deflection, and elasto-plasticbehavior of the hull components. Much research has been carried out in developing asimplified model due to the expense and time consuming process of full modeling. Lu

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and Pang investigated the ultimate strength of a ship hull under axial compressioninduced by vertical longitudinal bending without considering of strain hardening. [25]Thereafter, Lu developed an analytical capability to predict the load-deformationrelationships and the ultimate strength of double hull cells under axial compression,which incorporated strain hardening due to the highly ductile nature of the AL-6XN. [24]

For the investigation the effects of welding in ship construction, Dydo et al [26]researched buckling distortion that is caused by compressive stresses between stiffeners.2D thermal finite element models of the weld cross section in conjunction with a 2Delastic-plastic mechanical finite element model were used to predict the longitudinalstress induced along the weld. The equivalent axial load was then applied to the 3Dstructural model and the Critical Buckling load was predicted.

In order to calculate the deformations per time step by local temperature history,Ramasy [27] investigated predictive methods of assessing the effects of the weldingprocess using the finite element method to be used in welding simulation for shipstructures. This study provided information to help decide on mesh densities which arefeasible and sufficiently accurate.

Murugan [28] investigated the temperature and residual stress distributions pertime step in back step welding process to reduce the residual stresses in welded joints ofship construction with 3D welding modeling of T-beam. However, these 3D weldingsimulations were limited to the simple structure of T-beam and weld geometries andfocus primarily on the heat affected zone.

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1.5 The objectives of present researchThe prediction of residual stresses can be done on local models while the

computation of global deformations requires the modeling of the whole structure. Themesh sizes involved with this kind of simulation are very important due the movement ofthe heat source and the very high temperature gradient near the weldment. This may leadto unreasonable CPU time. Due to this reason, the accurate analysis of globaldeformation is currently lacking. In fact, comparisons between the coupled model withshell and volume elements and the 3D model with only volume elements applied to thesame weld problem are practically nonexistent.

This study couples in the same analysis shell and volume elements. This methodenables one to simulate more efficiently the welding of thin structures as the solid volumeelements can be limited to an area close to the heat affected zone, with the rest of thestructure modeled using shell elements. Non-linear thermal and mechanical behavior isavailable in shells. The computation is optimized in the sense that the additional degreesof freedom associated with volume elements are largely eliminated. Compatibilityelements must be defined to transfer rotations between solid and shell elements. [29]

The purpose of this research is to develop a comprehensive 3D finite elementmodel and compute global deformation of the ship structure.

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Chapter 2 - Comparison between the coupled model with shell elementsand the 3D volume model of a fillet welded T-beam

2.1 Properties of material (AL6XN)AL6XN stainless steel (45Fe-25.7Ni-21Cr-6.3Mo) is one of the leading materials

being considered for Navy hull fabrication. Therefore, this material was used in thefollowing computations to compare results between shell and volume elements.2.1.1 Thermal properties

Variation of thermal conductivity and volumetric specific heat with temperaturewere considered in the thermal model. [24, 30]

Models including magnetohydrodynamic effects, thermo-solutal buoyancyeffects, and Marangoni or surface tension effects offer new insight into the formation ofthe melt pool in welding. [31, 32] By artificially increasing the thermal conductivityabove the melting temperature, one can achieve a reasonable approximation for theeffects of convective mixing without much increase in complexity or solution times. Tocompensate for weld pool convective heat transfer of AL-6XN material, a highconductivity value, 160 W/m-K, was used in the weld pool. [33] Heat of fusion is theenergy required to change a solid at its melting temperature to liquid at the sametemperature. The release or absorption of latent heat of fusion was simulated by anartificial increase in the value of specific heat over the melting temperature range. Thelatent heat was taken as 2.1 x 109 J/m 3; the melting range was 1320-1400C.

Thermal property data for AL6XN stainless steel used in the analysis are given inFigure 2,3.

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2000500000Temperature (C)

500

0.180.160.14~

~ 0.12( )::1--cO 1cEO .8 ECii ~ 0.08E -Q; 0.06.cI - 0.04

0.020+----------,-----,--------,----------,o

Figure 2 - Adjusted Thermal Conductivity of AL6XN

0.03

0.025-('/')E 0.02~J--t1 0.015Q)I():E 0.01()Q)0 -Cf) 0.005

2000500000Temperature (C)

5000+---------,------,-----------,---------,o

Figure 3 - Adjusted Specific Heat ofAL6XN13


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2.1.2 Mechanical propertiesTemperature dependent values of properties such as modulus of elasticity,

Poisson's ratio, and yield strength, coefficient of thermal expansion (or thermal strain)were provided to the model. The mechanical properties used in the study are given inFigure 4 to 7.

When a material is deformed repeatedly, its mechanical properties may continueto change. This behavior can be accounted for by using adapted strain hardening modelsand isotropic strain hardening model was used in the analysis. Figure 7 obtained fromSYSWELD database approximately represents the behavior of AL6XN stainless steel.

250000

-~ 200000..........~:g 150000enctlQ)'0 100000en:::J:::J-g 50000

~O + - - - - - - r - - - - - . - - - - . - - - - - - - , - - - - - . - - - . - - ~ . - . - - - - - ,o 200 400 600 800 1000 1200 1400 1600

Temperature (C)

Figure 4 - Modulus of elasticity of AL6XN

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150000 1000Temperature (C)

50O + - - - - - - - , - - - - - - - - - - - , r - - - - ~ - - - - - - ,o

400350.-8: 300~

- 250..c..-0>C 200~..-(J) 150"C 100>-

Figure 5 - Yield Strength of AL6XN

0.03

400 600 800 1000 1200 1400Temperature (C)2000-++""----,---,---. . . ,-----,----,----,-----------,

o

0.025c'cu 0.02......-(J)

~ 0.015E....Q)~ 0.010.005

Figure 6- Thermal Strain of AL6XN

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700600

__ 500co

~ 400-/)C/) 300~-+-'

C/) 200

-- ....------ ..................... - ......

.........-- -+-20C- - I I - - 500C

1400C

0.2.15.1Plastic Strain

0.05

100O ~ ~ ~ ..... r - - ..........,.l---.......:-----------,o

Figure 7- Temperature Dependent Strain HardeningIn a coupled shell-solid analysis using SYSWELD, there are many things

that are different from standard 3D analysis. Mechanical properties of shell elementsshould give the thermal expansion coefficient instead of thermal strain in volumeelements. For the plastic part of the stress strain curve, volume elements give the valuesof plastic strain and the difference between the stress at that strain and the yield stresswas provided to the model, while shell elements give the values of plastic strain andstress at that strain. [34]

2.2 Model generationAT-beam made of two plates of thickness 9 mm with a fillet weld between them

was taken up for the investigation. The width of the non-butting member of the T-beamwas 160mm and butting member was 122.5 mm.

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Of the two fillet welds of T-beamon either side of the butting member, firsta one sided fillet weld was considered.The fillet width was 8 mm. The length ofthe T-beam was taken to be 128 mm. Thesize of the T-beam was chosen to be smallto reduce the computational time requiredfor the analysis. The sketch of the T-beamtaken for investigation is shown in Figure 8. Figure 8- Shape of Plates

For full volume model of T-beam, 8 noded linear hexahedron volumetric elements(H8 elements) in SYSWELD were used to construct the geometry. 4 noded linearquadrilateral elements (Q4 elements) were used on the surface to apply the convectiveand radiative boundary conditions. The fillet weld bead that arises due to deposition ofmetal was divided into finer meshes using P6 elements. The exposed surface of the weldbead was divided using Q4 elements to apply the boundary conditions. The total numberof nodes in the model was 8606, and the number of elements in the mesh was 11704.

For shell-volume coupled model, 4 noded linear quadrilateral elements (Q4elements) were used to apply shell elements with the thickness of 9mm. A convectioncoefficient is defined for the two sides of the shell elements. In mechanical analysis, thenumber of degrees of freedom for shell elements (ux, uy, uz, rx, ry, rz) and for threedimensional elements (ux, uy, uz) is different. In order to obtain compatibility betweenthe movement of the plates modeled with 3D and 2D elements, special elements called

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"compatibility" or "transition elements" are added in the connection section area. Arelation is therefore created on the nodes of the 3D section to ensure that globaldisplacement remains perpendicular to the mean plane of the shell element to which if isconnected. The three-dimensional mesh at the connection with the shell elements has tobe composed of 2 layers corresponding to the half-thickness of the shell, to correctlyapply relations of compatibility. [35] The total number of nodes in the model was 8246,and the number of elements in the mesh was 11158.

The meshed views of the solid T-beam and the mixed element model are shown inFigure 9, 10 respectively.

Figure 9 - mesh of full-volume model

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Figure 10-mesh of shell-volume coupled model

2.3 Thermal Model (thermal source modeling)

The heat transfer model best suited for arc-welding applications is the Goldak, ordouble ellipsoid, source. (See Figure 11) Goldak's source corrects the Rosenthal model'spoint source assumption by distributing power through a volume of specified size andshape.

This size and shape is adjusted through a number of Gaussian parameters, eachindependently controlling the width, forward length, rearward length, and depth of

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heating. By manipulating these parameters, the heat source can be changed to reflect avery wide variety ofwelding conditions.

Figure 11 . Goldak SourceThe formulation of the Goldak model is shown in Equations 2.1 and 2.2. By using

different parameters for the front and rear ellipsoids, it is possible to specify anasymmetric distribution of power. Here, fr and J,. are the fractions of power sent to thefront and rear ellipsoids, respectively. Parameters a, b, c/' and c;- determine the shapes ofthe ellipsoids as shown in Figure 11. Finally, Q is the total power that enters the part,given by Q =rjVI , where rj is the arc efficiency, V is the voltage, and I is the current.[10]

(2.1)

(2.2)

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Goldak's heat source model was used in this study. The code has a provision toapply this heat source model to the welding problems. In the model, the heat source wasmade to traverse along the length of T-beam at a 45 inclination to deposit the fillet weld.

Heat transfer to the ambient takes place by convection and radiation. Bothconvection and radiation heat transfer were considered in the model. The convective heattransfer coefficient of 15 W/m2-K was used. The emissivity value used in the analysiswas 0.5. To simulate material deposition during welding, the 'activation/deactivation'function of SYSWELD was employed. In the thermal analysis, the elements wereactivated a little in front of the heat source to avoid numerical problems. The thermalanalysis was carried out up to 501Os, till the T-beam cooled down to room temperature,after welding.

The welding parameters are as follows: Voltage: 35 V, Current: 250 A,Arc efficiency: 75 %

The case considered was continuous forward welding over the 128 mm full lengthof T-beam. The weld speed was 5 mrn/s and the duration of weld deposition was 25.6s.Cooling phase started at 25.6s and the analysis was completed after 501Os.

2.4 Mechanical Model

The transient temperature distribution file obtained from thermal analysis wasgiven as input to the mechanical model. The boundary conditions or restraints applied tothe T-beam during mechanical analysis are shown in Figure 12.

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The points A, Band C of Figure 12 were used to estimate the progress inproportion to displacement with weldment. The displacement between point A, a startpoint of shell elements in the coupled model, and weldment is 29mm, point B is 73.5mmand point C is 118mm. The direction of arrows means the direction fixed.

Figure 12 Restraints ofModelAs in thermal analysis, elements representing filler metal were activated in

mechanical analysis whenever required. In the mechanical analysis, the elements wereactivated slightly behind the centre of the heat source. The stress analysis was carried outup to 5010s as in the case of thermal analysis. At 5000s, the restraints of the T-beam werereset to an unrestrained condition, resulting in "spring back" and redistribution of stressesand deflection in the T-beam.

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2.5 Thermal ResultsThermal results for both models are shown in Figure 13 to Figure 18. The

temperature and stress contours were obtained using the post processing module ofSYSWELD.

CONTOURSTempTime 10Com put .Ref G1

Min = 20Max = 1969.- 197.247Il!!!iII 37 4.494_ 551.741_ 728.988~ 906.236,".:< I 1083.48CJ 1260.73c :J 1437.98I';:""Y,I 1615.22_ 1792.47

Figure 13 - Volume Model at 10 seconds

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CONTOURSTempTime 20Comput .Ref 8li

Min = 20Max = 1939.-194.472_ 368.944_ 543.416_ 717.888. 892.361~ 1066.83c::::Jc:J 1241.3c :J 1415.78jc,,,,!,j 1590.25_ 1764.72

Figure 14 -Volume Model at20 secoudsCONTOURSTempTime 250Com put .Ref 81

Min = 2 3 . 1 3 ~Max = 157.1- 35.3115IIiliIiI 47 .4903IIIII!I 59.6691

_71 .8479lE I 84.0268

I , , ~ j 96.2056c::J 108.384c::J 120.563p)C",q 132.742_ 144.921

Figure 15 -Volume Model at 250 seconds

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CONTOURSTempTime 10CompuLRef GI

Min;; 20Max;; 1964.- 196.74111III 373.482.. 550.22311\III1 726.964mDn 903.705""""! 1080.45c::J 1257.19c::J 1433.93""'"",,,1 1610.67_ 1787.41

Figure 16- Coupled Model at 10 seconds

CONTOURSTempTime 20Comput.Ref Gil

Min;; 20Max;; 1939.- 194.462_ 368.923_ 543.385.. 717.847~ 892.309

, . ,1066.77r:=J 1241.23r:=J 1415.69b i i ~ , . 1 1590.16_ 1764.62

Figure 17- Coupled Model at 20 seconds.

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CONTOURSTempTime 250Comput.Ref 81

Min = 23.37;Max = 160.2-35.8243_ 48.2713. . . 60.7183.. 73.1653

JBil 85.612311 98.0593c :J 110.506c :J 122.953..... 135.4",,,,.,,,,1_ 147.847

Figure 18- CoupledModel at250 seconds

The results of temperature at point A, Band C of Figure 12 were compared inorder to estimate the progress in proportion to displacement with weldment. (Figures 19,20,21)

In Figure 19, the peak point of temperature in 3D volume model is 133.5C at130seconds and the peak point in coupled model is 130JoC at 140seconds. The peaktemperature of both models at A point is almost same, while the temperature of coupledmodel decreases slowly compare to the temperature of volume model. This is due to thedifference ofheat transfer between shell and volume elements.

In Figure 20, the peak temperature in volume model is 51.0C at 516seconds andthe peak point in coupled model is 56.3C at 652seconds. The rate of difference is 9.4%

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and the delayed time of peak point is 136seconds. The temperature at point B of coupledmodel decreases slowly compared to the temperature of volume model at point A.

The tendency of temperature at point C is similar to that at point B (Figure 21).Although the absolute values of temperature are small, the difference of temperaturebetween both models increases a little and the delayed time of peak point is also longerthan point B. The difference of temperature between volume model and coupled model atpeak point is 9.2C and that is large as compared to 5.2C of point B.

__ : volume model------: coupled model

---- --------

160140

6120o..........

~ 100:::J+- '~ 80Q.)0-E 60~ 40

20o o 1000 2000 3000 4000

Time (5)5000 6000

Figure 19- Temperature at Point A

27


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__: volumemodel------: coupled model6050

-.00'-'40Q)....:::l- 30Q)0. .E 20~

100

0 1000 2000 3000 4000Time (8)

5000 6000

Figure 20- Temperature at PointB

1000 2000 3000 4000 5000 6000Time (8)

60

-.5000'-'40~:::l-30Q)0..E 20~

10

0 0

...........r ,I .... ,I .....I ' ....

I ' ....I. .....__: volumemodel------: coupled model

............-

....-.................. -

Figure 21- Temperature at Point C

28


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The reasons for the differences in temperature between the volume m odel andcoupled shell/solid model are

i) the difference in heat transfer between the shell and volume elements at theconnecting line (When shell elements are connected with volume element, themiddle node of both volume elements is connected w ith the node of shellelement.)

ii) the difference in heat loss through heat convection and radiation (In thevolume model, the heat loss can occur through edges as well as both of thefront and rear parts of plate, while the heat loss in the shell model occurs atonly through the front and rear faces of the plate.)

iii) the difference element in the meshes of shell and volume elements(size,calculating method, averaging method of result, ...etc.).

2.6 Mechanical ResultThe thermal results in the previous section were used to create the mechanical

models. The results for distortion are of more interest than the results of stresses at shellelements, because the purpose of this research was to develop a comprehensive 3D finiteelement model in order to compute global deformation of assembled ship structures. Theresulting displacements for both models are shown in Figures 22 to Figure 25. Thecontours in these figures representthe displacements in the x-direction.

29


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CONTOURSUxTime 16Deformed shapeComput.Ref Glob

Min = -0.0205;Max = 1.61834-0.1284211III 0.277411_ 0.426403.. 0.575395BiiI 0.724386~ ~ : ~ ~ ~ ~ ~ t J::::J 1.17136!'f'C":d 1.32035_ 1.46934

Figure 22- Volume Model at 16 seconds (deformed shape x 10)

CONTOURSUxTime 5010Deformed shapeComput.Ref Glob;

Min = -0.1739;Max =4.39886-0.241738_ D.65745_ 1.07316_ 1.48887~ 1.90459' .. 'c,! 2.3203:::::::J 2.73601:::::::J 3.151 72

3.56744l"k,,.'H_ 3.98315Figure 23- Volume Model at 5010 seconds (deformed shape x 10)

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CONTOURSUxTime 16Deformed shape _Comput.Ref GlobE

Min = -0.04756Max. = 1.61103- 0.103219_ 0.254001_ OA04782.. 0.555564l iB 0.706345I " , - ! 0.857127c:::I 1.00791c:::I 1.158691.30947I",;;;,,:!_ 1.46025

Figure 24-Coupled Model at 16 seconds (deformed shape x 10)CONTOURS

UxTime 5010DefDr med sh ape _CompuLRef GlobE

Min = -0.23156Max =4.37173- 0.186921.. 0.6D5401.. 1.02388.. 1.44236~ 1.86D841:,


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The results of distortion in the x-direction at point A, B, C were compared inorder to estimate transient distortion relative to displacement from weld fusion zone. (SeeFigures 26, 27, 28, 29, 30, 31) The values of distortion of both volume model andcoupled model at each point per time step show a good agreement. The difference ofdeflection at point A after being cooled is 0.06 mm (the distortion of volume model is1.16mm and that of coupled model is 1. lOmm), that at point B is 0.05 mm (the distortionof volume model is 2.60mm and that of coupled model is 2.55mm) and that at point C is0.04 mm (the distortion of volume model is 4.04mm and that of coupled model is4.00mm). There is no difference of distortion relative to displacement from weld fusionzone.

-- - - - - - - - - - - - - - - - - - - - -__ : volume model------: coupled model

1.41.2EE 1

'- "- 0.8Q)E 0.6)uco 0.40-CJ)0 0.2

0- 0.2 1000 2000 3000

Time (5)4000 5000 6000

Figure 26- Deflection (ux) of Point A (0 s to 5010 s)

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--------------, . , . ." , , --1.41.2EE 1' - '-3 0.8EQ) 0.6uro 0.4c..(/ )(5 0.2

o- 0.2 20 40

Time (8)

__: volume model------: coupled model

60 80

Figure 27- Deflection (ux) of Point A (0 s to 70 s)


3 ---2.5EE 2- '....cE-1.5Q)u 1roc..(/) 0.500

1000-0.5 2000 3000 4000Time (8)

5000 6000

Figure 28- Deflection (ux) of Point B (0 s to 5010 s)

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32.5EE 2---Q) 1.5EQ)u 1ro

Q .(J) 0.500

-0.5 20 40


60 80Time (5)

Figure 29- Deflection (ux) ofPoint B (0 s to 70 s)

4.54

E 3.5E 3-- 2.5Q)E 2Q)u 1.5roQ . 1(J)o 0.5o-0.5 1000 2000 3000

Time (5)

: volume model------: coupled model

4000 5000 6000

Figure 30- Deflection (ux) of Point C (0 s to 5010 s)

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4.54

E 3.5E 3....-- 2.5)E 2)c.> 1.5o0- 1n0 0.5

0-0.5 20 40

Time (5)


60 80

Figure 31- Deflection (ux) of Point C (0 s to 70 s)

In the mechanical models of welding presented, longitudinal stresses (y-direction)show the largest stress contours compared with those of other directions. The results oflongitudinal stresses for both models are compared and are shown in Figure 32 to Figure35. At the case of the coupled model, the stress contours of shell and solid elements aredisplayed separately because the stress results of shell elements can not be showed withthe solid elements in SYSWELD. In addition, the values of stress in the connected nodesare the added values of both results from solid and shell elements.

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~Longitudinaldirection

CONTOURSSigma 22Time 16Com put .Ref 81

Min = - 3 2 5 . ~Max = 50B.2

- -300- -233.333.. -166.667-100-mJ -33.3333I , , : ' ~ : - H 33.3333

c:::J 100c:::J 166.667\;;,:" ,,,:! 233.333_300

Figure 32-Volume Model at 16 seconds

CONTOURSSigma 22Time 5010CompuLRef 81

Min = - 2 5 4 . ~Max = 740.1

- -300- -233.333.. -166.667-1 DD.. -33.33331,'1 33.3333c:::J 100c:::J 155.667233.333" ' t ~ ~ ' i ! . ' !_ 3 0 0Figure 33-VolumeModel at 5010 seconds

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CONTOURSSigma 22Time 16Comput.Ref 81Min = - 3 2 5 . ~Max = 508.2

- -300-BI -233.333_ -166.667-1 00.. -33.3333

le.,1 33.3333c :J 1DOc:::J 166.667h,W1,H 233.333_300


37


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CONTOURSSigma 22Time 5D10Comput.Ref 81

Min = - 2 5 4 . ~Max = 740.1

--300-.. -233.333.. -166.667-10 D-iliiJ -33.33331'>,',;1 33.3333c:::J 100c:::J 166.667

!0:i,,,",,,! 233.333_300


38


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The stresses in the volume elements obtained from the coupled model are almostsame with those obtained from the volume model entirely composed of solid volumeelements. The results of longitudinal stresses at points A, B, C were compared in order toestimate the stress evolution in relation to displacement from the welded zone. (SeeFigures 36, 37, 38, 39, 40, 41) The absolute values of longitudinal stresses at shellelements are relatively small, when compared to equivalent stresses in the volumeelements of welded part. However, the values of stress for both the volume model andcoupled shell model at each point per time step show a little difference though thetendencies of these stresses are similar.

10050


o1000 2000 3000 4000 5000 6000

(J) - 50(J)~U5 -100-150-200

,----------------------------

Time (8)

Figure 36- Longitudinal stress of Point A (0 s to 5010 s)

39


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10050

--oQ. 0~.........enen(]) -50........(f )-100-150


110. 60 80 100 120", " .... .... ........

.... _-....... _--

Time (5)Figure 37- Longitudinal stress of Point A (0 s to 100 s)

- - - --------- -----------

__: volume model------: coupled model50

40-- 30oQ.~.........en 20en(])s........ 10f)

0-10

1000 2000 3000Time (5)

4000 5000 6000

Figure 38- Longitudinal stress of Point B (0 s to 5010 s)

40


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---------------


5040

-o 300.~'- "(J) 20(J)Q)s..U5 100

-10 20 40 60 80 100 120Time (5)

Figure 39- Longitudinal stress of Point B (0 s to 100 s)

6000000


4000000 3000

- - - - - - - - - ---------.

1000

302520

'"15 //ro I0 . 10 I~ I'-" 5 I~ 0 +-1;.-1-------, ,---,------,--------,-------,r-------,

~U5 -5-10-15-20-25

Time (5)

Figure 40- Longitudinal stress of Point C (0 s to 5010 s)

41


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100 1200000'I\

.....

'" \ \ \ \ \I\\III\I\ , -"",, '"------

o-2-4

......... - 6co0.. _8~--l - 10Ul~ -12C15 -14

- 16- 18-20

Time (8)Figure 40- Longitudinal stress of Point C (0 s to 100 s)

The difference of residual stress at point A after cooling is 36.6Mpa (the residualstress of volume model is -145.2Mpa and that of coupled model is -108.6Mpa), that atpoint B is 3.0Mpa (the residual stress of volume model is -1.2Mpa and that of coupledmodel is 1.8Mpa) and that at point C is 7Mpa (the residual stress of volume model is18.9Mpa and that of coupled model is 25.9Mpa). Although the values of the nodes in theconnecting region show the difference of 36.6Mpa, this difference is small, whencompared to the stresses in the volume elements of welded part. (See Figure 41)

In Figure 41, the longitudinal stresses after cooling according to displacementfrom the weld fusion zone are presented. The residual stresses of both models show thesimilar results.

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Point C

__ : volume model------: coupled modelPoint B

120000

600500400300.-....coQ . 200--n Point Aen 100~-n 0-100

-200-300

Displacement from weld fusion zone (mm)

Figure 41- Longitudinal stresses in relation to displacement from welded zone

The most different value within the results of residual stresses shows in theconnecting region between the shell and solid elements.

2.7 Conclusion about Comparison of both modelsThe results of the coupled model with shell and volume elements and the 3D

model with only volume elements applied to the practical welding problem of T-beamwere compared in this chapter.

The Followings are the major observations of the present comparison:

43


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i) The difference in temperature between both models slightly increases and thedelayed time to reach the peak temperature is also taken longer in proportionto displacement from weld fusion zone. The temperature for shell elementscools down slowly. This difference, however, can be ignored because theabsolute values of temperature at shell elements are very small.

ii) The values of deformation at coupled model are almost same with those atvolume model. Therefore, this coupled model of shell and volume elementscan be considered as an effective method to estimate the global distortion of alarge structure such as ship construction.

iii) The values of residual stress for both the volume model and coupled shellmodel show a little difference though the tendencies of these stresses aresimilar. Especially, the temperature at connecting region should be consideredcarefully. This difference also can be ignored due to the fact that the absolutevalues of stresses at shell elements are relatively small.

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Chapter 3 - Comparison of the coupled elements models with differentboundary conditions

3.1 Properties ofmaterialAL6XN stainless steel is used in this chapter and the same thermal and

mechanical properties of chapter 2 are applied.

3.2 Model generationThe vertical height of the butting member of the T-beam is 78mm. All dimensions

of T-beam are same with what was used in chapter 2 except the vertical height of thebutting member. Both sides fillet welding was considered.

The total number of nodes in the model was 8201, and the number of elements inthe mesh was 11116. The meshed views of the T-beam are shown in Figure 42.

Figure 42 - mesh ofmodel

45


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3.3 Thermal source modeling

The double ellipsoid source that is the same source with chapter 2 was appliedand all of the parameters in this heat source were same but both sides fillet weld.

After the first weld deposition time (25.6s), a cooling time of 60s was allowedbefore the second fillet weld deposition was started on the other side of the vertical plate.Thus, the two welds art not deposited simultaneously. The thermal analysis was carriedout up to 50 lOs.

3.4 Mechanical Model

The boundary conditions applied to the T-beam during mechanical analysis areshown in Figures 43, 44, 45 separately. The BC I is the same BC in previous chapter, andthe z-direction displacement is fixed. In the BC IT, the x-direction displacement of bothedges in butting plate additionally. The BC III constrained the two end points of themiddle line at non-butting member in order to make the displacement of four edges inthis plate free. The direction of arrows means the direction fixed.

The points A, Band C in Figure 44 and lines DD', EE', FF' in Figure 45 wereused to compare the results for each boundary condition. The displacement between pointA and weld fusion zone is 11.5mm, point B is 29mm, and point C is 73.5mm and thelines are in the middle part of T-beam.

46


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Figure 43 - Boundary Conditiou (Be) I ofModel

Figure 44 - Be II ofModel

47


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..

48

3.5 Thermal Results

jjjjjjjjjjjj

jjjjjjjjjjjjjjjjjjjjjjjjjjjjj

jj

FF'

DD'

At 5000s, the restraints of the T-beam were remove

EE' .-

Figure 45 - Be III ofModel

Thermal results for the three models are identical, and are shown in Figure 46,

the SYSWELD code

Figure 47 and Figure 48.


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CONTOURSTempTime 16CompuLRef 81Min = 20Max = 19D9- 191.767.. 363.533_ 535.3_ 707.066

IPD 878.833I ' " . ! 105D.6c=I 1222.37c=I 1394.13hi';"'" 1565.9_ 1737.67

Figure 46 - Contour of temperature at 16 seconds

CONTOURSTempTime 95.4999Comput.Ref 81

Min = 20.73Max =2039- 204.275_ 387.819.. 571.363.. 754.907ram 938.451

",.,,1 1121.99c=I 1305.54c=I 1489.08p"",.:"'1 1672.63_ 1856.17


49


56/96

CONTOURSTempTime 200CompuLRef 811

Min = 47.36EMax = 367.9- 76.5137_105 .661_ 134.808.. 163.955~ 193.1 02

222.25c" 'c.',:1:::::J 251.397:::::J 280.544t;.>;je;\'d 3D 9.691_ 338.838


The results of temperature at point A, Band C of Figure 43 per time step weredisplayed in order to estimate the temperature evolution in relation to displacement withwelded zone. (See Figure 49)

In Figure 48, the temperatures of point A, the point closest to the weld fusionzone, shows the highest values and two peak points influenced by both sides weldinghaving started at different times. The temperatures of points B and C hardly show theinfluence of both sides being welded with a time delay between depositions of theseparate :fillet welds, but the values of temperature are higher than those of one sidedweld in previous chapter.

50


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1200000

__ : Point A___ : PointB------: Point C

."

400 600 800Time (5)

,,."

200

;-'-- ......( ....../ .......II("

II, ". , '. . . .o

500450

_400o~ 3 5 0~ 300::J+ J~ 250Q)0.200E~ 150

10050o

Figure 49 - Temperature at Point A, B, C (Os to 1000s)

3.6 Mechanical ResultsThe thermal results were used to create mechanical models with different

constraints. The results of displacement for the three models are shown in Figure 50 toFigure 56 and the contours of result represent the normal displacement, the magnitude ofthe displacement vector.

51


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CONTOURSnorm UTime 16Deformed shape XComput.Ref Global

Min = 4.88142e-Max = 2.53303-0.230276IIIiI 0.460551_ 0.690827.. 0.921103mDI 1.151381.3816581 .61193c :J 1.84221,,,,,"','" 2.07248_ 2.30276

Figure 50- Normal displacement ofBC I at 16 seconds (deformed shape x 10)

CONTOURSnorm UTime 101Deformed shape XComput.Ref Global

Min = 6.19116eMax = 4.05585-0.3687136lIIDI 0.737427_ 1.10614Ii!IIIIiI 1. 47485~ 1.843571,",,12.21228c :J 2.58099c :J 2.94971

1 ~ . ' c i ; " , 1 3.31842_ 3.68713

Figure 51- Normal displacementofBC I at 101 seconds

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CONTOURSnorm UTime 5010Deformed shapeComput.Ref G l o b ~Min = 0.037353Max = 4.37212-0.431423_ 0.825493.. 1.21956

_1 . 61363lEiI'fil 2.0077c:::::J 2.40177c:::::J 2.79584c:::::J 3.189911-;,-,,01 3.58398_ 3.97805

Figure 52- Normal displacement ofBC I at 5010 seconds

CONTOURSnorm UTime 99.4999Deformed shape XCompu t .Ref Global

Min = 2.87276eMax = 3.34659-0.304235_ 0.608471... 0.912706.. 1.21694l e i 1.521181,',>1 1.82541c:::J 2.12965c:::J 2.43388I.";,,,,! 2.73812_ 3.04235

Figure 53- Normal displacement ofBCn at99.5 seconds

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CONTOURSnorm UTime 50] 0Deformed shapeComput.Ref Globe

Min = 0.033392Max =3.64998-0.362173IlIIII 0.690954_ 1.01973

_1 .348511.6773mlmI 2.00608"".>1I:=J 2.33486I:=J 2.66364

2.992421 ; V ; : " ~ l ' l ; " , : - : 1_ 3.3212Figure 54- Normal displacement ofBCn at 5010 seconds

CONTOURSnorm UTime 99.4999Deformed shape XComput.Ref Global

Min = 2.42872e-Max =3.9125-0.355682I11III 0.711363.. 1.06705_ 1.42273Il!I1l!il 1. 77B411",,1 2.13409I:=J 2.48977I:=J 2.845453.201141 ' ~ ~ ' j . ' ! , 1_ 3.55682

Figure 55- Normal displacement ofBC i l l at 99.5 seconds

54


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CONTOURSnorm UTime 5010Deformed shape XComput.Ref GlobalMin = 4.21491eMax =3.23099-0.293755IlII!IIIl 0.587487_ 0.88121.. 1.17493!ImJ 1.46865

1,.,:,1 1.76238c=J 2.0561c=J 2.349822.643541'",'.:,,1]_ 2.93727

Figure 56- Normal displacement ofBCmat 5010 seconds

In order to compare the distortion ofT-beam, the angular change and longitudinalbending distortion was tabulated.

The results of displacement after being cooled are shown in Table 3-1. Theangular change a, (3, y and longitudinal bending distortion d in Figure 57 are the degreesand displacement ofline DD', EE', FF' in Figure 44.

55


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(a) Angular change--..Transversedirection

________~ " \ 0- - - - - - I - - - - - - - - - ~

'Y\)-1IIIIIIIII

+

.r-------~ - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - l - ~ - - - - - - - - - - - - - - - - - ---..Longitudinaldirection

(b) Longitudinal bending distortionFigure 57-Distortion in Welding

Boundary DistortionCondition dyI 1.88 1.91 0.18 0.065mmII 1.50 2.05 -0.41 0.064mmIII 2.00 1.82 0.07 0.062mm

Table3-1 - Distortion after removing the restraints

The final results of distortions in the cross-section after removing the restraints onthe T-beam are slightly different depending on the boundary conditions, while the

56


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longitudinal bending distortions have almost same values. Especially, the final result ofthe model with BC II is different as compared to BC I and III. (See Figures 58, 59, 60, 61,62) The interesting part of the model with BC IT is that the displacement shows a largechange of values at the instant that restraint is released. This is because the BC I, IIIbasically allowed the free-movement of vertical plate while the constraint of BC II wasfixing the distortion of model during welding and cooling. When the constraint wasremoved, the suppressed distortion occurred abruptly.

After the first welding and 60 seconds cooling, the angle changes of BC I, II arevery different with those of BC III due to the fact that both of BC I and II constraint thefour comers of non-butting member and BC ITI does the two end points of the middle lineat non-butting member. The angle changes of three models, however, are converged tosimilar values when the other side welding is finished. Although the difference ofdistortion reduced after welding of both side, the results were varied greatly by boundarycondition.

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2.52 ....................................................................................................

ID 1.5~e>Q) 1"'0-- 0.5

----------------------------1_ : B.C. I___: B.C. II------: B.C. III

o-0.5 1000 2000 3000 4000 5000 6000

Time (s)Figure 58- a Angle change (0 s to 5010 s)

25000

_ :B .C . I:B.c. II

------: B.C. III

150

.........................................,.1' '/-------------

100

I ..,.

50

. r--------: I.,,.,,.

2.52

- 1.5)Q)l -e>Q) 1"'0-- 0.50

-0.5Time (s)

Figure 59- a Angle change (0 s to 200 s)

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-. ..

_ : B.c. I___: B.C. II------: B.C. III

2.52

.- 1.5)Q)l -e> 1)"0--C!l. 0.50-0.5 1000 2000 3000

Time (5)

4000 5000 6000

Figure 60- PAngle change (0 s to 5010 s)

,.'I :-----'1 :..--------/ "

I :r :.

2.52

.- 1.5Q)Q)l-e>Q) 1"0--C!l. 0.50-0.5

.. .. .. .. .. .. .. .. .. .. .. .. .. ..

50 100Time (5)

150

_ :B .C . I___ : B.C. II------: B.C. III

200 250

Figure 61- PAngle change (0 s to 200 s)

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21.5

....... 1)~0> 0.5)"0-- 0-0.5- 1

2

:B.C. I___: B.C. II------: B.C. III

.... ..

I ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Il ' 2000 4000! 6000

Time (8)Figure 62- y Angle change (0 s to 5010 s)

...5

.......Q)~ 10>Q)"0; : 0.5o-0.5

................ -_ ..

#,'/ "". ...... - - - - - - - - -

50

:B.C. I___ :B.c. II------: B.C. III

......................................

1 O ~ - - - - -1-5e- - - - -ZOO

Time (8)

250

Figure 63- y Angle change (0 s to 200 s)

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The results of longitudinal stresses that have the largest stress values at threemodels are shown in Figure 64 to Figure 66.

CONTOURSSigma 22Time 5010Com put.R ef 81

Min = -225.:Max = 714.7

- -300-. -233.333.. -166.667-100.-1M! -33.3333he,.';:;! 33.3333c::J 100c::J 166.667233.333"';,'1,,,{1_ 3 0D

Figure 64- Longitudinal stresses ofBC I at 5010seconds

61


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CONTOURSSigma 22Time 5010Comput.Ref 81Min = - 2 3 1 . ~Max = 715J!

- -300- -233.333_ -166.667-} 00..le I -33.3333I.",'--.! 33.3333c::J 100c::::I 166.667

n , ' ~ ; 5 i . ; , " , 233.333_3DO

Figure 65- Longitudinal stresses ofBC II at 5010seconds

62


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CONTOURSSigma 22Time 5010CompuLRef 81

Min = -231.Max = 7 1 5 . ~

- -300-l\'IIl1I -233.333_ -166.667-100- -33.33331",1 33.3333c::::J 100c::=:J 166.667

r , , ~ t ; ~ t 1 233.333_300

Figure 66- Longitudinal stresses ofBe ill at 5010seconds

The results of longitudinal stresses at point A, Band C ofFigure 43 per time stepwere displayed at Figures 67, 68, 69.

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6000_ :B .C . I___: B.C. II------: B.C. III

4000 5000

----------- - - ~ - : : - ---'--""-- ......- ~ -20015010050- 0 + - - J l - - - - - . - - - - ~ - - _ . _ _ _ _ _ - - _ _ , _ - - - _ . _ _ _ _ - - _ ,~';;; -50

en~ -100 t.....(J ) -150-200-250-300 Time (5)

Figure 67- Longitudinal stress of Point A (0 s to 5010 s)

40200- -20elQ .~-- -40en

enCD......... -60J)-80

-100-120

1000 2000 3000 4000 5000-------- - ~ - - . ~ - - -_ :B .C . I___: B.C. II------: B.C. III

6000

Time (5)Figure 68- Longitudinal stress of Point B (0 s to 5010 s)

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200150100 - - : B.C. I---: B.C. II- 50 ------: B.C. IIIuQ .~- 0n

en 3000 4000 5000 6000)......... -50I)

-100-150-200

Time (s)

Figure 69- Longitudinal stress of Point C (0 s to 5010 s)

The results of longitudinal stresses with different constraints are similar, though theresults of BC II show a bit of difference due to the restraints of the vertical plate.Therefore, it could be analogized that the most influenced factor of stresses at weldingsimulation is the contours of temperatures per time steps and the boundary conditionsapplied in this chapter did not affect so much.

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Chapter 4 - Welding simulation of a practical problem (the hull of ship)

4.1 Model generationA single cell section of a double hull welded box beam was simulated. This cell

with a cross section shape of a cellular box is fabricated using AL-6XN steel plates. Alldimensions of the cell were based on a prototype double hull section. The dimensions areshown in Figure 70.

26 1/16"

T5/16"

I I"11III ,. "IIIl ,.

5/16" 5/16"..... ... ..

...r 4"

... ...l'I I

..... I ~ ~.. 25_3/4_"-----.h+- 5/16"~ 273/4" ~Figure 70- Cross section of box cell

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The length of box cell used in the finite element models is 3 feet 2 and 3/4 inches.It is believed that this length is sufficient to obtain satisfactory results that could estimatea states of distortion for longer beams and still allow reasonable computation times andstorage.

One-quarter of this cell was meshed due to the assumption of symmetryconditions. This assumption implies that the welding proceeds on all four edgessimultaneously. The total number of nodes in the model was 10231, and the number ofelements in the mesh was 15868. The meshed views of this model are shown in Figure69.

4.2 Thermal and Mechanical modeling

The applied heat source is a double ellipsoid source and both sides on the vertical

plate arc fillet welded. In the model, the heat source was made to traverse along thelength of T-beam at a 45 inclination to deposit the fillet weld metal. Some of thewelding parameters are given in the Table 4-1.

Convective heat transfer coefficient 15 W/m2-KEmissivity 0.5

Voltage 35 VWelding parameters Current 250 A

Arc efficiency 75 %Table4-1 - Distortion after removing the restraints

After the first weld deposition to 197s, the model was cooled for 5000s and thesecond weld deposition of the other side was started. At 5000s, the restraints of the T

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beam were reset to an unrestrained condition. The thermal analysis was carried out up toSOlOs. The boundary conditions applied to this cell box during the mechanical analysisare shown in Figure 71.

Figure 71 - Boundary Condition of Cell box (114 Model)

4.3 Thermal ResultsThermal results for this model are shown in Figure 72, Figure 73 and Figure 74.

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CONTOURSTempTime 50.0999Comput.Ref Glo

Min 20Max = 277BJ

-20- 173.333.. 326.667_4BOI&lI 633.333

I ' ~ ' ; ; ' d 7B6.667C:::t 940c=J 1093.331246.67=400Figure 72 - Contouroftemperature at 50.1 seconds

CONTOURSTempTime 150.001Comput.Ref Glo

Min = 20Max = 2B36.

-20-. 173.333_ 326.667.. 4BOIE i 633.3331'_'1 7B6.6870 940C J 1093.331248.87! s : ; : - " ~ k J_1400

Figure 73 - Contourof temperature at 150 seconds69


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CONTOURSTempTime 1000Comput.Ref GleMin = 20.0B3Max = 118.51- 29.030B11II37.9781_ 48.9254.. 55.8728~ 64.B2011,;c',i ( 73.7 875r=J B2.714Br=J 91.8822100.809=09.557


4.4Mechanical ResultsThe results of displacement for the symmetric cell are shown in Figure 75 to

Figure 77 and the contours ofresult represent the magnitude of the displacement vector.

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CONTOURSnorm UTime 3DDeformed shapeComput .Ref GlobMin::; 0.0 0 0 9 9 ~Max::; 0.79001=.0727219

I i III 0.144451_ 0.216181.. 0.28791m!fii 0.35964

0.431369~ 0.503098r::::::J 0.5748280.646557,,",*:;,4_ 0.718287Figure 75 - Normal displacement at 30 seconds

CONTOURSnorm UTime 102.6Deformed 9hapeComput.Ref G l o b ~

Min::; 0.002112Max::; 1.68112- 0.15475II l II 0.307387_ 0.460024.. 0.612661~ 0.765298le,.1 0.917935r::::::J 1. 07057r::::::J 1.223211.375851:,,";"-


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CONTOURSnorm UTlme5D1DD ef or me d s ha peCompuLRef Glob

Min = D.D 2273:Ma x = 9.1389!5- D.85148_ 1.68D23_ 2.5D897.. 3.33772~ 4.166471CO '.:""1 4.99521r:::::I 5.82396C J 6.65271

7.481451 , ; ~ w : " , 1_ 8.31D2

Figure 77 - Normal displacementat 5010 seconds

The results oflongitudinal stresses that have the largest stress values for thismodel are shown in Figure 78 to Figure 80.

In Figure 80, high tensile residual stresses are produced in areas near the weldand the longitudinal stresses in areas away from the weld are compressive.

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Figure 78 - Longitudinal stress at 30 seconds

73

CONTOURSSigma 22Time 3DComput .Ref 81Min = -26 D.!Max = 3 8 7 . ~

- -300- -233.333.. -166.667-1 DD-BiJ -33.33331"'",,,1 33.3333t:=I 1DDt:=I 166.667!;'W\i@ ~ ~ ~ . 3 3 3-


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Figure 79 - Longitudinal stress at 102.6 seconds

74

CONTOURSSigma 22Time ID2.6Comput.Ref 13:Min = -279.Max = 433.i

- -3DD-. . -233.333_ -166.667-IDD-tBlI -33.33331.'.'::;,:1 33.3333c:::J 1DDc:::J 166.667

1 ' , " J ' i ~ ; : ( i ; 1 233.333_ 3DD


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CONTOURSSigma 22Time 5010Comput.Ref 81

Min = - 1 6 8 . ~Max = 639.4

- -300- -233.333.. -166.667-100.-imJ -33.333333.3333""';'S""!::=lIDO

: : :J 166.667! ~ 4 ; : 0 1 233.333_300

Figure 80 - Longitudinal stress at 5010 seconds

In Figure 81, the residual stresses after cooling according to displacement from theweld fusion zone are presented.

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600500400-~ 300-n

en 200)....+-'C/)

1000

-100 50 100 150 200 250 300 350

Displacement from weld fusion zone (mm)

Figure 81- Longitudinal stresses in relation to displacement from welded zone

The boundary condition that was used in this chapter may not precisely replicate

the state of stress in the "actual" problem due to the fact of that one-quarter symmetry ofa cell box is assumed. However, it is expected that this will provide a reasonable estimateof the final distortion. In addition, the model presented here are too small to adequatelysimulate the complete behavior of an entire hull structure. These results, however, showthat a practical problem in welded ship construction can be simulated by using thecoupled model of shell and volume elements.

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Chapter 5 - Conclusions and Future Work

5.1 Future WorkThe greatest limitations in modeling a large structure are computation time and

storage requirements. The advantage of plate and shell elements is that the elements canbe fairly coarse and still deliver reliable results. Therefore, to use solid elements inregions of high thermal gradients and plates and shells elsewhere offers a significantreduction in solution times and storage requirements without a painful loss of accuracy.

In the simulations considered here, only simple models such as T-beam and singlecellular box beam of the double hull were considered. Eventually, an entire hull ship,with more complicated geometry, should be simulated using this technique. (See Figure82)

Figure 82- Design of double hull in ship77


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When a three-dimensional mesh is generated to accurately simulate welding, theentire region that will be welded must be very refined. Therefore, any model that has alarge welding region presents enormous computational problems in terms of CPU timeand storage.

5.2 ConclusionsThe temperature, distortion and residual stresses of the coupled model with shell

and volume elements and the 3D model with only volume elements in a welded T-jointwere investigated in this study. The all results for a coupled shell/solid volume modelshowed the same tendencies and similar values obtained from an equivalent solid volumemodel. Therefore, a coupled model can be considered as an effective method to estimatethe global distortion of a large structure, such as ship double hull structures.

Finally, models of both sides welded T-joints with different constraints weresimulated and compared. According to the boundary conditions, the results of distortionsvaried greatly and the stress concentration occurred at the place that was fixed. It isimportant to recognize that boundary condition constraints play a critical role indetermining distortion for welded structures.

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AppendixListed here are the main input files for a single cell section of adouble hull welded boxbeam simulation discussed the chapter 4. The second mechanical input file for solvingthe released constraints is not presented because this file is almost same with the firstmechanical file except the constraints part.

HEAT.DAT (Thermal model data)NAMESEARCH DATA 101COMPATIBILITY PENALTY 200*6MIXING SOLID SHELLSOLID ELEMENT GROUP $PART$SHELL ELEMENT GROUP $SHELL$RETURNDEFINITIONT-JOINT CONTINUOUS WELDINGOPTION THERMAL METALLURGY SPATIALRESTART GEOMETRYMATERIAL PROPERTIESELEMENTS GROUP $PART$ / C=-10001 KX=-10002 KY=-10002 - KZ=-10002 RHO=l MATE=lELEMENTS GROUP $BEAD1$ / C=-10001 KX=-10002 KY=-10002KZ=-10002 RHO=l STATE=-5 MATE=lELEMENTS GROUP $SHELL$ / C=-10001 KX=-10002 KY=-10002KZ=-10002 RHO=l MATE=l H=7.9375CONSTRAINTSELEMENTS GROUP $SKINPART$ / KT=l VARIABLE=10ELEMENTS GROUP $SHELL$ / KT=l LOWER UPPER VARIABLE=10LOAD1 WELDING/ NOTHINGELEMENTS GROUP $PART$ / QR=l VARIABLE=-100ELEMENTS GROUP $BEAD1$ / QR=l VARIABLE=-100ELEMENTS GROUP $SHELL$ / TT=20 LOWER UPPERELEMENTS GROUP $SKINPART$ / TT=20TABLE10001 / 1 20 0.004030 500 0.004836 1200 0.005239 1293 0.00529 - 1300 0.0054 1310 0.0060 1325 0.02525 1330 0.02600 1333 0.026251388 0.02625 1392 0.02600 1395 0.02525 1400 0.0066 1405 0.0058 - 1420 0.0053599 1600 0.005359910002 / 1 20 0.0137 100 0.0137 500 0.0250 1283 0.0382 1306 0.0421327 0.05048 1397 0.152 1412 0.156 1445 0.1600 1570 0.1600 - 1700 0.1600

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10 / FORTRANfunction f{t)c radiat ion losses f = sig * e * ( t + to) (t**2 + to**2)e = 0.5sig = 5.67*-8to = 20 .to = 20 . + 273.15tl = t + 273.15a = t1 * t1b to * toc a + bd tl + tod = d * cd = d * ed = d * s igc convective losses = 15 W/m2f = d + 15.g=1.0*-6f=f*greturnEND

Heat Source Definit ion100 / FORTRANFUNCTION F{X)DIMENSION X(5)

xa = X [1 ] ;ya = X [2] ;za = X [3 ] ;time X[4] ;c i n i t i a l posi t ion of heat source in the new framexc 7.14375;yc = 1.0;zc = 11.1125;c Translationxa xa xcya = ya - ycza = za - zcc rotat ion matrix

al = 0.7071;a2 = 0.0;a3 -0.7071;bl = 0.0;b2 = 1.0;b3 = 0.0;c l = 0.7071;c2 = 0.0;c3 0.7071;c rotationaa a1 * xabb = a2 * yacc a3 * zaxx = aa bb cc + +aa = b1 * xabb = b2 * ya

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cc = b3 * zayy aa bb cc + +aa = c1 * xabb = c2 * yacc = c3 * zazz = aa bb cc + +c Q=U*Iuu = 35.0;i i = 250.0;q = uu*i i ;q q*6.0;q q*1.7320508; Ilq=q*sqrt(3)q = ql3 .1415927;q q/1.7724539; II q/sqr t(pi)c EFFICIENCYe=0.75;q=q*e;c WELDING VELOCITY mm/swv=-5.0

c PARAMETERS OF WELDING POOLa= 4.5; IIHalf width of weld pool (from T-Joint welded piece)b= 4.9; IIDepth of weld pool ( es timat ion using AWS Doc.A3.0-94)Yf= a * 0.75; IILength of weld pool in front of center (Goldak'spaper)Yr= a * 1.5; IILength of weld pool behind center (Goldak's paper)c Fit t ing power base to meshQc = 1.0; II Energy for a density = 1.Qe = 1./Qc; II density of energyc Proportion of heat in front and rear (Non sYmmetric Gaussiandistr ibut ion)c Note: Qf + Qr = 2Qf = 0.6; II Fraction of energy in front of HS (Goldak 's paper)Qr = 1.4; II Fraction of energy in the rear of HS (Goldak's paper)

c POSITION OF HEAT SOURCE CENTERtim1=0.0tim2=time-tim1center = wv*tim2;center = wv*time;i f (yy .GT. center) Qg=Qr;i f (yy .LE. center) Qg=Qf;i f (yy .LE. center) cc=Yf;i f (yy .GT. center) cc=Yr;Qg=Qg*Qe;Qg=Qg/a;Qg=Qg/b;Qg=Qg/cc;

c CALCULATION HEAT SOURCE BY GOLDAKS FORMULArx=xx;rx=rx*rx;rx=-rx;rx=rx*3.0;s=a*a;rx=rx/s;

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rx=exp (rx) ;ry=center-yy;ry=ry*ry;ry=-ry;ry=ry*3.0;e=cc*cc;ry=ry!e;ry=exp (ry) ;rz=zz;rz=rz*rz;rz=-rz;rz=rz*3.0;dc=b*b;rz=rz!dc;-rz=exp(rz);coef=ry*rx;coef=coef*rz;f=coef*Qg;f = f*q;RETURNEND

5 / FORTRANFUNCTION F(X)DIMENSION X(4)XX X(l);YY X(2);ZZ = X(3) ;TT X(4) ;VY =-5.0;C OUTPUT PARAMETERSC F=l ELEMENT ACTIVATIONC F=-l ELEMENT DEACTIVATIONC F=O NO EFFECTF=lVYT=VY*TTVYT=VYT-0.01IF(YY.LT.VYT) f=-lRETURNEND

RETURNSAVE DATA 102SEARCH DATA 102RENUMBER ITERATION 50RETURN

SAVE DATA 102SEARCH DATA 102TRANSIENT NON-LINEAR EXTRACT 0BEHAVIOUR METALLURGY 2 FILE META.DATALGORITHM BFGS IMPLICIT 1 ITERATION 250PRECISION ABSOLUTE NORM 0 FORCE 1*-10 DISPLACEMENT 1

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METHOD ITERATIVE NONSYMMETRICALINITIAL CONDITIONSNODES / TT 20ELEMENTS GROUP $PART$ / P 1 0ELEMENTS GROUP $SHELL$ / P 1 0ELEMENTS GROUP $BEAD1$ / P l O I S -1ELEMENTS GROUP $BEAD2$ / P l O I S -1

TIME INITIAL 0.00.25 STEP 0.125 / STORE 1SEARCH DATA 102ASSIGN 19 TRAN102.TITTRANSIENT NON-LINEAR EXTRACT 0BEHAVIOUR METALLURGY 2 FILE META.DATALGORITHM BFGS IMPLICIT 1 ITERATION 200PRECISION ABSOLUTE NORM 0 FORCE 1*-10 DISPLACEMENT 1METHOD ITERATIVE NONSYMMETRICALINITIAL CONDITION RESTART CARD LASTTIME INITIAL RESTART

1 STEP 0.2 / STORE 16 STEP 0.25 / STORE 1201 STEP 0.3 /STORE 1210 STEP 1 / STORE 1260 STEP 2 / STORE 1500 STEP 5 / STORE 1800 STEP 20 / STORE 15000 STEP 100 / STORE 15004 STEP 0.5 / STORE 15010 STEP 1 / STORE 1RETURNSAVE DATA 102DEASSIGN 19

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MECH.DAT (Mechanical model data)SEARCH DATA 102DEFINITIONT - WELD JOINT

OPTION SHELL SPATIAL MULTI" THERMOELASTICITYRESTART GEOMETRYMATERIAL PROPERTIESELEMENTS GROUP $PART$ / E=-10001 YIELD=-10004 LX=-10003 LY=-10003LZ=-10003 MODEL=3 NU=-10002 SLOPE= -10008 PHAS=2 TF=1400ELEMENTS GROUP $BEAD1$ / STATE=-4 E=-10001 YIELD=-10004 LX=-10003

LY=-10003 LZ=-10003 MODEL=3 NU=-10002 SLOPE=-10008 PHAS=2 TF=1400ELEMENTS GROUP $BEAD2$ / STATE=-6 E=-10001 YIELD=-10004 LX=-10003

LY=-10003 LZ=-10003 MODEL=3 NU=-10002 SLOPE=-10008 PHAS=2 TF=1400ELEMENTS GROUP $SHELL$ / H=7.9375 INTE=902 TYPE=4 E=-10001 YIELD=

10004 --LX=-10021 LY=-10021 LZ=-10021 MODEL=3 NU=-10002 SLOPE=-10023 PHAS=2TF=1400ELEMENTS GROUP $SKINPART$ / TYPE=5ELEMENTS GROUP $SKINBEAD1$ / TYPE=5ELEMENTS GROUP $SKINBEAD2$ / TYPE=5ELEMENTS GROUP $ELEM_TRAN_SH$ / E=200000000 SHAPE=l TYPE=9

CONSTRAINTSNODES 27101 / UX UYNODES 27100 / UXNODES 27102 / UXNODES 27103 / UXNODES 27104 / UXNODES 27105 / UXNODES 27106 / UXNODES 27107 / UXNODES 27108 / UXNODES 27109 / UXNODES 27110 / UXNODES 27111 / UXNODES 27112 / UXNODES 27205 / UZNODES 27206 / UZNODES 27207 / UZNODES 27208 / UZNODES 27209 / UZNODES 27210 / UZNODES 27211 / UZNODES 27212 / UZNODES 27213 / UZNODES 27214 / UZNODES 27215 / UZNODES 27216 / UZNODES 27217 / UZ

LOAD1 WELDING/ NOTHING

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TABLE

10001 / 1 24 195000 93 189000 204 180000 316 171000 427 161000538 152000 982 90000 1093 72000 1200 45000 1260 41000 1300 - 20000 1320 10000 1350 5010002 / 1 0 0.29 900 0.3010003 / -10006 -1000610006 / 1 20 0.0000000 100 0.001224 300 0.004396 400 0.006080 5000.007872 600 0.009686 700 0.011628 800 0.013728 1200 0.0231281250 0.024477 1300 0.025728 1320 0.02652010021 / -1 0022 -1 002210022 / 1 20 0.0000153 100 0.0000153 200 0.0000155 300 0.0000157 400

0.000016500 0.000016410004 / -1 0007 -1 000710007 / 1 21 365 93 325 149 290 204 270 260 255 316 235 371 230 427230 - -482 220 538 215 982 70 1093 39 1200 31 1260 28 1300 20 1320 10 1350 110008 / -1 0009 -1 000910009 / 7 20 10010 500 10011 1450 1001210010 / 1 0 0 0.01 23 0.02 60 0.04 102 0.06 136 0.08 168 0.10 198 0.15

27010011 / 1 0 0 0.01 23 0.02 42 0.04 70 0.06 92 0.08 109 0.10 126 0.15

15610012 / 1 0 0 0.01 0.5 0.02 0.5 0.04 0.5 0.06 0.5 0 .08 0.5 0.10 0.5

0.15 0.510023 / -1 0024 -1 002410024 / 7 20 10025 500 1002610025 / 1 0 365 0.01 388 0.02 425 0.04 467 0.06 501 0.08 533 0.10 563

0.15 63510026 / 1 0 218 0.01 241 0.02 260 0.04 288 0.06 310 0.08 327 0.10 344

0.15 3744 / FORTRAN

FUNCTION F(X)DIMENSION X(4)XX=X( l ) ;YY X(2);ZZ = X(3) ;TT = X(4);VY =-5.0;

C OUTPUT PARAMETERSC F=l ELEMENT ACTIVATIONC F=-l ELEMENT DEACTIVATIONC F=O NO EFFECT

F=lVYT=VY*TTVYT=VYT+0.1

IF (YY.LT.VYT) f=- l85


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RETURNEND

RETURNSAVE DATA 106SEARCH DATA 102SEARCH TRAN 102TEMPERATURE METALLURGY TRANSIENT SHELL CARD 0 TO 800 STEP 1SEARCH DATA 106TRANSIENT NON-LINEAR STATIC EXTRACT 0BEHAVIOUR PLASTIC METALLURGY 2ALGORITHM BFGS IMPLICIT 1 ITERATION 200PRECISION ABSOLUTE NORM 0 FORCE 1 DISPLACEMENT 1*-3METHOD NONSYMMETRICAL TEST 1 ITERATIVEINITIAL CONDITION

ELEMENTS GROUP $BEAD1$ / IS -1ELEMENTS GROUP $BEAD2$ / IS -1

TIME INITIAL 00.25 STEP 0.125 / STORE 2

RETURNSAVE DATA TRAN 106SEARCH DATA 106ASSIGN 19 TRAN106.TITTRANSIENT NON-LINEAR STATIC EXTRACT 0BEHAVIOUR PLASTIC METALLURGY 2ALGORITHM BFGS IMPLICIT 1 ITERATION 300PRECISION ABSOLUTE NORM 0 FORCE 1 DISPLACEMENT 1*-3METHOD NONSYMMETRICAL TEST 1 ITERATIVEINITIAL CONDITION RESTART CARD LASTTIME INITIAL RESTART

1 STEP 0.2 / STORE 36 STEP 0.25 / STORE 4210 STEP 1 / STORE 10260 STEP 2 / STORE 10500 STEP 5 / STORE 6800 STEP 20 / STORE 3

5000 STEP 100 / STORE 3RETURNSAVE DATA 106DEASSIGN 19

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References

[1] K. Masubuchi, "Analysis of Welded Structures-Residual Stresses, Distortion, andTheir Consequences" Pergamon Press, 1980.

[2] Y.V.L.N. Murthy, G. Venkata Rao, P. Krishna Iyer, "Numerical Simulation ofWelding and Quenching Processes Using Transient Thermal and Thermo-ElastoPlastic Formulations" Computers & Structures, vol. 60, No.1, pp. 131-154, 1996.

[3] P. Michaleris, A. DeBiccari, "Prediction of Welding Distortion" Welding Journal,. vol. 76(4): 172-180s, 1997

[4] S. Sarkani, V. Tritchkov, G. Michaelov, "An efficient approach for computingresidual stresses in welded joints" Finite Elements in Analysis and Design, vol.35, pp.247-268,2000.

[5] Bora Yildirim, "Nonlinear Thermal Stress/Fracture Analysis of Multilayer Structuresusing Enriched Finite Elements" Lehigh University, 2000.

[6] R Dykhuizen, D. Dobranich, "Scaling Analysis for LENS process" Sandia NationalLabs, 1998

[7] V. Pavelic, R Tanbakuchi, a.A. Uyehara, and P.S. Myers, Welding Journal ResearchSupplement, vol. 48, pp.295-305, 1969

[8] E. Friedman, Journal Pressure Vessel Technology, Trans. ASME, vol. 97, pp.206-213,1975

[9] F. W. Krutz, L.J. Segerlind, Welding Journal Research Supplement, vol. 57, pp.211216, 1978

[10] J. Goldak, A. Chakravarti, M. Bibby, "A New Finite Element Model for WeldingHeat Sources" Metallurgical Transactions B, Volume 15B, pp. 299-305, June 1984.

[11] N.S. Boulton, H.E, Lance Martin, "Residual Stresses in Arc-welded Plates" Proc.Inst. Mech. Engrs., vol.133, pp 295-347, 1936

[12] D. Resenthal, "Mathematical theory and heat distribution during welding andcutting"Welding J. vol. 20 (5), pp 220-234, 1941

[13] K. Masubuchi, F.B. Simmons, RE. Monroe, "Analysis of thermal stresses and metalmovement during welding" Technical Report NASA-TM-X-61300, N68-37857,Battele Memorial Institute, RSIC-820, Redstone Scientific Information Center, 1968

[14] 1.H. Argyris, 1. Szimmat, and K.J. Willam, "Computational Aspects of WeldingStress Analysis" Computer Methods in Applied Mechanics and Engineering, vol. 33,pp. 635-666, 1982

[15] E.F. Rybicki, D.W. Schmueser, R.B. Stonesifer, J.J. Groom, and H.W. Mishler, "AFinite-Element Model for Residual Stresses and Deflections in Girth-butt weldedpipes" Journal of Pressure Vessel Tech., vol. 100, pp 256-262, 1978[16] V.I. Papazoglou, K. Masubuchi, "Numerical Analysis of Thermal Stresses duringwelding including phase transformation effects" Journal of Pressure Vessel Tech., vol.104, pp 198-203, 1982

[17] a.A. Vanli; P. Michaleris, "Distortion Analysis of Welded Stiffeners" Journal ofShip Production, vol. 17(4), pp 226-240, 2001

[18] P. Tekriwal. 1. Mazumder, "Finite element analysis of three-dimensional transientheat transfer in GMA welding" Welding 1. vol. 67, pp 150-156, 1988

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[19] P. Tekriwal, J. Mazumder, ''Transient and residual thermal strain-stress analysis ofGMAW" 1.Material Technology, vol.113, pp 337-343, 1991[20] R.I. Karlsson, B.L. Josefson, "Three-dimensional FE analysis of temperatures andstresses in a single-pass butt-welded pipe" Journal of Pressure Vessel Tech., vol. 112,pp 77-84, 1990[21] S.B. Brown, H. Song, "Finite element simulation of welding of large structures"

Journal ofEngineering for Industry, vol. 114, pp. 441-451, 1992[22] S.R. Daniewicz, M.D. McAninch, B. McFarland, and D. Knoll, "Application ofdistortion control technology during fabrication of large offshore structures"AWS/ONRL International Conference on Modeling and Control of Joining Processes,Orlando, Fla., 1993[23] M.V. Deo, P. Michaleris, 1. Sun "Prediction of Buckling Distortion of WeldedStructures" Science and Technology ofWelding and Joining, 2002[24] L.W. Lu, 1.M. Rides, P. Therdphithakvanij, S. Jang, 1. Chung, "CompressiveStrength of AL-6XN Stainless Steel plates and Box columns" ONR N00014-99-0887,ATLSS report No.02-04, Lehigh University, Bethlehem, PA, 2002[25] L.W. Lu, A.A. Pang, "Structural Instability Failure Modes: Survey of ExistingModels and Methods of Analysis" Final Report for phase 1.1, TDL L91-01, ATLSS,Lehigh University, Bethlehem, PA, 1992[26] J.R. Dydo, W.Cheng, "Stainless steel buckling and angular distortion study" Navalsurface warfare center Project No. 42372-GDE, 1999[27] A.C. R

Documents

Welding Simulation of Ship Structures Using Coupled Shell and Sol