LICENTIATE THESIS. Finite Element Modelling and Simulation of Welding of Aerospace Components

Transcription

1 003:7 LICENTIATE THESIS Finite Element Modelling and Simulation of Welding of Aerospae Components ANDREAS LUNDBÄCK Department of Applied Physis and Mehanial Engineering Division of Computer Aided Design 003:7 ISSN: ISRN: LTU - LIC /7 - - SE

2 Prefae The researh presented in this thesis has been arried out at the Division of Computer Aided Design at Luleå University of Tehnology in lose ooperation with Volvo Aero and Motoren und Turbinen Union, Germany. The finanial support has been provided by the MMFSC 1 - projet, a European Union funded projet within the 5 th framework programme and Luleå University of Tehnology. I would first like to thank my supervisor Professor Lars-Erik Lindgren for his support and valuable guidane during the ourse of this work. My olleague Daniel Berglund deserves speial thanks for his support and guidane in the initial phase of this work. Many thanks also to all my friends and olleagues at Luleå University of Tehnology for all the disussions during the offee brakes. It is inspiring to work within suh a pleasant working environment. Finally I would like to thank my family: Ann-Katrin, Vitor, Luas and Clara. Thank you for your support, enouragement and just for being there! Luleå Maj 003 Andreas Lundbäk 1 Manufaturing and Modelling of Fabriated Strutural Components

3 Abstrat Fusion welding is one of the most used methods for joining metals. This method has largely been developed by experiments, i.e. trial and error. The problem of distortion and residual stresses of a struture due to welding is important to ontrol. This is espeially important in the aerospae industry where the omponents are expensive and safety and quality are highly important issues. The safety requirements and the high osts of performing experiments to find different manufaturing routes is the motivation to inrease the use of simulations in design of omponents as well as its manufaturing. Thus, in the ase of welding, one an evaluate the effet of different fixtures, welding parameters et on the deformation of the omponent. It is then possible to optimise a hain of manufaturing proesses as, for example, the welding residual stresses will affet the deformations during a subsequent heat treatment. The aim of the work presented in this thesis is to develop an effiient and reliable method for simulation of the welding proess using the Finite Element Method. The method may then be used when designing and planning the manufaturing of a omponent, so that introdution of new omponents an be made with as little disturbane as possible. In the same time the developed tool will be suitable for the task to perform an optimal design for manufaturing. Whilst this development will also be valuable in prediting the omponent's subsequent inservie behaviour, the key target is to ensure that designs are reated whih are readily manufatured. If this understanding is aptured and made available to designers, true design for manufature will result. This will lead to right first time produt introdution and minimal ongoing manufaturing osts as proess apability will be understood and designed into the omponent. When reating a numerial model, the aim is to implement the physial behaviour of the proess into the model. However, it may be neessary to ompromise between auray of the model and the required omputational time. Different types of simplifiations of the problem and more effiient omputation methods are disussed. Methods for alleviating the modelling, in partiular the reation of the weld path, of omplex geometries is presented. Simulations and experiments have been arried out in order to validate the models. Keywords Finite Element Method, Welding, Manufaturing Simulation, Aerospae Engineering

4 Table of Contents 1. INTRODUCTION THE FINITE ELEMENT METHOD IN A HISTORICAL PERSPECTIVE BACKGROUND AIM AND SCOPE OF PRESENT RESEARCH.... WELDING IN AEROSPACE ENGINEERING WELDING METHODS...3. EFFECTS OF WELDING SIMULATION OF WELDING GENERAL ASSUMPTIONS IN MODELLING CURRENT WELDING SIMULATIONS CREATION OF WELD PATH HEAT INPUT MATERIAL MODEL ELEMENT ACTIVATION EFFICIENT COMPUTATION SUMMARY OF APPENDED PAPERS PAPER A PAPER B PAPER C DISCUSSION AND FUTURE WORK REFERENCES...14

5 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components 1. Introdution 1.1 The Finite Element Method in a Historial Perspetive The history of the finite element method is about hundred years, but it took another fifty years before the method beame useful. In 1906 a paper was presented where researhers suggested a method for replaing the ontinuum desription for stress analysis by a regular pattern of elasti bars. Later in 1943, Courant [1] proposed the finite element method as we know it today. None of the forgoing work was of any pratial use though, sine there were no omputers available at that time to solve the large set of simultaneous algebrai equations related to the method. In the early 1950 s engineers, mainly in the aerospae industry, started to use the method of finite element more frequently. It was still only a number of exlusive groups that where able to use the method, sine digital omputers had not beome widespread yet and they were very expensive. The atual name finite element method was oined by Clough in 1960 and in the late 1960 s and early 1970 s large general-purpose programs emerged, suh as ANSYS, NASTRAN and MARC. However, these programs were still written for a partiular mainframe, it was not until the mid-1980 s general-purpose programs began to appear on personal omputers and thereby beame more widespread. Today hundreds of thousands engineers all over the world are using the finite element method in their everyday work. The above text is an extrat from the books by Cook et al. [] and Belytshko et al. [3]. In the paper by Felippa [4] a omprehensive review of the history of FEM an be found. 1. Bakground This researh is a part of the projet Manufaturing and Modelling of Fabriated Strutural Components (MMFSC). This is an EU funded projet within the 5 th Framework Programme with a number of aeroengine ompanies. The work presented here has been done in lose ooperation with Volvo Aero Corporation (VAC) and Motoren und Turbinen Union (MTU). The main objetive of the MMFSC projet is to develop, for aero-engine strutures, alternative manufaturing strategies to single-piee asting, whih is urrently supplied by a non-eu manufaturer, and whih leaves little room for in-house design flexibility. MMFSC [5] Fabriation, the alternative to single-piee asting, is less reliant on fixed tooling and an use ombinations of materials and tehniques (asting, forging, sheet forming, welding, mahining et.), eah to its greatest advantage where needed. Also a substantial improvement in the utilisation of material is antiipated ompared to a single-piee asting. This is due to that different material thiknesses an more easily be assigned in different parts of the omponent when the method of fabriation is used. The need for fabriation is of speial interest for large omponents where there is only a few (one) manufaturers available. This leads to long delivery times and high osts. 1

6 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components Fabriation is not easily implemented in the manufaturing proess due to the high safety requirements and the lak of fundamental understanding of the proess. A number of manufaturing proesses are analysed within the MMFSC projet. The effet of the individual proesses is studied and also the ombined effets of previous proesses. The long term goal, outside the sope of this work though, is to be able to reate a virtual prototype of the omponent. The virtual prototype will be built up from the designed geometry and the result from all the manufaturing proesses applied. After the manufaturing of the omponent is ompleted the virtual prototype will be upgraded, if there are any, and fed with the in-servie loadings. Figure 1 is a somewhat extended figure from Runnemalm [6]. The extension is that the whole lifetime of the omponent is added, the in-servie loading and possible upgrading. This will give valuable information, both when maintenane deisions are made and when designing the next generation of omponents. Feedbak Produt requirements Conept phase Inventory of known methods DESIGN Tools for funtional evaluation Definition phase Computer based engineering models Preliminary preparation Tools for planning of manufaturing MANUFACTURING Verifiation phase Detailed Preparation Physial produt Data from omponent in-servie applied to digital opy of produt Digital version of produt Servies Maintenane upgrading et. Feedbak Figure 1. Use of omputer models for design of omponents, manufaturing routes and supporting maintenane. 1.3 Aim and Sope of Present Researh The aim of the work presented in this thesis is to develop a method and a model for simulation of the welding proess of large and omplex omponents. The simulations an then be used when designing and planning the manufaturing of the fabriation of omponents. The researh question is: Is it possible to simulate the proess of welding of a omplex omponent with adequate auray for prediting the distortions in the final geometry of the omponent? The work has been foussing on validation of the model on smaller test piees so far. The welding methods that have been studied are laser and eletron beam welding and the material used is Inonel 718.

7 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components. Welding in Aerospae Engineering.1 Welding Methods There exist a number of different welding methods. The most ommon methods in the aerospae industry are Gas Tungsten Ar Welding (GTAW), Eletron Beam welding (EB) and Laser beam welding. In the book by Radaj [7], a thorough desription of these proesses an be found. In Figure the power densities for the different welding proesses are shown. Stone [8] desribes both the history and the physis of the EB welding proess in some detail. Below a short introdutory of these proesses will follow. Figure. Power density for different welding proesses, Radaj [7]. In the ase of GTA-welding the heat is generated by the disharge between the anode and the athode using a non-melting eletrode. An inert gas is used as shield against oxidation and the proess an be arried out with or without filler material. The power density of this proess is the lowest of those mentioned above. Material thiknesses between 0.5 and 3 mm an easily be welded with single-pass welds. If larger thiknesses are to be welded, then multi-pass welding has to be adopted. In laser beam welding a high power density beam, oherent foussed light, is direted at the welding spot, optial lenses are used to fous the light. The beam is absorbed in a thin surfae layer and if the power density is adequate the surfae is fused. A digging proess now starts, provided that suffiient power is applied, and a vapour apillary is formed. The vapour apillary is the atual welding heat soure. If the work piee is moved relative to the beam the vapour apillary will form a keyhole. The penetration depth is restrited to 5 10 mm, depending on whih type of laser used, due to the defous of the beam. Eletron beam welding is another high power density welding method. The power density is even higher than in laser beam welding. The proess is similar to the laser welding proess, but in EB-welding it is a hot athode that aelerates eletrons towards the welding spot and eletro-magneti lenses are used to fous the beam. Whilst the penetration depth of the laser proess is restrited to relative small depths the penetration depth in EB-welding an reah up 3

8 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components to 30 mm. One major drawbak with EB-welding is that it has to be arried out in vauum. The reason why it has to be arried out in vauum is that the eletrons would be retarded or deteriorated by other partiles too muh otherwise. Reently medium vauum and nonvauum eletron beam welding systems has been introdued, whih will extend the usability of this proess.. Effets of Welding During the welding proess a loal area is heated up rapidly with high thermal gradients as a onsequene. The material expands as a result of being heated but the expansion is restrained by the surrounding older, and stronger, bulk. This will give rise to the thermal stresses. Sine the yield limit is lowered in the area of elevated temperature, plasti strains will develop in the weld region. When the weld area ools down the material in that area will be too small, i.e. the volume has been redued. During ooling the material will retrieve its strength, normally at an elevated level due to plasti hardening, whih in turn gives rise to the residual stresses. The deformations due to welding are driven by the thermal expansion (temporarily) and the residual stresses (permanently). Stress and deformation are largely opposed. A high degree of geometrial restraint in welding results in high stresses and small deformations while an unrestrained weld produes lower stresses but larger deformations. As a onsequene the welding reliability of the design is assessed primarily on the basis of welding residual stress analysis, whereas welding feasibility in manufaturing is assessed primarily on the basis of welding deformation analysis. In Figure 3 the basi deformation modes for a retangular plate with entri joining weld are presented. Figure 3. Deformation modes of a retangular plate with a entri jointing weld seam. 4

9 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components In the book by Radaj [7], the residual stresses are defined and ategorized as following. Residual stresses are internal fores, in equilibrium only with themselves over the whole domain of the body, without external fores ating. Stresses arising during the welding proess, due to inhomogeneous thermal expansion, an be referred to as internal stresses if the body is mehanially unonstrained and are termed thermal stresses. The residual stresses an be distinguished in different levels, first, seond and third order residual stresses. First order residual stresses, I, extend over marosopi areas and are averaged stresses over several rystal grains. Seond order stresses, II, ats between rystals or rystal subregions. Third order residual stresses, III, at on the interatomi level, e.g. single disloations. It is mainly the first order stresses that are of interest for engineering purposes and thus also in this thesis. 3. Simulation of Welding The method of finite element was originally adopted for linear-stati strutural analysis and dynamis. The method was later extended for dealing with geometri and material non-linear problems. The pioneering work within simulation of welding in the early 1970s, e.g. Ueda and Yamakawa [9] and Hibbit and Maral [10], inluded material non-linearity and the oupling between thermal and mehanial analysis. In the latter also geometri nonlinearity s, suh as large strain and deformations where enountered for. Maral [11], in his review, later stated that welding is perhaps the most nonlinear problem enountered in strutural mehanis. In the review by Goldak et al. [1] it is suggested that the diffiulties experiened by the pioneers, but still eminently qualified experts in nonlinear FEM, Hibbit and Maral disouraged others from entering the field. Their expertise is demonstrated by the fat that MARC, developed by Maral and Hibbit, and ABAQUS, developed by Hibbit, are the most highly regarded ommerial FEA-software for nonlinear problems. Despite this, quite a few researhers have entered the field during the last three deades and a list of what has been done would be very long. A large number of reviews whih summarizes the work during this thirty-year period have been published, e.g. [11-16]. One of the most reent is the omprehensive review, in three parts, by Lindgren [14-16]. This review not only ontains a large number of referenes of what has been done earlier and the state of the art today, but also reommendations of how and what to inlude in a model depending on the aim of the welding simulation. 3.1 General Assumptions in Modelling Before a model for simulation of welding is reated some questions have to be answered, what is the aim of this simulation?, whih auray is desired?, what kind of phenomena should be aptured?, et. In this work, the finite element models have been 3D solid element models as the aim of the simulations have been to validate the welding model on relatively small geometries. Later work will involve more omplex geometries and then shell elements may be needed. In the paper by Lindgren [17], definitions of different auray levels and omplexity levels, regarding the geometry representation, are presented. The models used in this work an be regarded as aurate and standard 3D models appropriate for obtaining residual stresses, as stated in [17]. 5

10 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components The finite element type used in all the simulations is a linear eight-noded element. Belytshko et al. [3] argues that it is better to use a larger number of linear elements than fewer higher order elements when non-linear problems are analysed. The oupling between the thermal and the mehanial analysis is done by the staggered approah. In the staggered approah the thermal analysis is lagging one step behind the mehanial analysis. The short time steps taken make this approximation negligible. To keep the strain field onsistent, onstant temperature through the element is assumed in the thermal analysis. Large deformation and an additive deomposition of the strain rates are also assumed. 3. Current Welding Simulations In order to simulate a omplex omponent or a hain of manufaturing proesses, as mentioned in the introdution, a reliable model has to be developed for eah speifi proess. It is important to know whih auray and reliability that an be expeted of the model when simulations are to be performed on a full sale omponent. This is espeially true if, as in this ase, it is a very expensive omponent. It is not partiularly probable that extensive measurements are going to be performed on suh omponents in prodution. Simulating a hain of proesses is not meaningful if not all the simulation models in that hain are aurate and reliable, a hain is not stronger than the weakest link. Figure 4 is a kind of roadmap of the steps that have been taken, or will be investigated, to realize the above stipulated. The approah within the MMFSC projet is to first validate the numerial models for eah proess individually on smaller test piees. When this is done, more omplex geometries and eventually the whole manufaturing hain will then be analysed. The first step towards welding simulation of a omplex geometry was to develop a method for reation of the weld path. A material model has been built up by utilization of the extensive material tests preformed within the projet. Different heat soures for the heat input are tested and validated and an element ativation tehnique is implemented to simulate the fusion of the welded material. Two strategies for effiient omputation, adaptive meshing and parallel omputation, have been evaluated. Other methods that are of interest are the substruturing and the loal/global tehnique. In the following setions eah part in Figure 4 will be explained in some detail. FE-Geometry Weld Path Validation Material Model Heat Input Element Ativation Simple Geometry Evaluation Effiient Computation Adaptive Meshing Parallel Computation Loal/Global Substrutures Complex Geometry Figure 4. Roadmap of the different steps towards more omplex geometries. 6

11 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components 3.3 Creation of Weld Path A method to determine the position of the heat soure in eah time inrement has been developed. This method alleviates the proess of defining the weld path espeially if the path is an arbitrary 3D line. The weld path is first defined in a system, e.g. a CAD-system, where the tools for handling omplex geometries normally are more developed than in the preproessors of the FE-systems. The weld path is thereafter exported as oordinate points to a file. During the initiation of the simulation the file with the weld path oordinates is imported and proessed into the FE-system via user subroutines, Figure 5. CAD Input file for FE-model FEA User subroutines Weld path Data Figure 5. Strategy for the reation of weld path. This method requires that there exist a geometry whih an desribe the weld path. The geometry may onsist of lines, shell- or a solid geometry. An example when utilizing this method for reation of an intriate weld path is shown in Figure 6. The figure is part of the paper by Lundbäk [18], a desription of the method in detail an be found in Lundbäk [19]. Figure 6. Example of usage of the desribed method. 7

12 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components 3.4 Heat Input In a welding simulation it is essentially the temperature hange, translated into thermal expansion in the mehanial analysis, whih is the external load in the model. The inrease of the temperature an generally be modelled in two different ways, presribed temperatures or by presribed heat input. When presribing the temperatures the temperature is given in eah node for the speifi time and position. The temperature is usually linearly ramped to the presribed value and thereafter followed by a onstant-temperature phase. This method has been used quite frequent, but mainly in D analysis. The other method, presribed heat input, whih is the today most ommonly used method, applies the heat input as a heat flux at the integration points whih is then onverted to the nodes as temperature loads. The most ommonly used heat soures of this kind have a Gaussian distribution, but heat soures with onstant distribution has also been used. Goldak et al. [0] proposed a volumetri heat soure, see Equation 1 and Figure 7, the so-alled double ellipsoid. This heat soure onsists of two ellipti regions, one in the front of the ar entre, z > 0, q f x, y, z 6 3 f f Q e 3 ab f 3x 3 y 3z a b f e e (1a) and the other behind the ar entre, z < 0. q r x 3x 3 y 3z 6 3 f rq a b r, y, z e e e 3 abr (1b) r f z a Welding diretion b y x Figure 7. Geometrial definition of the double ellipsoid heat soure. The double ellipsoid heat soure was initially intended to be used for modelling of GTAwelding [0]. Later Goldak et al. [1] reported that they had reeived the most aurate temperature field by ombining three heat soures, a double elliptial dis on the surfae, a double ellipsoid to model the diret impingement of the ar and another double ellipsoid to model the stirring effet of the molten metal. To model deep penetration welds, suh as eletron and laser beam welding, they reommended a onial distribution of power density 8

13 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components with a Gaussian distribution radially and a linear distribution axially. However, the atual formula for this onial heat soure was not presented in the paper. Stone et al. [1] used a ombination of a irular surfae flux and a oni volumetri soure. Both these soures had a uniform distribution of the power density. In Lundbäk and Runnemalm [], a ombined double ellipsoid and onial-ellipti heat soure is presented. The formula for the frontal part in the onial-ellipti heat soure, z > 0 as in the above definition, an be seen in Equation. q x, y, z a b 1 d z 3 1 d y x 6 f 3 f Q a e 1 e b () All the parameters, exept for b and d, orresponds to those in Equation 1a. The parameter b is the depth of the one, whih should be equal to the thikness of the material and d is the derease of the one width at the bottom surfae. Comparing these two methods, presribed temperatures and presribed heat input, it an be said that presribing the temperatures an be easier to use as means for heat input in some ases. This is espeially true in the D ase but less true in the 3D ase where the method of presribed heat input is probably easier to implement and use. The auray in the heating phase is also better in the latter method. There exist more advaned heat soure models, e.g. [3-5]. Sudnik et al. [3] used a thermodynamial steady-state model to alulate the thermal field in a laser beam weld. The result from suh models an be used in different ways, either by mapping of the temperatures diretly into the FE-model, i.e. presribed temperatures, or the result an be used as a validation of the FE-result. Hughes et al. [5] used a detailed finite volume model of the weld pool to alibrate the heat soure parameters in the FE-model automatially. In this work a model, modified to fit eletron beam welding, from Sudnik et al. [3] has been used to validate the FE-results. The gain by using the result from suh a model is that information and knowledge about the shape of the thermal field an be obtained. Some of these results an be obtained with experiments, i.e. ross setion mirographs. Other results, suh as the thermal field in the welding diretion inside the material, are in pratie impossible to obtain with experiments. The reason why the presribed temperature method was not hosen is that mapping the temperatures from a non-analytial model is a relatively time-onsuming task. Further it requires diret aess to the thermo-dynamial model, whih was not the ase in this work. 3.5 Material Model Two different materials and material models are used in this thesis, a martensiti stainless steel and the nikel based Superalloy Inonel 718. The material model for the stainless steel is a rate-independent termo-elastoplasti model. No aount is taken for the hardening due to plasti deformation or phase hanges tough. In the material model for Inonel 718 plastiity indued hardening is inluded. 9

14 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components 3.6 Element Ativation The welding proess an be performed with or without filler material depending on whih proess used and the requirement on the weld geometry. In the aerospae industry no underutting in the welds is aepted, i. e. the thikness of the material in the weld an not be less than in the surrounding material. Filler material is ommonly used in GTA and laser beam welding but less ommon in eletron beam welding. Nevertheless, some kind of element deativation and ativation has to be used disregarding of the welding proess if for example a butt welding is going to be modelled. Two different tehniques an be used, quiet elements or born dead. When using quiet elements the elements are ative during the whole analysis but the stiffness and the thermal ondutivity is very low so that the inative elements do not affet the rest of the model. With the other method, born dead element, the elements that are inative is not part of the system of equations until they are ativated. In this work the born dead tehnique has been used exlusively. The thermal and mehanial ativation is separated to enable the element to be heated up thermally but not ontribute to the mehanial stiffness. The riterion when an element is to be ativated is set as a distane relative the position of the origin of the heat soure. The plasti strain should be zeroed as long as the element is in liquid phase. Lindgren et al. [6] ompared the two methods on a multipass welding analysis of a thik plate. They found that both methods gave very similar result but the method of born dead elements was somewhat more effetive with respet to omputational ost. Different problems may arise depending on whih method used. Dereasing the stiffness, of the quiet elements, too muh will give an ill-onditioned stiffness matrix with numerial problems as a result. On the other hand, when using the born dead tehnique, if the nodes are ompletely surrounded by inative elements then these nodes will not follow the movements of the ative neighbour nodes. This an result in severely distorted, or even ollapsed, elements. Lindgren et al. [6] solved this problem by a smoothing tehnique. Lindgren and Hedblom [7] later developed a tehnique to ontrol the volume of the ativated elements, i.e. the filler rate, whih also optimised the position of the nodes for minimized element distortion and orret geometrial shape of eah weld pass. 3.7 Effiient Computation There exist a number of methods for dereasing the omputational time, or atually the walllok time of the simulation. The most obvious and straightforward is of ourse to redue the geometrial dimension, e.g. from a 3D solid model to a D plane strain model. Whether this is feasible or not depends on the sope of the simulation [17]. If it is deided that the analysis should give a detailed desription of the weld region and the whole struture should be taken into aount for, then the only hoie is a solid model at least lose to the weld. Below, some of these tehniques are desribed. Adaptive meshing is a tehnique that hanges the mesh density due to some riterion. The riteria an for example be temperature or strain gradients. If an element fulfils the riterion, e.g. it has a too steep strain gradient, it will be divided into smaller elements. The hild elements reated will inherent the properties and result, suh as temperature and strains, from the parent element. Sine this method does not hange the topology in the same sense that remeshing does and the mapping of data is kept to a minimum it is a relatively heap method 10

15 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components with respet to omputational ost. Due to that the mesh is loally refined by dividing elements, free nodes will our. These nodes must be onstrained to keep the mesh onsistent. This method was used in Berglund et al. [8]. The number of elements in the model will ontinuously inrease if the reated elements are not merged bak into the parent element, i.e. oarsening. If the loally refined area is ontrolled geometrially the method is alled rezoning. Runnemalm and Hyun [9] presented a tehnique that ombined error measurements from both the thermal and mehanial gradients and mesh refinement and oarsening. In this way they ould keep the number of elements to a minimum but still be able to keep a high resolution in areas with steep gradients. Mixing of shell and solid elements is of speial interest when performing welding simulations on thin-walled strutures. The solid elements are then onentrated near the weld region and the shell elements further away. Shells are superior to solids in the far field region as they improve the bending behaviour and the number of elements an be redued dramatially. In the region near the ar, solid elements are often required. This is due to that there is large gradients trough the thikness in that area and shell elements, by definition, are not suitable to model those. Näsström et al. [30] showed that a model with ombined solid and shell elements an be used in suh strutures. The substruture tehnique in welding is a tehnique where part of the mesh in the model is ondensed into a superelement and is thereby treated as a linear-elasti part of the struture. The rest of the struture is treated as non-linear, hereafter alled the loal zone. The stiffness from the superelement is then ating as a boundary ondition on the loal zone. Brown and Song [31] presented a tehnique for both dynamial rezoning, i.e. adaptive meshing, and substruturing. The position of the loal zone was frequently updated so that it followed the moving heat soure. Sine the substruture is unable to deal with non-linear phenomena, suh as plastiity, thermal expansion et., it is important to keep the loal zone large enough. Exept for the savings in omputational ost, there an be even larger savings in memory usage. This is due to that the stiffness matrix is redued in size when ondensing the elements into a superelement. Another method, similar to substruturing in some sense, is the use of a loal and global model. The loal model onsists of a dense mesh whih aommodates the heat soure and the global model provides the stiffness from the surrounding struture as boundary onditions to the loal model. Andersen [3] used this approah in the mehanial analysis, but the full model was used in the thermal analysis. The final method that will be presented in this setion is parallel omputation. Parallel omputation indues no simplifiations, hanges in geometri representation or anything as the above methods. It is simply a method to derease the omputational time, or atually the wall-lok time, for an analysis to be ompleted. There are similarities with the two above methods, substruturing and the loal/global approah. The model is divided into subdomains, domain deomposition, one subdomain for eah omputer proess. Boundary onditions are applied on the nodes on the interfae between eah subdomain and then the system of equations is solved for eah subdomain loally. An iterative proedure then starts to obtain equilibrium in the whole model. Esaig and Marin [33] studied different methods for domain deomposition to solve non-linear problems. They did not utilize parallel 11

16 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components omputation, they used this method for separating the elasti and plasti regions in a model. The idea with this is that the bandwidth dereases and the loal stiffness matrix representing the subdomains that are in the elasti region do not have to be realulated. They showed that a speedup fator between and 4 ould generally be ahieved. The limit of effiieny for parallel omputation is due to the ommuniation ost. That is, when the ost in time for ommuniation between the subdomains beomes higher than the gain for adding another proessor, then the limit is exeeded. Another limit, whih is more of a limitation when using this method in welding simulation, is the load balane between the proessors. As known, the non-linearities in welding simulation are highly loalised phenomena. This means that, generally, only one subdomain is dealing with a highly non-linear problem while the other is mainly linear. The result is that most of the proessors may be ideal muh of the omputational time, sine a linear problem is solved muh faster than a non-linear. In the work by Shi et al. [34] they showed that the speedup ratio for their problem was linear when solving the problem on a Shared Memory parallel omputer up to four CPUs. The speedup ratio, E n, is defined as the time for solving the problem on one CPU, T 1, divided by the time for solving the problem with n CPUs, T n, and the number of CPUs used, n, Equation 3. E n T T n 1 n (3) They also performed tests using a distributed parallel omputer, but here more CPUs where available. This test gave similar result, regarding the speedup ratio, as for the Shared Memory mahine up to 6 CPUs. When more than 6 CPUs was used the speedup ratio dereased rapidly so that the overall omputational time for 6 up to 16 CPUs where approximately the same. 4. Summary of Appended Papers 4.1 Paper A In this paper a method for alleviate the tedious work of defining the weld path is presented. The weld path an be defined in a CAD-system based on the geometrial model. The weld path is desribed by disrete oordinate points, whih are imported into the FE-model via user subroutines. The method is not restrited to a CAD-software for reation of the weld path, for example an off-line robot programming software ould also be used for this purpose. 4. Paper B A three-dimensional finite element model was used to simulate the laser beam welding proess of two stainless steel plate and experiments where performed to validate the model. Transient deformations and temperatures where measured during the experiment. A moving heat soure with a double ellipsoid shape was used for the heat input. To simulate the joining of the two plates, elements were ativated along the weld path using the borne dead tehnique. The material, a martensiti stainless steel, was modelled with temperature 1

17 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components dependent thermal and mehanial properties. Volumetri hanges, i.e. thermal dilatation, due to temperature and phase hanges were also inluded. No hardening, due to plasti strain or phase hange, where aounted for though. 4.3 Paper C In Paper C a thermo-mehanial model for simulation of eletron beam welding is presented. The model is validated experimentally and the result from an additional thermo-dynamial simulation is also used for validation of the thermal part of the FE-model. Two plates, made of Inonel 718, are butt welded together without addition of filler material. Parallel omputation is used to redue the overall omputational time. A ombined heat soure for modelling the deep penetration harateristi of the EB-weld is developed. The agreement of the results regarding the residual stresses and the temperature field is fairly good. The residual deformations, i. e. the butterfly angle, agrees with the experiment qualitatively but not in magnitude. 5. Disussion and Future Work The aim of the work presented in this thesis is to develop a method and a model for simulation of the welding proess of large and omplex omponents. The model must be reliable and effiient to be usable in the designing and planning of the manufaturing of the omponent. In order to derease the simulation time two different methods has been explored and used, parallel omputation and adaptive meshing. The method that is found to redue the simulation time the most is parallel omputation. Nevertheless, ombining those two methods would of ourse be preferable. Other methods that would be interesting to explore is the loal-global approah and mixing of shell and solid elements. The ultimate solution would of ourse be to ombine all of the above mentioned methods. In this thesis, the meaning of effiieny of a model is wider than just the omputational effiieny. The time for reation and definition of the model should also be inluded. Therefore a method for alleviating the tedious and time onsuming pre-proessing work of defining the weld path is developed. Not only the position of the heat soure is defined with this method, also the element deativation and ativation is automatially ontrolled via the weld path. Moreover, preliminary tests have been done using the rezoning tehnique. In these tests the position of the loally refined area where also defined using the weld path. Some of the developments needed to enable aurate welding simulations of large omplex strutures have been ompleted. However, the researh question posed in setion 1.3 annot be answered until a geometrially omplex model has been analysed. Validation of the heat soure has been refined ompared to the work by others through the use of ELSIM. The validation of the material modelling is based on the testing done in MMFSC and will be improved by the use of the approah in Alberg [35]. The ontinuing work will therefore fous on developing more effiient omputational methods. 13

18 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components 6. Referenes 1. R. Courant, Variational Methods for the Solution of Equilibrium and Vibration, Bulletin of the Amerian Mathematial Soiety, 1943, 49, pp R.D. Cook, D.S. Malkus and M.E. Plesha, Conepts and Appliations of Finite Element Analysis, third edition, Wiley & Sons, New York, T. Belytshko, W.K. Liu and B. Moran, Nonlinear Finite Elements for Continua and Strutures, Wiley & Sons, Chihester, C.A. Felippa, A historial outline of matrix strutural analysis: a play in three ats, Computers and Strutures, 001, Vol. 79, pp MMFSC website, 6. H. Runnemalm, Effiient Finite Element Modelling and Simulation of Welding, Ph.D thesis, Luleå University of Tehnology, No. 0, D. Radaj, Heat Effets of Welding temperature Field Residual Stress Distortion, Springer-Verlag, Berlin, H.J. Stone, The Charaterisation and Modelling of Eletron Beam Welding, Ph.D. Thesis, The University of Cambridge, Cambridge, United Kingdom, Y. Ueda and T.Yamakawa, Analysis of thermal elasti-plasti stress and strain during welding by finite element method, JWRI, 1971,, (), pp H.D. Hibbit and P.V. Maral, A Numerial, Thermo-Mehanial Model for the Welding and Subsequent Loading of a Fabriated Struture, Computers and Strutures, 1973, vol 3, pp P.V. Maral, Weld Problems, Strutural Mehanis Computer Programs, Charlottesville, University Press, 1974, pp J.A. Goldak, M. Bibby, J. Moore, R. House and B. Patel, Computer Modelling of Heat Flow in Welds, Metallurgial Trans B, 1986, 17B, pp L. Karlsson, Thermomehanial Finite Element Models for Calulation of Residual Stresses due to Welding, in Hauk et al. (eds), Residual Stresses, DGM Informationsgesellshaft Verlag, 1993, p L.-E. Lindgren, Finite Element Modelling and Simulation of Welding Part 1: Inreased Complexity, J. Thermal Stresses, 001, Vol 4, pp L.-E. Lindgren, Finite Element Modelling and Simulation of Welding Part : Improved Material Modelling, J. Thermal Stresses, 001, Vol 4, pp L.-E. Lindgren, Finite Element Modelling and Simulation of Welding Part 3: Effiieny and Integration, J. Thermal Stresses, 001, Vol 4, pp L.-E. Lindgren, Modelling for Residual Stresses and Deformations due to Welding Knowing what isn t neessary to know, in H. Cerjak (ed.), Mathematial Modelling of Weld Phenomena 6, 00, pp A. Lundbäk, CAD-support for Heat Input in FE-model, in H. Cerjak (ed.), Mathematial Modelling of Weld Phenomena 6, 00, pp A. Lundbäk, Modelling of Weld Path for Use in Simulations, Master s thesis, Luleå University of Tehnology, No. 7, J.A. Goldak, A. Chakravarti and M. Bibby, A new finite element model for welding heat soures, Metallurgial Trans B, 1984, 15B, pp

19 A. Lundbäk - Finite Element Modelling and Simulation of Welding of Aerospae Components 1. H.J. Stone, S.M. Roberts and R.C. Reed, A Proess Model for the Distortion Indued by the Eletron-Beam Welding of a Nikel-Based Superalloy, Metallurgial and Materials Transations A, 000, 31A, pp A. Lundbäk and H. Runnemalm, Validation of a Three Dimensional Finite Element Model in Eletron Beam Welding of Inonel 718, to be submitted for publiation. 3. W. Sudnik, D. Radaj and W. Erofeew, Computerized Simulation of Laser Beam Welding, Modelling and Verifiation, J. Phys. D: Appl. Phys., 1996, 9, pp T. Debroy, H. Zhao, W. Zhang and G.G. Roy, Weld Pool Heat and Fluid Flow in Probing Weldment Charateristis, in H. Cerjak (ed.), Mathematial Modelling of Weld Phenomena 6, 00, pp M. Hughes, K. Perileous and N. Strusevih, Modelling the Fluid Dynamis and Coupled Phenomena in Ar Weld Pools, in H. Cerjak (ed.), Mathematial Modelling of Weld Phenomena 6, 00, pp L.-E. Lindgren, H. Runnemalm and M.O. Näsström, Simulation of Multipass Welding of a Thik Plate, Int. J. Numer. Meth. Engng., 1999, Vol 44, pp L.-E. Lindgren and E. Hedblom, Modelling of Addition of Filler Material in Large Deformation Analysis of Multipass Welding, Int. J. Communiations in numerial methods in engineering, 001, Vol. 17, pp D. Berglund, L.-E. Lindgren and A. Lundbäk, Three-Dimensional Finite Element Simulation of Laser Welded Stainless Steel Plate, Proeedings of the 7th International Conferene on Numerial Methods in Industrial Forming Proesses, Balkema, Toyohashi, Japan, June 001, pp H. Runnemalm and S. Hyun, Three-dimensional welding analysis using an adaptive mesh sheme, Computer Methods in Applied Mehanis Engineering, 000, vol. 189, pp M. Näsström, L. Wikander, L. Karlsson, L.-E. Lindgren and J. Goldak, Combined Solid and Shell Element Modelling of Welding, IUTAM Symposium on the Mehanial Effets of Welding, 199, pp S.B. Brown and H. Song, Rezoning and Dynami Substruturing Tehniques in FEM Simulations of Welding Proesses, J. of Engineering for Industry, 1993, Vol. 115, pp L.F. Andersen, Residual Stresses and Deformation in Steel Strutures, Ph.D. Thesis, Department of Naval Arhiteture and Offshore Engineering, Tehnial University of Denmark, Y. Esaig and P. Marin, Examples of domain deomposition methods to solve nonlinear problems sequentially, Advanes in Engineering Software, 1999, Vol. 30, pp Q.-Y. Shi, A. Lu, H. Zhao, A. Wu and S. Wu, Preision and Effiieny Sensitivity of Some Key Tehniques in Thermo-mehanial Simulation of Welding Proess, Pro. of the 6 th Int. Conf. on Trends in Welding Researh, 003, pp H. Alberg, Material Modelling for Simulation of Heat Treatment, Lientiate Thesis, Luleå University of Tehnology, No. 7,

20 CAD-support for heat input in FE-model Andreas Lundbäk Computer Aided Design, Luleå University of Tehnology, Luleå, Sweden Abstrat Fusion welding is one of the most used methods for joining metals. This method has largely been developed by experiments, i.e. trial and error. The problem of distortion and residual stresses of a struture in and around a welded joint is important to ontrol. This is espeially important in the aerospae industry where the omponents are expensive and safety and quality are important issues. In this paper a method for alleviating the definition of heat input will be presented. 1 Introdution The developments during the last deades in welding simulations have lead to more realisti models and thereby from simple -D to more and more omplex 3-D models. This automatially requires more effort when reating the omputational models. The general CAD-programs have simplified the generation of mesh very muh. However, there is also need for a speifi support when reating welding models. The purpose of this paper is to present an approah that will alleviate the reation of omplex welding models. The user an then fous on modelling issues, like amount of heat input, material modelling et., instead of tedious work defining the heat input via the normal input file to the finite element ode. The heat soure should be able to move along any general 3D urve. The basi idea is that the user defines the weld path in a CAD-program with the geometry as basis. This information is later proessed in a FE-program by user-defined routines in order to reate nodal heat input orresponding to the weld for the finite element model. The heat soure is represented by a double ellipsoid but any heat input model an be implemented. Element ativation is used to onnet the elements along the weld path. Feedbak regarding energy input is given to the model, whih in turn adjusts the heat input so that orret amount of energy is given into the model. It is hoped that this simplifiation of the proess of modelling welding will ontribute to make simulations more ommonly used in the industry. Inreasing omplexity of models for welding simulation As the omputational apaity is inreasing and the FE-solvers are getting more effiient, the size of the used FE-models is steadily inreasing. Lindgren 1 states that the welding simulations are urrently only used in appliations where safety aspets are very important, like aerospae and nulear power plants, or when a large eonomi gain an be ahieved. One reason why welding simulation is not used in everyday pratie is of ourse the required omputer apaity. But the main reason is probably the lak of

21 expertise in modelling and simulation and the diffiulties in getting temperature dependent material parameters, espeially in the high temperature range. Figure 1 is taken from 1 and shows the inreasing sizes of models. 1E+8 Dof*nstep 1E+7 1E+6 1E+5 Josefson Andersson Size of fe-model for welding Jonsson Lindgren Goldak Karlsson CT Oddy Karlsson, RI Frike Lindgren Oddy Ravihandran Friedman Argyris 1E Year Figure 1. Size of omputational models of welding measured by degree of freedom multiplied by number of time steps versus year of publiation of work. Due to the inreasing size of the FE-models, the industrial appliations are also beoming more ommon with more omplex geometries as a onsequene. This leads to a need for speial designed user tools, see Figure. One example is the development of finite element odes so that they an be used for welding simulations. In the early 1970 s the first -D welding simulations appeared by for example Ueda and Yamakawa. Sine then the progress has led to extended models in 3-D, larger models and more omplex geometrial models. Ueda et al. 3 and Wang et al. 4 studied the effet of using instantaneous and moving heat soure in a three-dimensional simulation of a pipe-plate joint. Their reommendations were that a three-dimensional model with a moving heat soure was preferred. In this paper a method for introduing a moving heat soure into the model is presented. This method an be related to as one of the speial designed user tools, as desribed in figure. Inreased size of models More industrial appliations More omplex geometry Need for speial designed user tools Figure. Inreased size of models give rise to a need for speial designed user tools.

22 3 Implementation of CAD-support for heat input As disussed earlier, the over all omplexity of the FE-models is inreasing. In this setion a method for alleviating the reation of the geometrial omplex models of welding will be presented. The basi idea of this method is to give the user a tool so that the weld path an be defined along any general 3-D urve. A CAD-system, whih ontains the geometrial- or FE-model, is used to define the weld path. Figure 3 illustrates the ommuniation between the CAD- and the FE-system. The element mesh an be reated in the CAD- or in the FE-system, but if the mesh is reated in a FE-system then it has to be imported to the CAD-system to be able to define the weld path and the relation between the mesh and the weld path. CAD Input file for FE-model FEA User subroutines Weld path Data Figure 3. Struture of data flow between the CAD- and FE-program. A more thorough desription of what is to be done in eah program will follow in the subsequent setions. 3.1 Generation of weld path in CAD-system The weld path where the heat soure is to be applied is defined by n disrete points equally positioned along the weld path. The number of points along the weld path depends on the urvature. To be able to set the diretion of the ar a seond urve, whih will be referred as the referene-urve, must be added. In most ases the refereneurve an be reated as a opy or as an offset of the weld path. One example of how the referene-urve an be reated is shown in Figure 4 a). A surfae is swept between the two pipes, whih form a ollar, and the edge of that surfae an be used as refereneurve. Along the referene-urve n disrete points will also be plaed equally spaed. By using these two urves the user an now determine the welding diretion and the start and

23 .. end point of the weld. Another parameter,, is added to be able to define the rotational diretion of the heat soure, i.e. the ar, see Figure 4 b). The oordinates of the points along the weld path are then written to a file, weld path data in Figure 3, whih later will be proessed by the FE-program. Referene-urve Weld path Rotational diretion of ar handle Edge where the referene-urve is plaed a) b) Figure 4. (a) T-pipe with weld path, referene-urve and swept surfae, (b) Plate with stiffener where the parameter is used. 3. Proessing of weld path by user subroutines in FE-program During the initialisation of the simulation, a subroutine will read the data from the file reated earlier in the CAD-program. The oordinates of the disrete points that define the weld path will, together with the predefined welding speed and the urrent time in the simulation, determine where the origin of the heat soure is. This information is also used for deativation and ativation of elements, i.e. filler material. The model for the heat soure that is used is the double ellipsoid heat soure given by Goldak et al. 5 The definition of the model an be found in Figure 5 and Equations 1-3. This model was originally developed for TIG-welding simulations. Goldak et al. 6 later presented a onial heat soure that was more appropriate for laser beam and eletron beam simulation. The double ellipsoid heat soure model an though also be used for simulation of the laser beam welding if it is on a thin plate, Berglund et al. 7 Other, more advaned, heat soure models have been developed. Sudnik et al. 8 uses a quasi-stati thermodynami model for determining the geometri harateristis and the temperature fields of the laser beam weld. In this method the tehnologial parameters of the welding proess are used as inputs to the model. This makes it easier for the engineer

24 to perform welding simulations sine it uses, for the engineer, well-known parameters. One obstale still remains and that is to ouple the heat soure model to the FE-model. a r y a f z x b Welding diretion Figure 5. Definition of double ellipsoid heat soure model. Depending on if x is positive or negative, equals f or r, see Figure 5. 3x 3 y 6 3 f 3z Q a b, y, z e e e 3 a b q x (1) The sum of the fration, f, between the heat deposited in the front and the rear quadrant must equal two, that is. f f () f r To get ontinuity in the equations when x = 0 the following ondition must yield or f f a f f (3a) a f ar a r r (3b) ar a f The boundary limit of the heat soure is defined as the region where the heat input has been redued to 5% of the peak value. In Figure 6 the distribution of the heat input and the 5% ut off limit are illustrated.

25 Figure 6. Heat input distribution at the top surfae for the double-ellipsoid heat soure model. In eah time step the position of the heat soure will be alulated, that is, the point on the weld path that will define the origin of the heat soure. A subsequent point on the weld path and the point that is set as the origin define the welding diretion. A orresponding point on the referene-urve defines together with the -parameter the rotational diretion of the ar handle. Feedbak regarding the total energy input from the heat soure in eah time step is given to the model. This information is used to adjust the heat input in the following time step, whih ensures that the sum of the total energy given into the model in eah time step is orret. In a thermo-mehanial simulation the weld path will also be used to deativate and ativate elements along the weld path as mentioned earlier. The tehnique that is used for finding the elements that should be deativated is a box-searh tehnique. That is, a box is defined with proper dimensions and swept along the weld path. The elements that are inside the defined box will be deativated when the simulation is initiated. Ativation of these elements will our when the origin of the heat soure reahes the element. Different tehniques for ativation may be used, i.e. quiet elements (where the stiffness is very low when the element is inativated) or born dead tehniques (where the element that is inativated are not assembled to the system of equations until they are ativated). Depending on whih tehnique is used, different problems an our when the elements are to be ativated. If the quiet elements tehnique is used onvergene problems an our due to the differene in the stiffness in the elements. On the other hand if the born dead tehnique is used the stiffness matrix has to be renumbered eah

26 time an element is ativated. Severely distorted elements an our due to large deformations with either of these two tehniques. Lindgren & Hedblom 9 have developed a tehnique to ontrol the volume of the ativated elements, i.e. the filler rate, whih also minimizes the element distortion. This tehnique was applied for a -D model but it an be expanded to 3-D models. If the simulation is purely thermal the de-/ativation tehnique is not neessary. 4 Appliations Here are some examples of welding simulations that were performed using the desribed method. In Figure 7 a), the Graz flag, a thermal welding simulation on a shell mesh is performed. This simulation is of ourse of no realisti relevane, but it shows that a weld with a omplex weld path an be modelled without too muh effort by the user. To get an illustrative temperature field, the material has no thermal ondutivity. The weld path for the T-pipe in figure 7 b) is also easily modelled with the CAD- FE-program interfae. Figure 8 a) shows a thermo-mehanial welding simulation performed on a shell mesh. The geometry is two setions of a tail bearing housing (TBH), the outer ring and the vanes. This is a omponent of an aero engine and the outer ring has a diameter of approximately 1, m. Figure 8 b) shows the atual omponent. a) b) Figure 7. Examples of thermal welding simulations that an be performed using the CAD- FE-program interfae. (a) Dummy weld simulation whih forms the text Graz 001, the temperature field in C is shown on the fringe sale. (b) Welding simulation of a T-pipe, same pipe as desribed in figure 4 a), here it is also the temperature field in C that is shown on the fringe sale.

27 a) b) Figure 8. (a) Two simplified setions of a tail bearing housing, from an aero engine, are joined in a thermomehanial welding simulation. The variables shown are the temperature field in C, deformed shape and the ontours of the undeformed model, deformation sale fator is 0. (b) Photo of the tail bearing housing omponent. 5 Conluding remark A method for alleviating the definition of heat input has been implemented and demonstrated. Although I-DEAS has been used as CAD-system and MSC.Mar as FEsoftware, the method and the subroutines that have been written are general and an be used with other CAD- and FE-systems also. The only requirements are that the CADsoftware must be able to generate a file ontaining the weld path defined on the model and the FE-software must be able to reate the heat input via user routines. 6 Aknowledgements The finanial support was provided by the: Manufaturing and Modelling of Fabriated Strutural Components (MMFSC) programme. This is a projet within the 5th framework programme and Luleå University of Tehnology. A speial thanks to Daniel Berglund for fruitful disussions, feedbak and work on the deativation proedure. 7 Referenes 1. L.-E. LINDGREN: Finite element modelling and simulation of welding part 1: inreased omplexity, Journal of Thermal Stresses, 001, 4, Y. UEDA and T.YAMAKAWA, Analysis of thermal elasti-plasti stress and strain during welding by finite element method, JWRI, 1971,, (),

28 3. Y. UEDA, J. WANG, H. MURAKAWA and M. G. YUAN, Three dimensional numerial simulation of various thermomehanial proesses by FEM, JWRI, 1993,, (), J. WANG, Y. UEDA, H. MURAKAWA, M. G. YUAN and H. Q. YANG, Improvement in numerial auray and stability of 3-D FEM analysis in welding, Welding Journal, 1996, April, J. GOLDAK, A. CHAKRAVARTI, M BIBBY, A new finite element model for welding heat soures, Metallurgial Trans B, 1984, 15B, J. GOLDAK, B. PATEL, M. BIBBY and J. MOORE, Computational Weld Mehanis, AGARD Workshop Strutures and Materials 61 st Panel meeting, D. BERGLUND, L.-E. LINDGREN, A. LUNDBÄCK, Three-dimensional finite element simulation of laser welded stainless steel plate, NUMIFORM 01 The seventh Int. Conf. on Numerial Methods in Industrial Forming Proesses, 001, W. SUDNIK, D. RADAJ and W. EROFEEW, Computerised simulation of laser beam welding, modelling and verifiation, J. Phys. D: Appl. Phys., 1996, 9, L.-E. LINDGREN and E. HEDBLOM, Modelling of Addition of Filler Material in Large Deformation Analysis of Multipass Welding, Int. J. Communiations in numerial methods in engineering, 001, 17 (9),

29 Three-Dimensional Finite Element Simulation of Laser Welded Stainless Steel Plate D. Berglund Computer Aided Design, Luleå University of Tehnology, Luleå, Sweden Volvo Aero Corp., Trollhättan, Sweden Prof. L.E. Lindgren & A. Lundbäk Computer Aided Design, Luleå University of Tehnology, Luleå, Sweden ABSTRACT: A three-dimensional model was used to simulate laser welding of two stainless steel plates. The heat input was simulated as a moving heat soure. Elements where ativated along the welding path in order to aount for the joining of the material. Large deformations, temperature dependent material properties, volume hanges due to phase hanges are inluded in the model. Experiments have been performed in order to evaluate the auray of the model. 1 INTRODUCTION Joining strutures with laser welding is getting more ommon in the aerospae industry beause of the smaller heat effeted zone and less deformation ompared to ar-welding proesses. This is due to the more onentrated heat soure. A small fusion zone requires that the gap and the mismath between the plates are kept to a minimum. A simulation tool would derease the number of weld trials and thereby redue the ost. When reating a numerial model, the aim is to implement the physial behaviour of the proess into the omputer model. However, it may be neessary to ompromise between auray of the model and the required omputational time. The finite element method has been used in simulation of welding sine the early 70:ies (e.g. Ueda et al 1971a, 1971b, Hibbitt & Maral 1973). However, onsidering geometrial omplex details and/or fluid flow in the melted zone welding simulations are still a hallenge. Mainly two-dimensional analyses have been performed until the end of 80:ies. Then the first simulations using three-dimensional models were performed (Lindgren & Karlsson 1988). It is usually neessary to apply three-dimensional models for omplex strutures. Still threedimensional analyses are restrited to plates, pipes and similar simple strutures. The main reason for this is lak of omputational power. The physis of the welding proess in the molten zone is not well understood and not possible to simulate ombined with a omplex struture. One an perform distortion simulations with an aeptable auray using a simplified heat soure and material desription for this zone. It s neessary to verify the material properties, heat soure parameters and the simulation method before performing a welding simulation of a omplex geometry. This paper desribes one method to verify deformation modes when performing a welding simulation. The deformation studied in this ase is a ombination of the butterfly effet, ase in Figure 1 and the longitudinal bending behavior, ase 5. This ombined deformation is referred to as the bending mode. The seond deformation of interest is the gap between the welded plates. The geometry of the welded plate is in this ase mm. 1) ) 5) L 1/κ y Figure 1. Deformation modes. y x 4) EXPERIMENTAL SETUP v 6) 3) u 1/κ x A Nd-YAG laser with a feeding wire system see Figure, was used for this experiment. The foal length was 100 mm and the welding speed was kept

30 onstant at 30 mm/s. A stable keyhole was ahieved with a laser power of.5 kw. The experimental setup was designed to obtain as large, ontrolled deformation of the test plates as possible. The plates, see Figure 3, were fixed as a antilever beam to be able to observe the gap and the bending behavior during and after the welding proess. The plate halves were lamped without any gap by a 0 mm thik steel plate and two fore sensors measured the lamping fore. The plates were held in position by a support at eah side to minimize any movement behind the lamping area. An extensometer measured the gap in front of the plate and an LVDT-gauge was used to register the bending behaviour. The bending behaviour was measured at point 3 in Figure 3. To avoid damage to the measurement equipment the ending point of the welding was 5 mm from the edge of the speimen, point in Figure 3. Three thermoouples were positioned perpendiular to the weld diretion. The first gauge was positioned as lose to the melted zone as possible and the seond and third, a ouple of millimeters from the other, points 4, 5, and 6 in Figure 3. The temperature measurement worked as verifiation for the heat input. The sampling frequeny for all gauges was 30 Hz. Thermoouples Edge support Figure. Experimental setup. Table 1. Heat soure parameters. Parameter Power 500 W Effiieny 60 % a.0 mm b 3.4 mm f 1.5 r 1.0 Clamping plate Fore elements Laser Feeding wire Extensometer LVDT-gauge 1 Clamping area Figure 3. Experimental setup. y x Table. Position of points in Figure 3. Point no x y mm mm COMPUTATIONAL MODEL The primary aim of the numerial model was to predit the deformations measured in the experiment. The Finite Element program MARC was used. Simulations of large models in three dimensions are time onsuming. Two ways of reduing the omputational time is adaptive meshing or parallel omputing. A omparison of these approahes is shown in this paper. A double ellipsoid heat soure was used to simulate the laser beam heat input, see Figure 4. Four quadrati elements are required along eah axis to apture the infletion of the Gaussian distribution (Goldak et al. 1985). The parameters a and b, see Figure 5, were adjusted to obtain the orret heat flux input and orret shape of the melted zone. The heat soure parameters used in the simulation an be seen in Table 1. Heat loss to the surrounding was negleted. The welding path was generated separately in the solid modeller I-DEAS. The thermo-mehanial analysis was performed as a staggered approah as the updating of the geometry in the thermal analysis is one time step behind. The heat generated by the deformation was ignored. An updated Lagrangian formulation was used in the mehanial analysis. Large deformation and large strains were aounted for and an additive deomposition of the elasti, plasti and thermal strain rates was assumed, see Equation

31 ε + tot e p th = ε + ε ε (1) This an be motivated, as the elasti strains are small. The elements along the welding path are deativated initially in the mehanial analysis. These elements don t ontribute to the stiffness matrix but are ative in the thermal part. The elements are ativated when the entre of the heat soure will be within the element during the next time step. The elements used are eight noded brik elements and the temperature through the volume of the element is assumed to be onstant. Flux q upper urve in the dilatation figure was followed. Depending on the top temperature different urves were followed during the ooling phase. The lower urve in Figure 6 was followed if the top temperature had been higher than at point 1. Otherwise the upper urve was followed. Dilatation, th Temperature [ºC] 1 Upper urve Lower urve Figure 6. Thermal dilatation. Figure 4. Double ellipsoid heat soure. f r Figure 5. Heat soure vs. mesh. z a x 3.1 Material Model The material used in this paper is a martensiti stainless steel. The mirostruture will hange during welding beause of the high temperature and high ooling rate in the melted and heat effeted zone. The mirostruture will affet the mehanial field due to the volume hanges during phase transformation. The normal thermal expansion and the ontribution from the volume expansion are added together to a term alled thermal dilatation. Point 1 in Figure 6 shows the starting point for ferriteaustenite transformation and at point have all ferrite transformed to austenite. The martensiti transformation starts at point 3. The dilatation test in Figure 6 was performed with a heating rate of 100 C/s and a ooling rate of 10 C/s. During the heating the b y a x Figure 7 shows the temperature-dependent thermal properties (ondutivity and heat apaity) used in the analysis. When the material reahes the solidifiation temperature the thermal ondutivity was assumed to inrease five times to initiate the fluid flow in the melted zone. The latent heat is 338 kj/kg and the solidus and liquidus temperatures are 1480 and 1600 C, respetively. C [J/kg ºC] Temperature [ºC] [W/m ºC] Figure 7. Temperature dependent thermal ondutivity, λ and heat apaity,. The following temperature dependent material properties were needed for the mehanial analysis, Young s modulus E, Poisson s ratio ν, and the yield stress σ y, see Figure 8. A ut off temperature of 1500 C was used in this analysis. This means that if the temperature is higher than 1500 C, then the material properties were evaluated at the ut off temperature. The plasti behavior of the material is desribed by the von Mises yield funtion and no hardening was aounted for. Aumulated plasti strains were removed when an element was melted.

32 E [GPa], y [MPa] y ν E Temperature [ºC] Figure 8. Temperature dependent mehanial properties, yield stress σ y, Young s modulus E, Poisson s ratio ν. 3. FEM-model using adaptive meshing. The approah to use adaptive meshing redues the number of elements in the beginning of the analysis. Elements are added by splitting original elements along the weld path. Eah split element reates eight new ones. The new elements an in turn be split again, but in this model a restrition was set to one level of splitting. Whether an element is to be split or not is determined by the alulation of the relative temperature gradient in the atual element, whih is ompared with the maximum temperature gradient in the model, see Equation. gradient >f () maximum gradient In this model the value of f is set to That is, if f exeeds 0.75 the element will be split. The model ontained initially 7000 elements and nodes. No oarsening of the mesh was used sine it is not supported in the ode and a denser mesh is needed to desribe the residual strains and deformations. ν 450 MHz Sun Ultra 60 with GB ram. The simulation with the adaptive meshing tehnique was not ompleted beause of onvergene problem after.1 s. The adaptive and parallel models show similar deformation behaviour during the heating sequene. The measured and omputed temperature at point 4, 5 and 6 are shown in figure 8. The omputed temperatures are all lower than the measured. The position of the sampling points in the omputational model were not the same as in the experiment, see Table. The shape of the alulated and measured fusion zone is approximately the same but the top side of the weld is higher in the measured ase, see Figure 10b. Temperature [ºC] Measured Calulated Time [s] Figure 9. Measured and alulated temperature history for points 4, 5 and 6. a) b) Hardness [HV] Distane [mm] 3.3 FEM-model using parallel proessing. The simulation model an be subdivided in a number of sub models (domains). Eah domain is alulated on a different proessor and a iterative proedure assemble the sub solutions to the global solution (Mar Analysis Researh Corp 1998). The finite element mesh used in this model had elements and nodes during the whole simulation. The number of elements through the thikness of the plate along the weld path was six. A time step of 0.07 was used during the welding sequene but hanged adaptively during the ooling phase. 4 RESULTS The omputational time for the parallel FEM-model was approximately 7 days and was performed on a Calulated Measured Figure 10. a) Hardness test. b) Measured and alulated fusion zone. A hardness test was performed to verify the martensite transformation model. The hardness inreased signifiant up to mm from enter of the weld as shown in Figure 10a. The hardness has inreased from 70 HV in the base metal, to a value of 500 HV in the enter of the weld. The measured and al-

33 ulated deformation behavior an be seen in Figure 11 and 1. The omputational model, predit the bending behavior with aeptable auray during the heating sequene but not during the ooling phase. The bending deformation, stabilize at 0.3 mm during the ooling phase but the omputed deformation dereases rapidly to a value of 3 mm after 100 s. The omputed and measured gap diverges after 0.4 s. The final gap in the omputational model is four times larger than the measured one. The behaviour during ooling has the same tendeny in the experiments as in the simulation as an be seen Figure 1. Displaement [mm] Time [s] Calulated, am Figure 11. Bending behavior. Displaement [mm] Heating Measured Calulated, pm Calulated, pm Calulated, am Measured Heating Cooling Cooling Time [s] Figure 1. Gap at the end of the plate, pm-parallel Model, am- Adaptive Model. 5 DISCUSSION AND CONCLUSION A method to verify numerial welding models has been developed. The experimental setup an be used to evaluate the temperature field and deformation behaviour of thin plates. A numerial welding simulation of a stainless steel plate was performed. The auray of the absolute value of the deformation was not aeptable but the approah reveals the weakness of the model. Similar deformation behaviour was ahieved for both the adaptive and the parallel model. The measured temperatures were all higher than the alulated, see Figure 9. One unertainty is the high thermal ondutivity used in the model. A regular stainless steel have a ondutivity between 13 and 16 W/m K aording to Inropera & DeWitt (1996). Another unertainty is the effiieny of the laser beause of the bending and hange in gap during the welding proess whih will hange the absorbed power (Lampa et al. 1995). An error in the thermal field will effet the deformation behaviour. This is one of the reasons to the exponential inreasing error of the gap in the omputational model. Aording to Jonsson et al. (1985) has the thermal dilatation a large influene on the hange in gap width. The hardness test shows the existene of phase transformation up to mm from the weld entre. The hardness is dereasing from its maximum value of 500 HV at 1 mm, to 300 HV mm from the weld entre. This is not the ase for the omputational model where martensite is assumed to be reated as soon as the temperature has been higher than the initial ferrite-austenite temperature. This assumption gives a larger amount of reated martensite in the model, whih affets the hange in gap. Another parameter that will influene the deformation behaviour is the high yield stress of the reated martensite phase. The existing numerial model an predit the gap behaviour and the bending during the ooling phase, but the absolute value of the deformation is not possible to predit. 6 ACKNOWLEDGEMENT The finanial support was provided by NFFP (Swedish National Aviation Researh Program), Luleå University of Tehnology and Volvo Aero Corporation. 7 REFERENCES Goldak J, Patel B, Bibby M & Moore J Computational weldmehanis. AGARD Workshop - Strutures and Materials 61st Panel meeting, Oberammergau. Hibbitt HD & Maral P A numerial thermo-mehanial model for the welding and subsequent loading of a fabriated struture. Comp. & Strut. 3: Inropera FP & DeWitt DP Fundamentals of Heat and Mass Transfer. New York: John Wiley & Son. Jonsson M, Karlsson L & Lindgren L-E Deformation and Stresses in Butt-Welding of Large Plates With Speial Referenes to the Material Properties. Journal of Engineering Materials and Tehnology 107: Lampa C, Ivarson A, Runnemalm H & Magnusson C The Influene of Gap Width on Laser Welding. 14:th ICALEO.

34 Lindgren L-E & Karlsson L Deformations and stresses in welding of shell strutures., International Journal for Numerial Methods in Engineering 5: Mar Analysis Rersearh Corporation Theory and User Information, Palo Alto. Ueda Y & Yamakawa T 1971b. Thermal stress analysis of metals with temperature dependent mehanial properties. Pro. of Int. Conf. on Mehanial Behavior of Materials 3:10-0. Ueda Y & Yamakawa T 1971a. Analysis of Thermal elastiplasti strain and strain during welding by finite element method. Trans. JWRI ():

35 VALIDATION OF A THREE DIMENSIONAL FINITE ELEMENT MODEL IN ELECTRON BEAM WELDING OF INCONEL 718 Andreas Lundbäk Luleå University of Tehnology Luleå, 97187, Sweden +46 (0) anlu@ad.luth.se Henrik Runnemalm Volvo Aero Corporation Trollhättan, Sweden Abstrat A three dimensional finite element model for predition of the distortion and residual stresses indued during the eletron beam welding is desribed. The model is validated by experiments, butt-welding of two plates made of INCONEL 718. There are two major unertainties, material behaviour and heat input. Separate experiments have been made for obtaining material properties and the speial effort for determining a good model for the heat is desribed in this paper. Parallel omputation is used to redue the overall simulation time. A ombined onial and double ellipsoid heat soure is used to model the deep penetration harateristi of the eletron beam. The agreement between alulations and experiments is good with respet to the residual stresses. Disrepanies, in absolute values, were found when omparing the deformations. The model behaves qualitatively similar to the experiment tough. INTRODUCTION The paper desribes the development of the welding model and its validation in order to ensure the preditive apability of the welding simulations. They will be applied later for simulation of the fabriation of a strutural omponent used in an aero engine. The omponent is a Tail Bearing Housing (TBH) and an be seen in Figure 1. The test ase is a butt-weld of an Inonel 718 plate. The heat affeted zone was measured and a speial ode developed by Sudnik et al. [1] was also used to predit the molten zone. This information was used to develop a heat soure model, whih is a ombination of a onial soure and the double ellipsoid soure developed by Goldak et al. []. Residual stresses and deformations were measured and ompared with simulations. A quite good agreement was obtained between measurements and simulations.

36 Figure 1. Tail bearing housing on a generi aero engine. BACKGROUND Manufaturing simulations an be used to design the manufaturing proesses. Thus, in the ase of welding, one an evaluate the effet of different fixtures, welding parameters et on the deformation of the omponent. It is also possible to optimise a hain of manufaturing proesses where welding is one step, as for example the ombined effet welding residual stresses and heat treatment. It is also possible to evaluate the effet from the manufaturing on the in-servie behaviour of the omponent. The urrent work is part of an EC founded projet, Manufaturing and Modelling of Fabriated Strutural Components (MMFSC). One of its workgroups has the sope to predit omponent behaviour during manufaturing. Speifially four major proesses have been investigated. These are; forming/forging, welding, heat treatment and mahining. The approah within the MMFSC projet is to first validate the simulation model of eah manufaturing proess for a simple geometry. When eah individual simulation model is validated then the simulation of a hain of manufaturing proesses will be performed. Eah manufaturing proess is simulated by different partiipants within the MMFSC projet. The work at Volvo Aero Corporation (VAC) and Luleå University of Tehnology has foussed on the welding and heat treatment proesses [3-5]. Different FE-programs are used for simulating eah proess and therefore a neutral format is used to store the results at the end of eah proess. The ABAQUS.fin-format [6], is hosen as neutral format to store the geometry, nodes and topology, and the results suh as plasti strains and residual stresses. The safety requirements and the high osts of performing experiments to find different manufaturing routes is the motivation for VAC to inrease the use of simulations in design of omponents as well as their manufaturing, Figure. The use of the same type of models in development of the manufaturing proess as used in design of the omponent will also failitate the ommuniation between the manufaturing and design departments. The use of simulation also gives the opportunity to reate a digital opy of the manufatured omponent that an be subjeted to the same loadings as the omponent in servie. This loading an be obtained via sensors from the engine in-flight. This model an then be used to support maintenane of the omponent.

37 Produt requirements Feedbak DESIGN Tools for funtional evaluation Conept Definition Verifiation phase phase phase Computer based engineering models Inventory of Preliminary Detailed known methods preparation Preparation Tools for planning of manufaturing MANUFACTURING Feedbak FUNCTIONAL PRODUCT Physial produt Servies Data from omponent Maintenane, in-servie applied to upgrading et digital opy of produt Digital version of produt Figure. Use of omputer models for design of omponents, manufaturing routes and maintenane. EXPERIMENTS Two Inonel 718 plates are welded together. The sizes of the plates are 100x40x7 mm and 100x40x6 mm and an be seen, together with the lamping devie, in Figure 3. The plate with the thikness of 7 mm had a 1x1 mm lip, whih served as a root support, see the enlargement in Figure 3. The plates were first tak welded together without any gap between them and then butt welded. The distane from the weld entre to the lamping devie is 10 mm. Prior to welding the plates had been preipitation hardened. The parameters of the eletron beam welding proedure are given in Table 1. Table 1. Input values for the EB welding proess. Voltage (kv) Current (ma) Lens urrent (ma) Lens diameter (mm) Work distane (mm) Speed (m/min)

38 Figure 3. Clamping devie and plates to be welded. The inremental hole-drilling tehnique was used to measure the residual stresses. The position of the hole-drilling measurements an be found in Figure 4 and Table. The measurements at positions 1 and 6 measure the initial state of the plate sine it is assumed that the stresses indued by the welding proess are negligible that far away from the weld entre. Positions and 3 are plaed symmetrially 3 mm from the weld entre and the positions 4 and 5 are plaed in the middle of the plate, 3 mm and 13 mm from the entre, where the EB-weld proess is onsidered to be stable. Table. Position of strain gauges. Position X (mm) Z (mm) Figure 4. Plate with the strain gauge positions.

39 The distortion measurements performed in this study is done with an optial surfae measurement mahine. The butterfly angle, defined in Figure 5, of the plate after welding is measured at three positions, 5, 50 and 95 mm from the start point of the weld in the z-diretion. Figure 5. Definition of the butterfly angle. NUMERICAL MODEL The finite element simulation presented in this paper is a oupled thermo-mehanial simulation. The oupling between the thermal and the mehanial part is done with the staggered approah. In the staggered approah the updating of the geometry is lagging one step behind in the thermal analysis. The ode that has been used is the impliit finite element ode MSC.Mar. An updated Lagrangian and large deformation formulation was used together with additive deomposition of the strains. To avoid loking an underintegrated element with respet to the volumetri strain was used. All plasti dissipated energy was onverted into heat. The elements in both the thermal and mehanial analyses have linear shape funtions. Therefore a onstant temperature was transferred to the element in the mehanial analysis in order to ensure that the mapping between the thermal and mehanial strains would be onsistent. To redue the total wall lok time when performing the simulation, parallel omputation was utilised. The model is divided into sub domains and a separate solution is obtained for eah domain. An iterative proedure then assembles the loal solutions into a global solution of the whole model, MSC.Mar user handbook [10]. The time onsumed for solving the analysis was approximately 10 hours on six 1900 MHz PC-Linux mahines. The model ontained eight noded brik elements and 0804 nodes. The size of the elements in the weld region is 0.33x1x1 mm and the whole mesh an be seen in Figure 6. Symmetry ould not be used sine both the mehanial and thermal boundary onditions were not symmetri and the halves have different thiknesses, see Figure 3. A time step length of 0.5 s during welding ensured that the heat soure travelled only half the length of an element in the weld region for eah time step. The total time for the welding phase is 10 s. An adaptive time stepping method was used for the ooling phase, 6 inrements and a total time of 1000 s brought the plates bak into room temperature. After ooling, the plate was unloaded from the fixture in one single time step. During welding and ooling the nodes that belong to the area that would have been in ontat with the fixture are fixed in all diretions. In the unloading step, a pin joint at one end of the plate and a simple support at the other end replaed the fixed nodes used in the previous steps. The heat transfer between the plate and the fixture is imitated by a high onvetive heat transfer of 100 Wm - K -1. Heat losses due to radiation are not taken into aount for in the model and no free onvetion either due to that the welding proess took plae in vauum.

40 Figure 6. Finite element mesh. Element death and birth is done by first deativating one element row along the weld path exept the elements that represents the tak welds. This ours in an initial dummy step. Thermal and mehanial ativation is separated to enable the element to be heated up thermally but not ontribute to the mehanial stiffness. The ondition when an element is to be ativated mehanially is set as a distane relative the position of the origin of the heat soure. In this model the distane was set to 4 mm whih is approximately the distane where the temperature in the elements is entering the solid phase from liquid. The distane ahead the origin of the heat soure where the elements is thermally ativated is not as ritial as it is in the mehanial ase. This is due to that the heat ondution in the welding diretion an be negleted so a suffiiently long distane an easily be hosen. In pratie, for one pass welds all the elements ould most likely be thermally ative during the whole simulation. It should also be noted that the tak welds are not simulated so these elements are left ative in their nominal material state without any residual stresses from the takwelding.

41 Heat input model A ombined heat soure, Equation 1, is used to model the temperature field obtained in the thermal simulation, whih is desribed later, and from the experiment. The first part in Equation 1 is the double ellipsoid presented by Goldak et al. [1]. A desription of the double ellipsoid an be found in Figure 7 and equation a and b. The seond part is a double ellipti one and is defined in equation 3a and 3b. The -parameter gives the relative ontribution of the two heat soures. Figure 7. Definition of the double ellipsoid with its harateristi parameters. The geometri parameters a, b and have the same meaning for the ellipsoidal and onial heat soure. The onial heat soure has also an additional parameter d. The parameter d is a normalized parameter and an be given a value between 1 and 0. The energy intensity of the onial soure has a Gaussian distribution in the x-z plane as the double ellipsoid heat soure, see Figure 7. However, it has a linear derease through the depth whih is ontrolled by the parameter d. That is, if d equals 1 then the energy intensity, along a line parallel to the y-axis, is onstant through the depth. If d is set to 0, then the intensity will derease linearly to zero at the depth of b. The parameter b should be the thikness of the plate. The formulas are summarized in Table 1. The values of the heat soure parameters used in the model in this paper an be found in Table 4.

42 Table 3. Summary of formulas for ombined double ellipsoid and onial heat soures. See Figure 7 for an illustration of the parameters a, b and The parameter b is the thikness of the plate and d regulates the derease of the onial soure in the thikness diretion. q ombi q 1 q,, x y, z e x, y, z x, y z (1) Where the frontal part in the double ellipsoid is defined as: q e x, y, z a x y z f ef Q a e be ef e e e 3 ebeef (a) and for the rear part q e x, y, z a x y z f erq ae be er e e e 3 ebeer (b) The frontal part of the double ellipti one is defined as: q x, y, z a b 1 d z 3 1 d y x 6 f 3 f Q a f f e 1 b e (3a) and the rear part q x, y, z a b 1 d z 3 1 d y 6 x 3 f rq a r r e 1 b e (3b) The parameters f ef, f er, f f and f r are the frations between the front and rear quadrants in the ellipsoidal and the ellipti one funtions respetively. To obtain ontinuity between the front and rear quadrant of the funtions they must obey equation 4a, 4b, 5a and 5b. f ef ef ef er and f ef f er (4a,b) f f f f r and f f f r (5a,b)

43 Table 4. Values of the heat soure parameters used (mm). Parameter a e b e ef er a b f r d Value The total energy input into the model is related to the physial parameters aording to Equation 6, where U is the Voltage, I the urrent and the total effiieny of the proess. q dv UI qe( x, y, z) dv 1 ( x, y, z) (6) Due to the disretisation of the model, i.e. finite elements, the energy input will generally be lower than if analytially integrated over the whole domain as in Equation 6. This is mainly a problem if a too oarse mesh is used, whih often is the ase when welding simulations are performed, due to omputational limitations. This energy loss is ompensated for with a simple regulator in the user routine for the heat input into MSC.Mar, whih sales the heat input in eah time step toward the nominal heat input. As mentioned above the results from a thermo-dynamial simulation, performed in the finite differene ode ELSIM, has been used to validate the temperature field in the thermal FE-analysis. The width of the fused zone (FZ) in the ross setion an easily be measured in the experiment, whih also has been done. The FZ in the welding diretion on the other hand, is in pratie impossible to measure experimentally and therefore the result from the simulations with Elsim has been helpful when alibrating the heat soure parameters in the FE-analysis. ELSIM is based on the software DB-LASIM for simulation of the laser beam welding proess, presented by Sudnik et al. [1]. It solves the quasi-stationary energy equations for the thermodynami state. The software is apable of alulating the vapour-liquid interfae, liquid-solid interfae and also the weld reinforement. These results are obtained by solving different partial models in an iterative proess. Another important result obtained from the software is the tehnial effiieny. The effiieny an be used diretly as an input into the FE-model. The input to the software is the tehnial parameters used in the EB-welding mahine, an example of the input interfae is shown in Figure 8. Figure 8. Input interfae for the ELSIM software.

44 Material model The material model used in the analysis is a thermo-elasti-plasti model and the material is the nikel based super alloy, Inonel 718. Inonel 718 is a high temperature strength material that is ommonly used in the aerospae industry in areas that an be onsidered as hot. By hot it means that the temperature is ontinuously held, in servie, at temperatures of 500 C and above. The tail bearing housing is suh a omponent. The thermal properties, ondutivity and heat apaity versus temperature, are derived from Mills [8]. The latent heat in the solid/liquid transformation is separated from the speifi heat urve and it was set to 300 kj/kg in the interval C. The mehanial properties are ompiled from various soures. Young s modulus is derived from Zhang et al. [9] and the yield strength from experiments performed within the MMFSC projet and Bush et al. [14]. The thermal expansion is obtained from Babu et al. [7]. Poisson s ratio is held onstant at 0.9, due to lak of material data. The influene of Poisson s ratio has been shown to affet the result, with respet to global distortion and stresses very little [1-13]. RESULTS The temperature field from the simulation in ELSIM an be seen in Figure 9. This result was mainly used as a qualitative omparison of the thermal field in the welding diretion. As an be seen in Figure 10, the fused zone, highlighted with dashed lines, agrees fairly well with the experiment in the transverse diretion exept that full penetration has not been ahieved in the FE-model. A omparison between the results form ELSIM and the FE-model in the longitudinal diretion show that the thermal fields in this diretion are also fairly well aptured in the FE-model. The effiieny,, was alulated to 93% in the simulations with ELSIM whih would yield a power input of 1300 W. In the FE-model on the other hand, an effiieny of 110% was used, i.e W. The reason why a higher energy input was used is beause otherwise the fused zone beame far too small. Figure 9. Temperature field as a result from simulation with the finite differene software ELSIM.

45 Figure 10. Comparison of the fused zone between experiment (left photo) and FE-simulation. Butterfly angle Figure 11 shows the results of the butterfly angle in the FE-analysis ompared with the measured. Three different simulations are ompared, a-). Generally for all three simulations, the butterfly angle beomes slightly negative at the very beginning of the welding. After less than a seond it has hanged sign and starts to inrease. The total time for the heat soure to travel from start to end point is ten seonds. When the ooling phase starts the inrease of the butterfly angle is ignorable and after approximately fifteen seonds the angle is onstant throughout the rest of the ooling phase. In Figure 1, the transient displaement in the y-diretion for three points along the longitudinal free edge of the unonstrained plate is shown. Two parameters are varied in the simulations, the number of elements representing the tak welds, i.e. the size, and the position relative to the origin of the heat soure where the elements are ativated mehanially. In simulation a) and b) the position when an element is ativated is the same, 4 mm behind the origin, but the number of elements in the tak weld is 7 and 5 respetively, i.e. 7x1 mm and 5x1 mm (width x depth). The number of elements in the tak weld in simulation ) is 5, but ativation ours at the same position as the origin of the heat soure. The tendeny of the experimental urve and the one for simulation a) and b) are the same, the butterfly angle inreases with pratially the same tangent in all ases. It is the magnitude, or rather the development of the deformation in the very beginning of the weld that differs between the experiment and FE-analysis. There is a pronouned differene though in the slope of the butterfly angle along the weld line for simulation ). What an be noted is that the butterfly angle at the beginning of the weld is nearly exatly the same for all the simulated ases. It should also be noted that the time for solving the problem when ativation ourred at the same position as the origin of the heat soure, simulation ), inreased dramatially. The inrease was more than a fator of two, due to diffiulties in onvergene.

46 3,5 Butterfly angle ( ) 1,5 1 0,5 Earlier ativation Larger tak w eld Experiment simulation a) simulation b) simulation ) Distane along the weld line (mm) Figure 11. Butterfly angle from experiment and FE-simulation. 1, 1 Displaement (mm) 0,8 0,6 0,4 Heating Cooling 0, 5 mm 0 50 mm 95 mm -0, Time (s) Figure 1. Transient deformation in the y-diretion of three points (left). Definition of the three points (right). Residual stresses The result from the hole-drilling measurements and FE-analysis are presented in Figure 13 and Figure 14. The stresses are evaluated at the surfae and at the depth of 1 mm. Figure 13 orresponds to the positions 1, and 3 and Figure 14 to positions 4 and 5, defined in Figure 4. The agreement between the measured and alulated stresses is reasonable in both the transversal and longitudinal diretion. The maximum stresses are found in the longitudinal diretion and they are tensile with the magnitude of ~100 MPa, whereas they are mainly ompressive in the transverse diretion and about 700 MPa in magnitude. The experimental measurement of the stresses at position 6 is not

47 presented here sine they where found to be equal with those shown in Figure 13, position 1. These measurements show that there are signifiant stresses at the surfae but that they vanish at some depth. Transverse Stress (MPa) FEM surfae FEM 1,0 mm exp surfae exp 1,0 mm Longitudinal Stress (MPa) FEM surfae FEM 1,0 mm exp surfae exp 1,0 mm Distane transverse to plate (mm) Distane transverse to plate (mm) Figure 13. Residual stresses alulated and measured in the transverse diretion (left) and longitudinal diretion (right) 10 mm from the weld start, i.e. position 1, and 3 in Figure FEM surfae FEM 1,0 mm 100 FEM surfae FEM 1,0 mm exp surfae exp surfae Transverse Stress (MPa) exp 1,0 mm Longitudinal Stress (MPa) exp 1,0 mm Distane transverse to plate (mm) Distane transverse to plate (mm) Figure 14. Residual stresses alulated and measured in the transverse diretion (left) and longitudinal diretion (right) 50 mm from the weld start, i.e. position 4 and 5 in Figure 4. DISCUSSIONS An unrealisti high, 110%, effiieny for the heat input had to be used in the FE-model. It is believed that this is due to that a too oarse mesh has been used. The available time did not permit the use of a larger finite element model. Figure 15 shows the result from a test with only a thermal analysis that has been done. In this test the heat soure parameters was kept onstant and only the density of the mesh was hanged in the model. As an be seen, full penetration and, espeially in the

48 longitudinal diretion, a muh larger volume is heated up to the liquid temperature, FZ. This supports the assumption that the disrepany regarding the amount of energy input is due to the used element sizes. The measured and omputed butterfly angle in Figure 11 has the same variation along the plate but the measured angle is larger. This may be due the tak-welding proedure. The geometry was not measured before the butt-welding proedure. The different simulations show that the differene is not due to the unertainty in the size of the tak-welds or the way the element ativation is done. As mentioned in results, the omputation shows that the butterfly angle beomes slightly negative at the very beginning of the welding and later beomes positive. However, no transient data is available from the experiments and therefore it is not possible to determine whih part of the simulation that diverse form the experiment. Stone et al. [11] reported similar disrepany between experimental and simulated results for a bead-on-plate weld on a 9 mm thik plate in Waspalloy. They did not have any onlusion regarding this disrepany though. Figure 15. Two FE-models with different mesh density but the same heat soure parameters for omparing the size of the FZ.