Study of the distribution of tensions in lap joints welded with lateral beads, employing three dimensional finite elements

Computers and Structures 82 (2004) 1259 1266 www.elsevier.com/locate/compstruc Study of the distribution of tensions in lap joints welded with lateral beads, employing three dimensional finite elements Jose Lavado Rodrıguez a, *, Edelmiro Rua Alvarez b, Francisco Quintero Moreno b a Departamento de Mec. de Estructuras, University of Granada, Edificio Politecnico, Campus de Fuentenueva, Granada 18071 Spain b Polytechnic University of Madrid, Madrid, Spain Received 6 February 2003; accepted 14 February 2004 Available online 20 April 2004 Abstract This paper investigates the distribution of tensions in lateral beads joining lap welded plates, transmitting forces parallel to the axis of the beads. The research is done along the throat plane of the bead. Finite element technique is employed, doing a three dimensional analysis with volumetric elements, modelling the whole geometry of the joint exactly, i.e., plates and beads. This analysis shows a differential behaviour along the throat plane of the bead, in its length and thickness, noted in the norms, but not considered in structural design. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Lateral beads; Lateral welds; Finite elements; Tensional distribution 1. Introduction When designing lateral welded joints, current norms [6,7] consider that tensional distribution develops uniformly in the whole length and whole thickness of the throat of the weld. Several investigations set up bidimensional models, showing differential aspects in tensional transmission through lateral welds [2 5,8 12,14 16]. Faltus [8] established a two dimensional model, studying differential behaviour along the axis of the bead. He deduced that when beads are longer, the concentration of tensions is greater at the end of the weld, decreasing in the middle of the bead. Fischer [11] shows differential behaviour in the cross section of the bead. Those tensions are highest at the * Corresponding author. Tel.: +34-958249964; fax: +34-958249959. E-mail address: jlavado@ugr.es (J.L. Rodrıguez). root of the bead, in the lip joining both plates, and lowest at the external face of the bead. Both investigation employ two dimensional simplified models, which reproduce the phenomenon quite well, but not the three dimensional tensional flow between plates and weld. In this paper a three dimensional lap joint is studied, employing solid elements, modelling the volumes which make up plates and welds. An increasing load is applied parallel to the axis of the bead, studying the whole development of tensions through it. 2. Model of the joint The tool employed to model the three dimensional joint has been the university version of ANSYS 5.7 [1]. 2.1. Three dimensional model: simplifications In Fig. 1 is the investigated weld joint. 0045-7949/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2004.02.011

1260 J.L. Rodrıguez et al. / Computers and Structures 82 (2004) 1259 1266 E o ¼ 2:06E þ 11 Pa Modulus of transverse elasticity Fig. 1. Joint. This joint is formed by a central plate and two external plates. We have four lateral welds, forming a lap joint. Axial loads are applied at the left end of the joint (in central plate) and at the right one (in the two external plates). In this way the model avoids possible existence of moments. Central plate thickness is 2 t 1, and external plates thickness is t 2. There are two symmetric planes at the joint, which reduces the model size, decreasing the time necessary for running the model in a computer. The first we observe is in a horizontal plane, so the central plate now has a thickness of t 1. Second symmetry is in respect of a vertical plane, perpendicular to the longitudinal axis of the joint, which divides the joint in two equal portions. With these two symmetries we can study the model shown in Fig. 2, in which we observe all the dimensions in both plates and weld: G ¼ E x =2ð1 þ lþ where l is Poisson s modulus ðl ¼ 0:3Þ ¼> G ¼ 8:08E þ 10 Pa. ANSYS allows us to use different types of r diagrams. A multilinear response diagram has been adopted, called MISO (Multilinear Isotropic Hardening (MISO)), based on the Von Mises yield criteria. This diagram employed in the plates shows an elastic part, from zero to the yield point, and a plastic part, showed in Fig. 3. 2.2.2. Material of beads The material used for the welds is that employed by Dragados Off Shore Company in welding at Oresund bridge (Denmark). This electrode is Outershield 81K2- H, from Lincoln Electric Company. Its mechanics characteristics are: Yield strength: 6.18E+8 Pa. Ultimate strength: 6.53E+8 Pa. Modulus of longitudinal elasticity at elastic line L a b 1 b 2 t 1 t 2 weld length throat thickness of the weld width of the central plate width of the external plates thickness of the central plate thickness of the external plates E e ¼ 0:2 2:06E þ 11 Pa ¼ 4:12E þ 10 Pa Longitudinal modulus at plastic line E p ¼ 1:72E þ 8Pa Modulus of transverse elasticity 2.2. Characteristics of the materials that form plates and weld The mechanical characteristics employed in the model are those belonging to several specimen tests in a trial at the Polytechnic University of Madrid (Spain), in November 1999 [12]. 2.2.1. Material of plates The steel employed in the plates is S-460, with a yield strength of 4.51E+8 Pa, and an ultimate strength of 6.08E+8 Pa. It shows the next parameters: G e ¼ E e =2ð1 þ lþ ¼1:58E þ 10 Pa G p ¼ E p =2ð1 þ lþ ¼6:62E þ 7Pa where l is Poisson s modulus ðl ¼ 0:3Þ. As in plates, the diagram employed in the welds is a MISO type, with an elastic part, from zero to the yield point, and a plastic part. This is shown in Fig. 4. Modulus of longitudinal elasticity Fig. 2. Model. Fig. 3. r e diagram for the material employed in the plates.

J.L. Rodrıguez et al. / Computers and Structures 82 (2004) 1259 1266 1261 Fig. 4. r diagram for the material employed in the welds. 2.3. Type of finite elements employed in plates and bead The three dimensional joint studied is modelled with volumetric elements [13,17,19]. Version 5.7 of ANSYS program contains a library with several types of three dimensional elements, designed for a structural design, with an elastic plastic behaviour. From all of them SOLID95 has been chosen; with its 20 nodes it has much more accuracy than others with fewer nodes (SOLID45, SOLID185), for the same number of elements of the model. SOLID95 is a prismatic element. It shows three degrees of freedom per node, belonging to the three movements in space ðu x ; u y ; u z Þ. It can adopt irregular shapes without losing much precision in its behaviour. It shows nodes at corners and in the middle of ridges, adapting easily to models with more complex contours. Joining pairs of nodes the element can be converted into a triangular prism or into a four-angled prism (Fig. 5). 2.4. Meshing the model For meshing the model we have employed a basic concept in the finite element technique, for coming to a solution as exactly as possible: make the model denser in those areas where there is concentration of tensions. In the process of transmission of tensions from the plate to the weld we can see intuitively how the tensions will be much greater inside the volume that forms the bead, because the whole load carried by the joint must be transmitted along the weld. So the tensions must be lower in the plates than in the weld. When we are dealing with the plates, closer to the weld, tensions will be grooving gradually, up to a maximum in the contact faces of the plates with the weld. So the model must be much denser inside the weld, and in the vicinities of the plates with the weld; when we are not so close to the weld, we need few elements in the plates. Inside the volume of the weld we expect a greater concentration of tensions at the ends of the bead than in its middle zone. So the model must be denser in the ends of the beads than in the middle zone. This is more evident when the beads are longer. In this way the finite element model will have the following characteristics: 1. Maximum density of elements at the ends of the weld and in their vicinities, inside the plates. 2. High density of elements in the whole volume of the weld, but decreasing to its middle zone and in the vicinities, inside the plates. 3. Density of elements decreasing gradually in the plates when we move far away from the weld. 2.5. Residual stresses in the beads We assume the effects of the residual stresses introducing a decrease of temperature in the bead, which produces a peak in tensile stress of 2.5E+8 Pa in the direction of the longitudinal axis of the bead. This peak in longitudinal residual stress, estimated in many researches in welding processes, can be found in the literature [18]. 3. Results We have studied a large number of models, modifying the geometric variables of the joint (different length of the weld, and different widths and thickness of the plates). The results corresponding to a model are shown with a weld of 30 cm length, and next geometric values: a b 1 b 2 t 1 t 2 4mm 100 mm 80 mm 20 mm 40 mm Fig. 5. Element SOLID95. The model analysed with finite elements is next (Fig. 6). In Fig. 7 we show the details of meshing at the end of the weld.

1262 J.L. Rodrıguez et al. / Computers and Structures 82 (2004) 1259 1266 Fig. 6. Model of the joint. Fig. 8. Load ¼ 119.192 N. Fig. 7. Details of meshing. The model is loaded up to the stage where plasticity is achieved in the whole bead, employing the next load steps: Step 1. 119.192 N Step 2. 238.383 N Step 3. 417.170 N Step 4. 494.316 N Step 5. 568.342 N Fig. 9. Load ¼ 238.383 N. In Figs. 8 12 we show the tensions obtained with the criterion of Von Mises at each load step. We have analysed the tensions at the throat plane of the weld too, compiling the values of the tensions of comparison at the nodes of the inside ridge of the bead (in contact with the plates) and at the exterior ridge (in the external face of the bead). In the next sequence we observe these tensions. Analysing the tensions obtained we can observe some interesting results. (1) In elastic phase the contribution of the weld is very different along its whole length and thickness; the tensions concentrate at their internal corners, in contact Fig. 10. Load ¼ 417.170 N.

J.L. Rodrıguez et al. / Computers and Structures 82 (2004) 1259 1266 1263 with the plates, decreasing the contribution at the middle of the weld and at the external face of it. So comparing the tensions at the internal ridge, between the ends of the weld and the middle points, in elastic phase, the stress ratio is 12 1 (see the tensions belonging to a load of 119.192 N in Fig. 13). We also observe how the contribution decreases very much when we are moving towards the external face of the weld. In longer welds this difference of tensions between the ends and the middle zone of the bead is much stronger. We analysed another two models, increasing the weld length to L ¼ 60 cm. and L ¼ 120 cm., obtaining the next stress ratios between the ends of the weld and the middle points. relations of thickness in plates t 1 and t 2 (see Fig. 3). When we increase progressively the thickness of plate t 1 maintaining constant the thickness t 2, the tensions grow at the side corresponding to the less rigid plate too (with smaller thickness t). (3) When weld material reaches the plastic phase the tensions become uniform along the whole plane of throat of the bead. Nevertheless, in the analysed model we observe how even with a carried load of F ¼ 494:316 N (i.e. almost 90% of the ultimate load of the bead) there is no plasticity in the external face of the bead (the yield strength is 6.18E+8 Pa). The ultimate load is somewhat greater than the last load step analysed (F ¼ 568:342 N); at this load step Weld length L (cm) Width of central plate, b 1 (mm) Width of external plates, b 2 (mm) Thickness of central plate, t 1 (mm) Thickness of external plates, t 2 (mm) 60 100 80 20 40 35 120 100 80 20 40 1000 Stress ratio The model analysed is from a joint, with long beads and narrow plates. The difference between tensions is not so high when the width of the two plates (b 1 and b 2, Fig. 2) grows, because the inflexion of the tensions is greater, tensions travel a longer path inside the plates, working the weld more uniformly. So we analysed another two models, but now with plates much more wide, obtaining the next stress ratios between the ends of the weld and the middle points. practically the whole throat section of the weld is plastic. We need to say that the ultimate load of the model with finite elements is greater than that expected in reality, due to the meshing of the model. The maximum shear stress (ultimate stress) that material of the weld is able to carry is s max ¼ 6:53E þ 8= p 3 ¼ 3:77E þ 8Pa Weld length L (cm) Width of central plate, b 1 (mm) Width of external plates, b 2 (mm) Thickness of central plate, t 1 (mm) Thickness of external plates, t 2 (mm) 30 2000 1960 20 40 2.5 60 2000 1960 20 40 5 120 2000 1960 20 40 10 Stress ratio We can see a very different behaviour for the wide joints, compared with the narrow joints. When plates are wider the contribution of welds increases in the whole length. (2) In the elastic phase there is another differential behaviour of the welds: there is no symmetry of tensions; in the model analysed the Von Mises tensions concentrate more in the wider plate. Analysing other models, we increased progressively the b 1 dimension, maintaining constant b 2, with the result that the tensions grow up at the end of the weld corresponding to b 2, i.e. the less rigid plate. We also analysed models with different So the ultimate shear stress in the whole plane of the throat must balance the exterior load. In this way, the maximum real load carried by the bead is 3:77E þ 8Pa 0:30 m 0:004 m ¼ 452:651 N I.e., the ultimate load should be 80% of the load obtained in calculation. The model analysed shows more than 16.000 nodes (more or less 50.000 degrees of freedom). The calculation time with a PC Pentium III were 15 h. In models with weld length L ¼ 5 cm the results are much more exact, obtaining ultimate loads corre-

1264 J.L. Rodrıguez et al. / Computers and Structures 82 (2004) 1259 1266 Fig. 11. Load ¼ 494.316 N. However, in structures subjected to a fatigue process the behaviour of the welds in the elastic phase is very important; as we can deduce from the results obtained in the study with finite elements, with relatively low state of loads the ends of the beads are in plasticity, being for the most part in the mid zone of the bead working at a very low tension, as the longer the weld and the narrower the joint the greater the effect. The ultimate load of the bead in structures subjected to a fatigue process can be much lower than those established in the design rules. (5) In the European Norms the design tension for a welding project is the tension of the base metal, preventing the rupture of the pieces before the rupture of the welds of the joint. The electrodes employed nowadays in welded joints have much higher yield strengths than those of the base metal, not taking advantage of the resistance of the electrodes, in non-fatigue processes. The Norms should adopt the resistance of the electrode employed in the weld, instead of the resistance corresponding to the base metal, for non-fatigue processes. 4. Conclusions In this paper the whole process of transmission of tensions in lateral welds has been analysed, in lap welded joints transmitting loads parallel to the axis of the beads, employing a three dimensional model with volume finite elements. The most important conclusions that we can extract are: Fig. 12. Load ¼ 568.342 N. sponding to the real one, employing the same number of nodes in the model. In any case, the results analysed in welds with L ¼ 30 cm. shows perfectly the phenomenon; we could refine the model, but this means employing many nodes in the model, and an excess of time in operations. (4) The results obtained show important differences in the behaviour expected in welds subjected to nonfatigue process and fatigue process. In structures where the magnitude of the forces vary less, at the end of the load process the whole bead works uniformly, at the same tension, because the plastic capacity of the weld is high. This has been corroborated in several testing carried out by the authors in 1999 [12]. We tested lap joints with welds with lengths up to L ¼ 60 cm, obtaining a full plasticity in the welds. The Norms nowadays consider this, i.e. the whole welds of the joint working at a uniform tension, with a full plastic behaviour. (1) In the elastic phase of the bead: The development of the tensions makes the beads work much more at their ends than at their mid zone, so that the longer the beads and the narrower the plates the greater the effect. In wider joints, the work of the bead is more uniform in its whole length. The tensions are higher in the internal ridge of the bead, in contact with the plates, decreasing when we move closer to the external face of the bead. When the stiffness ratio of the plates is higher, more asymmetric is the behaviour of the bead, accumulating the tensions at the end corresponding to the less rigid plate. (2) In the plastic phase of the bead: With non-fatigue processes we reach a full plasticity in the beads, with the contribution of the whole throat section. In this case the hypotheses of the Norms are correct, assuming that the bead works uniformly in its whole throat section plane. In structures subjected to a fatigue process the behaviour in elastic phase is important, because with relatively low loads the ends of the beads have already achieved plasticity, and the mid zone of the weld is still working at a very low tension,

J.L. Rodrıguez et al. / Computers and Structures 82 (2004) 1259 1266 1265 Fig. 13. Tensions of Von Mises at the throat plane. so that the longer the weld and the narrower the joint the greater the effect. The ultimate load of the weld in structures subjected to fatigue processes can be much lower than the load predicted in the Norms. (3) In the European Norms the design tension for welding project is the tension of the base metal of the plates. In the theoretic models studied in this article, contrasted with several tests carried out in the laboratory, we have obtained, for a non-fatigue static process, much more resistance than that obtained by applying the Norms, in accordance with the quality of the electrode employed. The Norms should adopt the resistance of the electrode employed in the weld, instead of the resistance corresponding to the base metal, for non-fatigue processes. References [1] Ansys, Revision 5.7. Universitary version. Swanson Analysis Systems Inc; 1998. [2] Bornscheuer FW, Feder D. Traglastversuche an Laschenverbindungen aus St 37 mit Flanken-und Stirnn ahten. Schw Schn 1966;18(7):305 8. [3] Butler LJ, Kulak GL. Strength of fillet welds as a function of direction of load. Weld J 1971;36(5):231 4 [Welding Research Council].

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