Finite element analysis and simulation of welding: a bibliography (1976 - 1996)

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Modelling Simul. Mater. Sci. Eng.4 (1996) 501–533. Printed in the UK

Finite element analysis and simulation of welding: abibliography (1976–1996)

Jaroslav MackerleLinkoping Institute of Technology, Department of Mechanical Engineering, S-581 83 Linkoping,Sweden

Received 14 February 1996, accepted for publication 23 July 1996

Abstract. This paper gives a bibliographical review of the finite element methods (FEMs)applied to the analysis and simulation of welding processes. The bibliography at the endof the paper contains references to papers, conference proceedings and theses/dissertationson the subject that were published between 1976 and 1996. The following topics areincluded: modelling of welding processes in general, modelling of specific welding processes,influence of geometrical parameters, heat transfer and fluid flow in welds, residual stresses anddeformation in welds, fracture mechanics and welding, fatigue of welded structures, destructiveand nondestructive evaluation of weldments and cracks, welded tubular joints, pipes and pressurevessels/components, and welds in plates and other structures/components.

1. Introduction

Welding is defined by the American Welding Society (AWS) as a localized coalescence ofmetals or nonmetals produced by either heating of the materials to a suitable temperature,with or without the application of pressure, or by the application of pressure alone, andwith or without the use of filler metal. There are various welding processes used in industrytoday. The main factors for their distinctions are the source of the energy used for welding,and the means of protection or cleaning of the welded material.

Arc welding is the most widely used process in industry because of its versatility andlow cost. Resistance welding is also a low-cost, high-production process used first of allin the assembly of car bodies and similar parts made of thin metal sheets. Other weldingprocesses to be named are solid-state welding, laser beam welding, induction welding,electroslag welding, electron beam welding, etc.

During last two decades many of the existing welding processes have been simulatedby numerical methods, especially by the finite element methods. A numerical simulationof a welding process is not easy, as it is a complex process involving the interaction ofthermal, mechanical, electrical and metallurgical phenomena. The welding process has thetransient character where a nonlinear, local zone translates through an elastic structure.

This paper gives a review of published papers dealing with finite element methodsapplied in the area of welding processes. For a more efficient information retrieval system,the lists of references of papers published between 1976 and 1996 are divided into thefollowing topics:

• modelling of welding processes in general• modelling of specific welding processes

0965-0393/96/050501+33$19.50c© 1996 IOP Publishing Ltd 501

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• influence of geometrical parameters• heat transfer and fluid flow in welds• residual stresses and deformations in welds• fracture mechanics and welding• fatigue of welded structures• destructive and nondestructive evaluation of weldments and cracks• welded tubular joints, pipes and pressure vessels/components• welds in plates and other structures/components.

This paper is organized into two parts. In the first, each topic is handled and current trendsin the application of finite element techniques are mentioned. The second part, an appendix,lists papers published in the open literature for the period between 1976 and 1996 on subjectspresented above. References have been retrieved from the author’s database, MAKEBASE[1, 2]. Readers interested in the finite element literature in general are referred to [3] or tothe author’s Internet Finite Element Book Bibliography (http://ohio.ikp.liu.se/fe/index.html).

2. Finite elements in welding processes

2.1. Modelling of welding processes in general

Many welding processes have been developed. They differ in the manner in which heatis applied and in the equipment used. Some of these processes require forging or pressing(plastic welding) to effect the weld; others bring the metal to a fluid state (fusion welding)and require no pressure.

The finite element simulations usually involve very dense meshes and emphasizeresolution within the local weld zone. In contrast to these studies, interactions betweenthe weld zone and the overall elastic welded structures can also be treated. In these casescomplications arise from the elastic coupling between the local weld zone and the overallstructure.

Some main topics include: thermal stresses in welds; finite element models for weldingprocesses—viscoplastic analysis, thermoviscoplastic analysis, thermoelastoplastic analysis,transformation plasticity; thermo-metallurgical modelling; study of the solid–fluid transitionzone; new material laws; microstructural and macrostructural analysis; computationalaspects of welding processes; element library and modelling; welding of large structures;weld analysis for long welds; reliability analysis; two- and three-dimensional simulations.

2.2. Modelling of specific welding processes

Fusion welding, electrical resistance welding, solid-phase welding, liquid-solid phase joiningand adhesive bonding are the most important categories that constitute the joining process.In this paper the first three categories plus other, not so frequently used, welding processesare handled. Definitions of welding processes can be found in [4].

Simulation of arc welding can be characterized by two stages—by tailoring the shapeof the fusion zone (melting) and simulating the solidification process within the prescribedshape. Arc welding is a group of welding processes which produces coalescence of metalsby heating them with an arc, with or without the application of pressure, and with orwithout the use of a filler metal. Gas tungsten arc (GTA) welding is a process whichproduces coalescence of metals by heating them with an arc between a tungsten electrodeand the work. Shielding is obtained from a gas or gas mixture; pressure and filler may ormay not be used. This process has sometimes been called tungsten inert gas (TIG) welding,

Finite element analysis and simulation of welding 503

a nonpreferred term. Gas welding includes processes where gases are used in a combinationto get a hot flame.

Resistance welding is a group of welding processes which produces coalescence ofmetals with the heat obtained from resistance of the work to electric current in a circuit ofwhich the work is a part, and by the application of pressure. Resistance spot welding is aprocess which produces coalescence at the faying surfaces in one spot by the heat obtainedfrom the resistance to electric current through the work parts held together under pressureby electrodes. It is commonly used, for example, in the automobile industry for its highefficiency and excellent quality control.

Laser beam welding offers high speed and precision, and provides consistent weldintegrity and low heat distortion, compared with conventional resistance spot welding.

Friction welding is a process where the heat for welding is produced by direct conversionof mechanical energy to thermal energy at the interface of the workpieces without theapplication of other energy or heat from other sources.

Listed references in the appendix include simulations of the following welding processes:arc welding, GMA welding, GTA welding, TIG welding, submerged arc welding, plasmaarc welding, solid-state welding, extrusion welding, friction welding, ultrasonic welding,resistance spot welding, butt welding, laser beam welding, laser microwelding, electroslagwelding, capacitor discharge welding, diffusion welding, thermite welding, single-pass andmultipass welding.

2.3. Influence of geometrical parameters

Welded structures usually involve complicated geometry and are under severe thermal loadsduring the process of welding. Geometric parameters significantly affect properties ofwelded structures. Their influence can be investigated by parametric studies. The resultsshould be valid for a wide range of other welded structures/components.

Some topics include: influence of geometrical parameters on stress concentration factors,on the strength of joints, on the fatigue strength, creep behaviour, etc.; effects of weldconfigurations on stress/strain fields; design concepts.

2.4. Heat transfer and fluid flow in welds

Heat and mass transfer that occurs in the weld and its surroundings as well as micro- andmacrophenomena affecting the weld properties are also complicated processes, and theircomprehensive and complete correct solutions have yet to be derived.

Some topics include: two- and three-dimensional heat transfer models, transient heattransfer, prediction of temperature distribution, thermal process with state or phase change,thermal shock studies, high-temperature creep, weld cooling, thermal prestraining analysis,viscous flow in welds, coupled fluid flow and heat transfer problems, analysis of a movingheat source, adaptive techniques.

2.5. Residual stresses and deformations in welds

Because a weld is locally heated by the welding heat source its temperature distributionsare not uniform and change as welding progresses. The strains produced during this processare accompanied by plastic upsetting and, as a result, residual stresses remain after weldingis completed. Shrinkage and distortions are also produced. Distortions and residual stressescause significant problems in the welding of large structures; they can be a major factor for

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cracking and fracture problems in structures. Preheating of joints is an effective method ofreducing the cooling rate of the weld which reduces these distortions and residual stresses.Postwelding heat treatment can also be used. It relieves internal stresses and controls themicrostructure of the weld.

Some topics include: two- and three-dimensional calculations of residual stressesand deformations in welds, thermomechanical analysis of residual stresses, transformationplasticity and residual stresses, the prediction of residual stresses, effects of residual stresseson significance of defects and weld joint strength, characterization of residual stresses,welding stresses during phase transformation, residual stresses generation and relaxation,residual stresses and their redistribution during annealing, residual stress formation duringplastic welding, mechanical stress relief treatment of residual stresses, residual stresses inthick section weldments.

2.6. Fracture mechanics and welding

Weld joints are characterized by differences in mechanical properties produced bygeometrical, material and metallurgical discontinuities. The heat affected zone is usuallya source of failure of welded structures/components. The quality of welding has a stronginfluence on the strength of fabricated structures. The presence of cracks, defects andresidual stresses is a danger to structures in service. The study of crack problems inconnection with welding has received much attention in experimental and computationalfracture mechanics.

Some topics in this area of interest are: two- and three-dimensional linear and nonlinearanalysis of cracks in welds, simulation of crack growth, dynamic crack propagation inwelded joints, behavior of cracks in a dissimilar weld, effect of metal mismatch on fracturemechanics parameters, failure of welds at elevated temperatures, creep fracture mechanics,continuum damage mechanics, creep damage mechanics, brittle fracture strength of welds,ductile fracture criteria for weld structures, stress intensity factor computations,J -integralestimation in weld geometries; ultimate strength of welded structures, weld toe cracks,through-thickness cracks, surface cracks, internal defects in welds, stress-corrosion cracking,cracks in pipe welds, finite elements for fracture mechanics analysis of welds, reliabilityanalysis.

2.7. Fatigue of welded structures

One of the main features of fatigue analysis of welds is the reduction in lifetime caused bynotch sensitivity due to stress concentration at the toe of the weld reinforcement. Paperspublished in scientific journals investigate the effects that welding has on fatigue crackgrowth, in particular the study of the rate of fatigue crack growth in the base metal, heat-affected zone and weld metal. The practical analysis of the weld-notch effect is of majorimportance in fatigue and fracture assessments.

Some topics of interest are: fatigue crack growth of welded joints; influence ofresidual stresses on the fatigue crack growth; influence of bending stresses on fatigue crackpropagation; influence of misalignment on the fatigue strength; effect of weld discontinuitieson the fatigue strength; effect of weld geometry on fatigue crack propagation; fatigue crackinitiation; influence of cathodic protection on the fatigue resistance; creep fatigue; fatiguepredictions of T-joints, cruciform joints, plate joints, fillet welded joints, thin-walled welds,spot-welded joints, corner welded joints, box-section beams, bellows, pressure vessels,pipes, offshore structures, ship structures.

Finite element analysis and simulation of welding 505

2.8. Destructive and nondestructive evaluation of weldments and cracks

A variety of weld cracking tests estimate the parameters of heterogeneous material resistanceagainst crack propagation. Quality control and nondestructive evaluation are essential ifwelding defects are to be eliminated and high reliability of welds is to be maintained.These destructive and nondestructive evaluations of weldments and cracks can be verifiedby the finite element computations.

Some subjects included in this section are: destructive and nondestructive experimentalanalysis and numerical verification; ultrasonic nondestructive testing (NDT), acousticemission monitoring; infrared thermography, explosive testing of weldments; experimentalmodal analysis, a strain gauge technique for fatigue crack monitoring, real-time controlmethodology in resistance spot welding, inverse finite element techniques for evaluationof measurements, experimental and numerical analysis of temperature distribution duringwelding, experimental and numerical determination of stress/strain concentration factors ofwelded joints, experimental and numerical studies of the failure behaviour of welded joints,experimental and numerical analysis of residual stresses.

2.9. Welded tubular joints, pipes and pressure vessels/components

The topics in this section deal with linear and nonlinear analysis of deformations andstresses of: pipe and elbow welds, tubular joints, offshore structures, cylindrical shells,pressure vessels and components, reactor technology components, tubular frame structures,storage tanks, etc.

2.10. Welds in plates and other structures/components

This last section handles the linear and nonlinear analysis of welds in: plates, gusset plates,beam-to-column connections, box beams, girders, lugs, diaphragms, honeycomb structures,endplate connections, stiffened panels, trusses and frames, solar receiver panels, weldedstructure gears.

Acknowledgments

The bibliography presented in the appendix is by no means complete but it gives acomprehensive representation of different finite element applications on the subjects. Theauthor wishes to apologize for the unintentional exclusions of missing references and wouldappreciate receiving comments and pointers to other relevant literature for a future update.

Appendix. A bibliography (1976–1996)

This bibliography provides a list of literature references on finite element applicationsin welding. Presented listings contain papers published in scientific journals, conferenceproceedings, and theses/dissertations retrospectively to 1976. References have been retrievedfrom the author’s database, MAKEBASE. The COMPENDEX database, Metals Abstractsand Applied Mechanics Review have also been checked. Presented references are groupedinto the same sections as listed in the first part of this paper.

The emphasis of this bibliography is to list, first of all, papers published in variousinternational journals. There have been numerous national and international conferencesand symposia held worldwide but the conference proceedings are a source of never-ending

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bibliographical confusion. No review on conference proceedings can ever be comprehensivebut some conferences dealing fully/partially with welding and finite elements have beenexamined and a selection of references is also presented in this paper. The main criticismof conferences is that the material presented is often a repetition of what is publishedelsewhere in the literature, and also the complaint of uneven quality of papers is often heard.Surveys have shown low usage of published conference proceedings in practice. Also, manyimportant conference papers are published later in an edited version in international journals.

References are not arranged chronologically but sorted in each category alphabeticallyaccording to the first author’s name. If a specific paper is relevant for several subjectcategories, the same reference can be listed under respective section headings.

Subjects not included in this bibliography are: optimization techniques, brazing andsoldering; solidification processes in general.

Modelling of welding processes in general

Anon 1984Modeling of Casting and Welding Processes II(New York: Metall. Soc. IME)Argyris J Het al 1982 Computational aspects of welding stress analysisComp. Meth. Appl. Mech. Eng.33 635–66Bammann D J and Oretga A R 1993 The influence of the Bauschinger effect and yield definition on the modeling

of welding processesModel. Cast. Weld. Adv. Solidif. Proc. (Palm Coast)pp 543–51Brown S B and Song H 1992 Finite element simulation of welding of large structuresJ. Eng. Industry ASME114

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Industry ASME115 415–23Budden P J and Phillips J 1987 The finite-element stress-analysis of welded joints1st Int. Conf. Comp. Tech. Weld.

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Orleans)PED 64 (ASME) pp 861–72Cerjak H (ed) 1995Mathematical Modelling of Weld Phenomena 2(London: Institute of Materials)Cerjak H and Easterling K E (eds) 1993Mathematical Modelling of Weld Phenomena(London: Institute of

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finite element methodPhD ThesisMcMaster UniversityChidiac S E and Mirza F A 1993 Thermal stress analysis due to welding processes by the finite element method

Computers Structures46 407–12Dawson P R 1980 Viscoplastic modeling of upset welding using the finite element methodProcess. Model. Tools

Proc. ASMpp 151–72DeGiorgi V G et al 1990 Numerical prediction of welded joint performance—relative criticality of weld defect

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29 95–113Friedman E 1978 Analysis of weld puddle distortion and its effect on penetrationWeld. J.57 161–6Gerald J and Ragout I 1994 Design concepts for large welded connectionsWeld. Res. Abroad40 32–5Giamei A F and Abbaschian G J (eds) 1988Modeling and Control of Casting and Welding Processes IV(Minerals,

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Mech.: Conc. Comp.ed S Valliappan (Rotterdam: Balkema) pp 889–97Henshall G Aet al 1990 Finite element analysis of interlayer welds loaded in tensionWeld. J.69 S337–45Hibbitt H D 1978 Application of the finite element method to welding problemsUS–Japan Sem. Interdisc. Finite

Elem. Anal. (Cornell University)pp 417–51Hsu M B 1977 Analysis of welds by the finite element methodNum. Model. Manuf. Proc.ed R F Jones (ASME)Jansson L G 1995 Nonlinear analysis of a guide and its stitch welds for repeated loadingComputers Structures56

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510 J Mackerle

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