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Bending capacity of girth-welded circular steel tubes
Journal of Constructional Steel Research 75 (2012) 142–151
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Journal of Constructional Steel Research
Bending capacity of girth-welded circular steel tubes Chin-Hyung Lee, Jeong-Hoon Baek, Kyong-Ho Chang ⁎ Department of Civil and Environmental Engineering, Chung-Ang University, 221, Heukseok-dong, Dongjak-ku, Seoul 156-756, Republic of Korea
a r t i c l e
i n f o
Article history: Received 13 November 2011 Accepted 22 March 2012 Available online 18 April 2012 Keywords: Girth-welded circular steel tubes Weld-induced residual stress and deformation Bending Nonlinear finite element analysis Buckling
a b s t r a c t In this paper, the buckling behavior of girth-welded circular steel tubes subjected to bending was investigated by numerical method. Finite element (FE) simulation of the girth welding process was first performed to obtain weld-induced residual stress and deformation employing sequentially coupled threedimensional (3-D) thermo-mechanical FE formulation. Elastoplastic large-deformation analysis in which the failure mode, the ultimate moment capacity and the moment versus end-rotation behavior of girth-welded circular steel tubes under pure bending were explored incorporating weld-induced geometric imperfection and residual stress was next carried out. Results showed that the flexural behavior of girth-welded circular steel tubes always involves local buckling near the girth weld on the compression side, which significantly affects the moment versus end-rotation response. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Circular steel tubes are increasingly used both in building and bridge structures due to their efficient geometry and to esthetic benefits that they offer over more traditional open cross sections. During their service life, these members are subjected to loading of various types such as axial loading, bending and torsion. In practice, girth welding of circular tubes is frequently needed due to the long geometry relative to the diameter and the wall-thickness. When two circular steel tubes are welded together, a non-uniform temperature field induced during the welding process produces undesired residual stress and deformation. The presence of welding residual stress and deformation can be a major concern in structural integrity assessment of girth-welded members [1]. Particularly, when combined with service loads, welding residual stress causes premature yielding and loss of stiffness and may lead to deterioration of load carrying capacity [2]. Moreover, welding deformation, i.e. weld depression induced by circumferential shrinkage of the weld region has been founded to have significant effects on the buckling behavior of cylindrical members [3]. Therefore, a good estimation of weldinduced residual stress and geometric imperfection, and an accurate prediction of the behavior of girth-welded members under loading are important for the production of an efficient and economic design and safety of the structure. This paper addresses the bending resistance of girth-welded circular steel tubes. Recently, finite element (FE) method has emerged as a useful and powerful numerical analysis tool. It can be employed to simulate
⁎ Corresponding author. Tel.: + 82 2 820 5337; fax: + 82 2 823 5339. E-mail address: ifi[email protected] (K.-H. Chang). 0143-974X/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2012.03.019
welding temperature field, welding residual stress field and welding deformation [4–9]. Over the last three decades or so, there have been significant research activities on the FE simulation focusing on the girth welding [10–14]. However, these studies have been limited to the axisymmetric condition which cannot reproduce the threedimensional (3-D) features in the girth welding process [15]. On the 3-D FE simulation, limited works have been published due to the high computational cost [15–20]. Much work has been devoted to investigating the behavior of circular steel tubes under bending in the elastic range [21,22] and plastic range [23–31]. However, their works have been generally related to hot-rolled or cold-formed sections. In the literature available on welded circular tubes in bending, Chen et al. [32] presented a FE model for longitudinally stiffened large diameter fabricated steel cylinders in pure bending. The model incorporates both initial geometric imperfections and residual stresses resulting from the welding of stiffeners to the cylinder and verified through the experimental program. The geometric imperfections measured from the test specimen were mapped into the FE model and incorporation of the residual stresses into the model was done by applying a distributed fictitious temperature loading that produced the initial strains necessary to set up the required residual stresses in the cylinder and stiffeners. Kiymaz et al. [33] examined the structural response of seam-welded stainless steel circular hollow section (CHS) flexural members incorporating residual stresses produced by the seam welding. For the residual stress analysis, they proposed a simpler stress-block model based on the measurements taken by Chen and Ross [34]. Nevertheless, as described, they did not implement direct simulation of the welding process due to the truly complex analysis procedure. Moreover, in their works, girth welding of the tubes was not considered.
C.-H. Lee et al. / Journal of Constructional Steel Research 75 (2012) 142–151
As for the bending behavior of girth-welded circular steel tubes, to the knowledge of the authors, very little attention has been received to date and therefore deserves special attention. Actually, Lee and Chang [2] assessed the behavior of girth-welded steel CHS members exposed to bending by a FE method taking weld-induced residual stresses into account. They simulated four-point bending tests of the CHS members. However, they focused on the effects of welding residual stresses and loading positions on the flexural behavior, and thus the bending strength and buckling mode depending on the diameter to thickness (D/t) ratio are still unknown. This paper deals with the numerical investigation on the buckling behavior of girth-welded circular steel tubes subjected to bending by a sequentially coupled thermo-mechanical analysis followed by a buckling analysis. FE simulation of the girth welding process was first performed to obtain weld-induced residual stress and deformation. Elastoplastic large-deformation analysis in which the failure modes, the limiting bending moments and the moment versus end-rotation behavior of the tube models with varying D/t ratios were explored incorporating weld-induced geometric imperfection and residual stress was next carried out. Finally, the paper concludes from the discussion of the numerical results. 2. FE simulation of the girth welding process In this section, FE methodologies for the simulation of the girth welding process are briefly described as similar approaches proposed in previous publications [2,15] were adopted to identify welding residual stress and deformation. The process of welding was simulated using 3-D thermo-mechanical FE formulation based on the in-house FE-code [35], which has been extensively verified against numerical results found in the literature and experiments [15,36]. The formulation consists of two stages, i.e. a transient thermal analysis followed by a transient mechanical (structural) analysis and considers temperature-dependent thermo-physical and mechanical properties of the materials. Because of the weak structural to thermal field couplings, these two analyses can be carried out in sequence. First, a thermal analysis solves for the transient temperature field and its history associated with the heat flow of welding. The resulting temperature history solutions are further utilized as the thermal loading in the subsequent mechanical analysis to obtain the transient and residual stress and deformation.
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2.1. Thermal and mechanical analysis The transient, non linear thermal solution is based on the heat conduction with the moving heat source, the convective and radiative boundary conditions. The combined heat source model in which the heat of the welding arc is modeled by a surface heat source with a Gaussian distribution, and that of the melt droplets is modeled by a volumetric heat source with uniform density was employed [37] in conjunction with the boundary conditions where radiation heat losses and convection heat losses are both taken into account employing the total temperature-dependent heat transfer coefficient [38]. As for the heat effects relevant to the molten metal of the weld pool, two methodologies were used: (1) the liquid-to-solid phase transformation effects of the weld pool are modeled by taking into account the latent heat of fusion, and (2) the thermal conductivity for molten metal is assumed to increase linearly between the solidus temperature and 3000 K by a factor of three, to allow for its convective stirring effect, as suggested in [1]. The latent heat, solidus and liquidus temperatures are 270 J/g, 1450 °C and 1500 °C, respectively. The subsequent mechanical analysis involves the use of the temperature histories computed by the preceding thermal analysis for each time increment as an input (thermal loading) for the calculation of transient thermal stress and deformation. In this analysis, rateindependent elastic–plastic constitutive equation was considered with the Von Mises yield criterion, temperature-dependent mechanical properties and linear isotropic hardening rule. The metallurgical and mechanical consequences of solid-state phase transformation were not considered because the influence that the metallurgical phase transformation [1] has on welding residual stress and deformation is negligible in mild carbon steels [37]. In the thermal and mechanical analyses, the process of sequential weld filler deposition is simulated using a consistent filler activation/ deactivation scheme [6]. A full Newton–Raphson (NR) iterative solution technique [39,40] was employed for obtaining a solution. During the thermal cycle, temperature and temperature-dependent material properties change very rapidly. Thus, full NR, which uses modified material properties and reformulates the stiffness matrix at every iteration step, was believed to give more accurate results [38]. Reduced integration scheme was implemented to facilitate convergence, and to avoid excessive locking during structural analysis.
Fig. 1. Dimensions of analysis model and welding direction.
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Table 1 Structural parameters of the analyzed models. Model
Diameter D (mm)
Thickness t (mm)
Length L (mm)
D/t
L/D
1 2 3 4 5
120 240 360 480 600
6 6 6 6 6
600 1200 1800 2400 3000
20 40 60 80 100
5 5 5 5 5
2.2. 3-D FE model FE simulation of the girth welding process was performed on a circular steel tube with a wall thickness (t) of 6 mm. Two circular tubes with “V” groove were assumed to be joined by single pass welding. Fig. 1 schematically shows the geometry and dimensions of the girth-welded tube. The nominal length (L) of the welded tube was assumed to be five times the outer diameter (D) of the cross-section. The figure also illustrates welding arc travel direction and welding start/stop position (θ = 0°). The type of welding process modeled using the aforementioned FE technique was FCA (Flux Cored Arc) welding process, for which the heat input and the welding velocity were chosen as 1300 J/mm and 5 mm/s, respectively. The welding procedures used are typical of industrial practice. In this work, the bending behavior of girth-welded circular steel tubes taking weld-induced residual stress and deformation into consideration was explored for five models with the structural parameters listed in Table 1. The D/t ratio was adopted as the main structural parameter because the most crucial geometric parameter of a girth-welded circular tube in flexure is the ratio of D/t by which the failure mode and the load capacity of the tube is strongly influenced. The ratios were generated by changing the diameter of the tubes only, keeping the identical thickness and cover typical thin and thick shells including the transition range [29]. The mesh refinement scheme for the FE model with D/t ratio of 20 is shown in Fig. 2. Because of the symmetry with respect to the weld centerline, only half of the tube needs to be modeled with 8-noded isoparametric solid elements and four layers. The adopted mesh design is a result of the considerations regarding weld-induced residual stress and deformation and the behavior of girth-welded circular steel tubes in bending. For the analysis of welding residual stress and deformation,
a fine mesh is used in the weld region and its vicinity due to the anticipated high temperature and stress gradients there. A few preliminary mesh sensitivity tests lead to using the present FE mesh with the smallest element size of 0.9 mm (axial) × 1.5 mm (thickness) × 12.1 mm (circumference). In order to facilitate nodal data mapping between thermal and mechanical analyses, the same FE mesh refinement was used with respective element types. The element type in thermal analysis is one which has a single degree of freedom, temperature, on each node, whilst in structural analysis the element type is the other with three translational degrees of freedom at each node. The mechanical boundary conditions were prescribed for preventing rigid body motion of the weld piece. The detailed boundary conditions used in the FE model are shown in Fig. 2 by the arrows. Mesh convergence study was also implemented to select suitable mesh density far from the welded zone for investigating the flexural behavior of the girth-welded tubes. The specific description on the mesh scheme is made next (Section 3.1). The other models with different D/t ratios have the same mesh density in and around the weld region except for that along the circumference considering computer power requirements and computational time. The material used here is a mild carbon steel tube (KS SPPS 420) complying with KS specifications [41]. Material modeling has always been a critical issue in the simulation of welding because of the lack of material information at high temperatures. Some simplifications and approximations are usually introduced to cope with this problem. These simplifications are necessary due to both scarcity of data and numerical problems when trying to duplicate the actual hightemperature behavior of the material [6]. In this work, due to the lack of material data especially at elevated temperatures, deterioration of its physical and mechanical properties with increasing temperature was assumed to be the same as the mild carbon steel with similar yield and tensile strength [36]. Fig. 3(a) and (b) shows the temperature-dependent thermo-physical and mechanical properties, respectively. Note that units in Fig. 3(a) are organized so that they can be shown on one graph for clarity. In Fig. 3(b), both the yield stress and elastic modulus are reduced to 5.0 MPa and 5.0 GPa, respectively, at the melting temperature to simulate low strength at high temperatures [1]. For the weld metal, autogenous weldment was assumed. This means that weld metal, heat affected zone and base metal share the same thermal and mechanical properties [42]. It must be recognized that in the FE modeling, residual stresses introduced by the fabrication process (seam welding) of the steel
Symmetry Plane
Z
90º 270º X
Fig. 2. 3-D FE model.
Y
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(a)
145
(a)
10
600
Residual Stress (MPa)
Density
8 Specific heat
6 4 Heat conductivity
2 0
0
200
400
600
800
1000
1200
Axial_90º Axial_180º Axial_270º Axial_0º
450 300 150 0 -150 0
1400
50
100
150
200
250
300
Distance from the weld centerline (mm)
(b)
(b)
400
300
150
200
100 E
100 0
0
200
400
600
800
50
1000
1200
1400
Residual Stress (MPa)
300
Young's modulus, E (GPa)
200
0
Axial_90º Axial_180º Axial_270º Axial_0º
150 0 -150 -300 -450 -600 0
50
100
150
200
250
300
Distance from the weld centerline (mm)
tube prior to the girth welding were ignored since the stresses have little influence on the bending resistance of circular steel tubes [33]. Moreover, the initial residual stresses in and around the girth weld are annealed during the welding process, and thus hardly affecting the evolution of final welding residual stress and deformation there. 2.3. Results and discussion Results are first presented for the investigation of weld-induced residual stresses in girth-welded circular steel tubes. Four different positions along the circumference are selected to portray welding residual stress distributions. The four positions have different circumferential angles from the welding start/stop position, which are 0°, 90°, 180° and 270°, respectively. Residual stresses in girth-welded thinwalled circular tubes are produced mainly from the circumferential shrinkage during the welding process. Fig. 4(a) and (b) depicts the axial residual stresses which act normal to the weld line at the four locations of the FE model with D/t ratio of 20 on the inside and outside surfaces, respectively, with respect to axial distance from the weld centerline. From the simulated results, it can be found that within and near the weld region, the predicted axial residual stresses are tensile on the inside surface and compressive on the outside surface. Fig. 5 shows a representative plot of the radial displacement distribution of the tube model on the outside surface after the welding. The weld depressions are presented at the locations where the circumferential angles are 0° and 90°, respectively. These results reveal that the diameter of the tube in the weld region and its neighborhood becomes smaller due to the circumferential shrinkage after welding; hence a bending moment through the thickness is generated there. This results in tensile axial residual stresses on the inside surface balanced by compressive stresses
Fig. 4. Axial residual stresses at the four locations: (a) inside surface, and (b) outside surface.
on the outside surface. A stress reversal from compressive to tensile on the outside surface away from the weld centerline is observed and vice versa on the inside surface. Moreover, the figure indicates that the diameter changes (weld depressions) are not uniform in the circumferential direction. It should also be mentioned that the axial residual stresses vary spatially. This is attributed to both the traveling arc along the circumference and the welding start/stop effects at the overlapping region [15]. Stresses acting parallel to the weld line are known as hoop stresses. Fig. 6 portrays the hoop residual stress distributions at the four locations. Regarding the hoop residual stresses, their magnitude is influenced by the axial residual stresses. This explains why on the outside surface, which is experiencing axial compression, the hoop
Displacement (mm)
Fig. 3. Temperature-dependent thermo-physical and mechanical properties of the material: (a) physical constants, and (b) mechanical properties.
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2
Radial_0º Radial_90º
0
50
100
150
200
250
Axial coordinate Fig. 5. Radial displacement distribution on the outside surface.
300
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(a) Residual Stress (MPa)
600
Hoop_90º Hoop_180º Hoop_270º Hoop_0º
450 300 150 0
3. Bending behavior of girth-welded circular steel tubes
-150 -300 0
50
100
150
200
250
300
Distance from the weld centerline (mm)
(b) Residual Stress (MPa)
600
Hoop_90º Hoop_180º Hoop_270º Hoop_0º
450 300
In this paper, the flexural responses of girth-welded circular steel tubes were examined by a nonlinear FE analysis using the in-house FE code [43] which employs layered shell elements based on the improved degenerated shell element [44,45] that is free of shear/ membrane locking problems and is suitable for thin or thick shell applications. Problems of flexure involving buckling are typically related to both of the following nonlinear types of behavior, namely: • geometric nonlinearity associated with buckling or large deflection, • material nonlinearity due to yielding or plastic deformation. This means that both geometric and material nonlinearities should always be taken into account in assessment of the bending behavior. In the present analysis, to describe the large deformation behavior and the material nonlinearity, the second Piola–Kirchhoff stress and the Green–Lagrange strain tensors [39] were used in the context of an incremental total Lagrangian formulation.
150 0 -150 -300 0
the preceding axial residual stresses, spatial variations are present along the circumference. Similar results were yielded through the other FE models with different D/t ratios except that with increasing D/t ratio, the region in and around the weld area subjected to plastic deformation becomes larger and the welding start/stop effects become more pronounced, which is consistent with the previous study [15] and not presented here.
50
100
150
200
250
300
3.1. Nonlinear FE model
Distance from the weld centerline (mm) Fig. 6. Hoop residual stresses at the four locations: (a) inside surface, and (b) outside surface.
residual stresses are less tensile at the weld region and its vicinity compared to those on the inside surface. Similar trends of stress reversal to the axial residual stresses are observed. Furthermore, through careful observation of the results, it can be known that like
The girth-welded circular steel tubes in bending were modeled using the layered shell elements which are shear deformable and have four nodes with five independent degrees of freedom per node (three for translation and two for flexural rotaion). The same mesh density as in the analysis of weld-induced residual stress and deformation was employed to make data mapping between the two structural FE models easy. A uniform mesh configuration away from the weld region except for the loading edges was carefully determined by carrying out a mesh
Rigid shell connecting end section nodes with reference node
Reference node
Z
X
Y
Bending moment applied at reference node along the Y-axis Fig. 7. Nodal constraints at the ends of the tube model.
C.-H. Lee et al. / Journal of Constructional Steel Research 75 (2012) 142–151
600.0
(a)
147
Z
Stress (MPa)
500.0 400.0
X
Y
300.0 200.0 100.0 0.0 0.00
0.05
0.10
0.1
0.20
0.25
0.30
Strain
(b)
Fig. 8. Piecewise linear stress–strain model.
convergence study with the aim of achieving accurate results whilst minimizing computational requirements, e.g., the suitable mesh size was found to be a uniform mesh of 7.0 mm (axial) × 12.1 mm (circumference) for the model with D/t ratio of 20. The longer side of the element lies in the circumferential direction, as the number of waves of the deformations along the circumference is generally small [46]. The through-thickness modeling was performed by the layers toward thickness in the element, i.e. four layers were used to discretize the computational domain through the thickness. It is worth noting that full FE model was constructed here due to the dissymmetry of boundary conditions adopted during the application of external loading (discussed afterward). In the analysis, in order to capture the bending behavior of girthwelded circular steel tubes realistically, three kinds of initial imperfections, i.e. global geometric imperfection along with weld-induced local geometric impefrection (weld depression) and residual stress were included in the numerical models. The global imperfection pattern was assumed to be a half-sine wave given by wg sin(πx/L), where x is the distance along the specimen, L is the specimen length and wg is the global imperfection amplitude which was consistently taken as L/500 [47]. The weld depressions were superimposed on the FE model seeded with the initial global deviations from the perfect circular tube associated with fabrication tolerances and minor damage during handling, i.e. the nodal displacements of each solid element on the outside surface caused by the shrinkage of the girth weld were passed to the corresponding nodal points in the shell element. The axial and hoop residual stresses of magnitude and distribution as given by the FE simulation of the welding process were introduced as initial conditions into the model, i.e. the residual stresses of each solid element were mapped into the integration points of corresponding layer through the thickness in the shell element.
No_Weld With_Weld
1.2
Moment (M/Mp)
1 0.8 0.6 0.4 0.2 0
0
0.05
0.1
0.15
0.2
0.25
Rotaion (θ) Fig. 9. Moment versus end-rotation response of the FE model with D/t ratio of 20.
Z
X
Y
Fig. 10. Deformed shape of the FE model with D/t ratio of 20 at the ultimate load: (a) tube model without girth weld (b) tube model with girth weld.
Positive pure bending moment was applied to the specimen with the weld start/stop position where the stress variation along the circumference becomes severe located at the top, thus exposing the specimen to the most unfavorable loading condition so as to obtain a conservative estimate of bending capacity. When preparing a FE model intended to replicate the bending behavior, special attention must be paid to the end constraints. From an extreme standpoint, the ends of the tube can be considered either to be prevented or free to ovalise. The restrained ovalisation of the ends can be easily simulated by constraining the displacements of the tube end nodes to those of a single node, which is placed at the centroid of the end section and acts as the reference node [31]. For the achievement of this condition, in the present study, a network of rigidly connected shell elements was placed at the end cross section. Large stiffness was assigned to these shell elements so that they provide much higher rigidity. The bending action was obtained by applying rotation increments directly to the reference nodes as concentrated couples as shown in Fig. 7. All nodes on the rigid plane were kinematically coupled for rotation in the same direction of the applied end moment. The boundary conditions adopted for the two ends of the tube were chosen such that the tube is simply supported, i.e. one reference node at either end of the tube was pinned and the other was left free to translate along the axial direction, thus avoiding interaction of axial strains. The endrotation under pure bending was monitored throughout the analysis. In this study, as indicated earlier, autogenous weldment was employed during the girth welding. Therefore, the representative true stress–strain relations for the girth-welded circular steel tubes were generated from the engineering stress–strain curves obtained from the tensile coupon tests [48] and material nonlinearity was incorporated into the numerical models by means of a piecewise linear stress–strain model with the Von Mises yield criterion to mimic, in particular, the strainhardening region, which is shown in Fig. 8. It is significant to note that, in the stress–strain model, the increase of yield stress in the weld metal and the heat affected zone induced by plastic deformations during the
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(a) No_Weld With_Weld
1.2
(a)1.2
No_Weld With_Weld
1
Moment (M/Mp)
Moment (M/Mp)
1 0.8 0.6 0.4
0.8 0.6 0.4 0.2
0.2 0 0
0
0.05
0.1
0.15
0.2
0
0.25
0.05
0.1
0.15
0.2
Rotaion (θ)
Rotaion (θ)
(b)
(b)
Z
X
X
Y
(c)
(c)
Z
X
Z
Y
Fig. 11. Bending behavior of the FE model with D/t ratio of 40: (a) moment versus endrotation response, (b) failure mode without girth weld, and (c) failure mode with girth weld.
welding process was not considered due to the lack of experimental data. This assumption seems to be reasonable, and justified for parametric comparative studies because material behavior contributes equally in the results of all cases and differences in structural response can be attributed to changes in the parameters. Incremental-solution strategies are required to trace the proper nonlinear equilibrium path in the analysis. Riks [49] introduced an incremental approach to the solution of snapping and collapse problems. In Riks's algorithm, it is assumed that loading is proportional and all load magnitudes vary with a single scalar parameter that is called ‘arc length’. In this study, the nonlinear load-deformation path was followed by the arc-length method combined with the Newton–Raphson iteration scheme [39].
Y
Z
X
Y
Fig. 12. Bending behavior of the FE model with D/t ratio of 60: (a) moment versus endrotation response, (b) failure mode without girth weld, and (c) failure mode with girth weld.
under pure bending, compared with the nonlinear prediction of the model without girth weld. The bending moments attained in the analysis have been normalized against the plastic moment capacity, Mp, defined by: Mp ¼ σ y Z
ð1Þ
where σy is the material yield stress and Z is the plastic section modulus, calculated as Eq. (2) in the case of circular hollow section.
Z¼
D32 −D31 6
ð2Þ
3.2. Results and discussion Results are first prepared for the model with D/t ratio of 20. Fig. 9 shows the predicted moment versus end-rotation response curve
where D2 is the outer diameter and D1 is the inner diameter. It is immediately apparent that these two responses are very similar except the extent of strain-hardening and show the typical bending
C.-H. Lee et al. / Journal of Constructional Steel Research 75 (2012) 142–151
149
(a)
(a)
No_Weld
1.2
With_Weld
No_Weld With_Weld
1.2
1
Moment (M/Mp)
Moment (M/Mp)
1 0.8 0.6 0.4
0.6 0.4 0.2
0.2 0
0.8
0 0
0.05
0.1
0
0.025
0.05
0.15
0.075
0.1
Rotaion (θ)
Rotaion (θ)
(b)
(b)
Z Z X X
Y
Y
(c)
(c)
Z
Z X X
Y
Y
Fig. 13. Bending behavior of the FE model with D/t ratio of 80: (a) moment versus endrotation response, (b) failure mode without girth weld, and (c) failure mode with girth weld.
behavior of circular steel tubes with low D/t ratio, i.e. a significant load increase exists between the onset of yielding and the limiting buckling moment induced by the material strain-hardening, resulting in ultimate moment capacity greater than the full plastic moment. In addition, before and after the ultimate moment, the rising and descending rates are relatively mild. The numerical failure mode of the tube model which does not contain girth weld is given in Fig. 10 and compared with the deformed girth-welded tube model at the ultimate load, where displacements are amplified with a coefficient of 1.5 in order to allow a better visualization of the deformations. The former model buckles by the Brazier ovalization mode [50], whereas the latter model exhibits a combined failure mode of flattening and local buckling near the girth weld on the compression side induced by the circumferential shrinkage during welding. This local buckling
Fig. 14. Bending behavior of the FE model with D/t ratio of 100: (a) moment versus end-rotation response, (b) failure mode without girth weld, and (c) failure mode with girth weld.
prevents the attainment of larger extent of strain-hardening in the moment versus end-rotation relationship, leading to lower ductility and ultimate moment capacity. The other moment versus end-rotation predictions are presented in Figs. 11–14 for the models with D/t ratios of 40, 60, 80 and 100 in that order, followed by the corresponding deformed shapes at the limiting buckling moment in which displacements are magnified by a factor of 1.5. It can be found that the moment ratio achieved by the FE model without girth weld becomes lower with the failure being less ductile as the D/t ratio increases. The D/t ratio reflects the resistance of circular tubes to local buckling. With an increase in D/t, which is equivalent to a decrease of the curvature, the out-of-plane stiffness of a curved panel of a given circumferential width is reduced [32]. Moreover, a large D/t ratio induces a nearly uniform distribution of compressive stress in the most highly stressed panels. This leads to a
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1.2
M/Mp
1.1
1
0.9
0.8
0
20
40
60
80
100
120
D/t Fig. 15. Ultimate bending capacity of circular steel tubes with and without girth weld depending on the D/t ratio.
lower level of buckling stress than would occur in a tube with a higher stress gradient resulting from a smaller D/t ratio [32,47]. The normalized moment capacity of the FE models with girth weld shows similar trends to their counterparts without girth weld. In addition, careful observation of the results unveils that the larger the ratio of D/t, the more significant the influence of weld-induced residual stress and deformation on the bending capacity becomes. The main possible reason for this phenomenon is believed to be the fact that as described earlier, plastic region near the girth weld becomes larger, whilst the local wavelength becomes smaller with the increase of D/t ratio. It should be noted that the flexural behavior of the tube models with girth weld always involves local buckling near the girth weld on the compression side accompanied by the tube center ovalization reflecting the D/t ratio, whereas the failure modes of the tubes with no girth weld are divided into three categories depending on the bending capacity that they achieve: (1) the Brazier ovalization, (2) combined mode of ovalization and local buckling and (3) local buckling. This local buckling alters the nature of moment versus end-rotation response and diminishes the limiting buckling moment of girth-welded circular steel tubes. Fig. 15 compares the effect of D/t ratio on the ultimate bending capacity of circular steel tubes with and without girth weld. This result corroborates the previous finding, i.e. the normalized moment capacity obviously decreases with the increasing ratio of D/t in both cases. Furthermore, it is clear that the influence of girth weld on the ultimate moment capacity becomes more pronounced as the ratio of D/t increases. 4. Conclusions This paper investigated the buckling behavior of girth-welded circular steel tubes subjected to pure bending by FE method. Sequentially coupled 3-D thermo-mechanical FE analysis for predicting residual stress and deformation induced by the girth welding of circular steel tubes with different D/t ratios was first performed. Nonlinear FE analysis which can identify the failure mode, the ultimate moment capacity and the moment versus end-rotation behavior of the girth-welded circular steel tubes taking weld-induced geometric imperfection and residual stress into account was next carried out. Based on the results in this work, the following conclusions can be made. a) 3-D FE model is essential to accurately simulate the girth welding of circular steel tubes because the weld-induced residual stress and deformation are by no means axisymmetric, which is induced by the traveling arc and welding start/stop effects. In addition, the region near the girth weld subjected to plastic deformation becomes larger and the welding start/stop effects become more pronounced with increasing the D/t ratio.
b) The moment capacity expressed as the ratio of the ultimate moment over the full plastic moment of girth-welded circular steel tubes becomes lower with the failure being less ductile and the influence of weld-induced residual stress and deformation on the bending capacity becomes more significant as the D/t ratio increases. This is believed to be due to the fact that plastic region near the girth weld becomes larger, whilst the local wavelength becomes smaller with the increase of D/t ratio. c) The flexural behavior of girth-welded circular steel tubes always involves local buckling near the girth weld on the compression side, which alters the nature of moment versus end-rotation response and diminishes the limiting buckling moment. d) In the buckling analysis, the initial geometric imperfection was taken to be symmetric with respect to the weld centerline. However, under the asymmetric condition, the asymmetric imperfection may produce different results from those achieved in this investigation, at which the future works are aimed. References [1] Taljat B, Radhakrishnan B, Zacharia T. Numerical analysis of GTA welding process with emphasis on post-solidification phase transformation effects on the residual stresses. Mater Sci Eng A 1998;246:45–54. [2] Lee CH, Chang KH. Numerical investigation on the behavior of circumferentially buttwelded steel circular hollow section flexural members. J Struct Eng 2011;137: 1395–404. [3] Edlund BLO. Buckling of metallic shells: buckling and postbuckling behaviour of isotropic shells, especially cylinders. Struct Control Health Monit 2007;14: 693–713. [4] Goldak J, Akhlagi M. Computational welding mechanics. Springer; 2005. [5] Lindgren L-E. Finite element modelling and simulation of welding, Part 1 Increased complexity. J Therm Stresses 2001;24:141–92. [6] Lindgren L-E. Finite element modelling and simulation of welding, part 2 improved material modelling. J Therm Stresses 2001;24:195–231. [7] Lindgren L-E. Finite element modelling and simulation of welding, part 3 efficiency and integration. J Therm Stresses 2001;24:305–34. [8] Lindgren L-E. Numerical modelling of welding. Comput Methods Appl Mech Eng 2006;195:6710–36. [9] Lindgren L-E. Computational welding mechanics (Thermomechanical and microstructural simulations). Woodhead Publishing; 2007. [10] Rybicki EF, Schmueser DW, Stonesifer RW, Groom JJ, Mishaler HW. A finite element model for residual stresses and deflections in girth-butt welded pipes. J Press Vessel Technol 1978;100:256–62. [11] Brickstad B, Josefson BL. A parametric study of residual stresses in multi-pass butt-welded stainless steel pipes. Int J Press Vessels Pip 1998;75:11–25. [12] Mochizuki M, Hayashi M, Hattori T. Residual stress distribution depending on welding sequence in multi-pass welded joints with X-shaped groove. J Press Vessel Technol 2000;122:27–32. [13] Yaghi A, Hyde TH, Becker AA, Sun W, Williams JA. Residual stress simulation in thin and thick-walled stainless steel pipe welds including pipe diameter effects. Int J Press Vessels Pip 2006;83:864–74. [14] Deng D, Murakawa H, Liand W. Numerical and experimental investigation on welding residual stress in multi-pass butt-welded austenitic stainless steel pipe. Comput Mater Sci 2008;42:234–44. [15] Lee CH, Chang KH. Three-dimensional finite element simulation of residual stresses in circumferential welds of steel pipe including pipe diameter effects. Mater Sci Eng A 2008;487:210–8. [16] Lindgren L-E, Karlsson L. Deformations and stresses in welding of shell structures. Int J Numer Methods Eng 1988;2:155–64. [17] Karlsson RI, Josefson BL. Three-dimensional finite element analysis of temperatures and stresses in a single-pass butt-welded pipe. J Press Vessel Technol 1990;112:76–84. [18] Fricke S, Keim E, Schmidt J. Numerical weld modeling — a method for calculating weld-induced residual stresses. Nucl Eng Des 2001;206:139–50. [19] Xu J, Chen L, Wang J, Ni C. Prediction of welding distortion in multipass girth-butt welded pipes of different wall thickness. Int J Adv Manuf Technol 2008;35: 987–93. [20] Lee CH, Chang KH. Prediction of residual stresses in high strength carbon steel pipe weld considering solid-state phase transformation effects. Comput Struct 2011;89:256–65. [21] Brazier LG. On the flexure of thin cylindrical shells and other section. Proc R Soc Lond 1927;A116:104–14. [22] Seide P, Weingarten VI. On the buckling of circular cylindrical shells under pure bending. ASME J Appl Mech 1961;28:112–6. [23] Sherman DR. Tests of circular steel tubes in bending. ASCE J Struct Div 1976;102: 2181–95. [24] Reddy BD. An experimental study of the plastic buckling of circular cylinders in pure bending. Int J Solids Struct 1979;15:669–83. [25] Tugcu P, Schroeder J. Plastic deformation and stability of pipes exposed to external couples. Int J Solids Struct 1979;15:643–58.
C.-H. Lee et al. / Journal of Constructional Steel Research 75 (2012) 142–151 [26] Gellin S. The plastic buckling of long cylindrical shell under pure bending. Int J Solids Struct 1980;16:397–407. [27] Kyriakides S, Ju GT. Bifurcation and localization instabilities in cylindrical shells under bending. I. Experiments. Int J Solids Struct 1992;29:1117–42. [28] Ju GT, Kyriakides S. Bifurcation and localization instabilities in cylindrical shells under bending. II. Predictions. Int J Solids Struct 1992;29:1143–71. [29] Yeh MK, Lin MC, Wu WT. Bending buckling of an elastoplastic cylindrical shell with a cutout. Eng Struct 1999;21:996–1005. [30] Alashti RA, Rahimi GH, Poursaeidi E. Plastic limit load of cylindrical shells with cutouts subject to pure bending moment. Int J Press Vessels Pip 2008;85: 498–506. [31] Guarracino F, Walker AC, Giordano A. Effects of boundary conditions on testing of pipes and finite element modeling. Int J Press Vessels Pip 2009;86:196–206. [32] Chen Q, Elwi AE, Kulak GL. Finite element analysis of longitudinally stiffened cylinders in bending. J Eng Mech 1996;122:1060–8. [33] Kiymaz G, Coskun E, Cosgun C. Behavior and design of seam-welded stainless steel circular hollow section flexural members. J Struct Eng 2007;133:1792–800. [34] Chen WF, Ross DA. Test of fabricated tubular columns. J Struct Eng 1977;103: 619–34. [35] Lee CH. A study on the mechanical characteristics of high strength steel for the application to the steel bridge. Ph.D. Thesis, Chung-Ang University, Korea, 2005. [36] Chang KH, Lee CH. Finite element analysis of the residual stresses in T-joint fillet welds made of similar and dissimilar steels. Int J Adv Manuf Technol 2009;41: 250–8. [37] Deng D, Liang W, Murakawa H. Determination of welding deformation in filletwelded joint by means of numerical simulation and comparison with experimental measurements. J Mater Process Technol 2007;183:219–25.
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Contents lists available at SciVerse ScienceDirect
Journal of Constructional Steel Research
Bending capacity of girth-welded circular steel tubes Chin-Hyung Lee, Jeong-Hoon Baek, Kyong-Ho Chang ⁎ Department of Civil and Environmental Engineering, Chung-Ang University, 221, Heukseok-dong, Dongjak-ku, Seoul 156-756, Republic of Korea
a r t i c l e
i n f o
Article history: Received 13 November 2011 Accepted 22 March 2012 Available online 18 April 2012 Keywords: Girth-welded circular steel tubes Weld-induced residual stress and deformation Bending Nonlinear finite element analysis Buckling
a b s t r a c t In this paper, the buckling behavior of girth-welded circular steel tubes subjected to bending was investigated by numerical method. Finite element (FE) simulation of the girth welding process was first performed to obtain weld-induced residual stress and deformation employing sequentially coupled threedimensional (3-D) thermo-mechanical FE formulation. Elastoplastic large-deformation analysis in which the failure mode, the ultimate moment capacity and the moment versus end-rotation behavior of girth-welded circular steel tubes under pure bending were explored incorporating weld-induced geometric imperfection and residual stress was next carried out. Results showed that the flexural behavior of girth-welded circular steel tubes always involves local buckling near the girth weld on the compression side, which significantly affects the moment versus end-rotation response. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Circular steel tubes are increasingly used both in building and bridge structures due to their efficient geometry and to esthetic benefits that they offer over more traditional open cross sections. During their service life, these members are subjected to loading of various types such as axial loading, bending and torsion. In practice, girth welding of circular tubes is frequently needed due to the long geometry relative to the diameter and the wall-thickness. When two circular steel tubes are welded together, a non-uniform temperature field induced during the welding process produces undesired residual stress and deformation. The presence of welding residual stress and deformation can be a major concern in structural integrity assessment of girth-welded members [1]. Particularly, when combined with service loads, welding residual stress causes premature yielding and loss of stiffness and may lead to deterioration of load carrying capacity [2]. Moreover, welding deformation, i.e. weld depression induced by circumferential shrinkage of the weld region has been founded to have significant effects on the buckling behavior of cylindrical members [3]. Therefore, a good estimation of weldinduced residual stress and geometric imperfection, and an accurate prediction of the behavior of girth-welded members under loading are important for the production of an efficient and economic design and safety of the structure. This paper addresses the bending resistance of girth-welded circular steel tubes. Recently, finite element (FE) method has emerged as a useful and powerful numerical analysis tool. It can be employed to simulate
⁎ Corresponding author. Tel.: + 82 2 820 5337; fax: + 82 2 823 5339. E-mail address: ifi[email protected] (K.-H. Chang). 0143-974X/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2012.03.019
welding temperature field, welding residual stress field and welding deformation [4–9]. Over the last three decades or so, there have been significant research activities on the FE simulation focusing on the girth welding [10–14]. However, these studies have been limited to the axisymmetric condition which cannot reproduce the threedimensional (3-D) features in the girth welding process [15]. On the 3-D FE simulation, limited works have been published due to the high computational cost [15–20]. Much work has been devoted to investigating the behavior of circular steel tubes under bending in the elastic range [21,22] and plastic range [23–31]. However, their works have been generally related to hot-rolled or cold-formed sections. In the literature available on welded circular tubes in bending, Chen et al. [32] presented a FE model for longitudinally stiffened large diameter fabricated steel cylinders in pure bending. The model incorporates both initial geometric imperfections and residual stresses resulting from the welding of stiffeners to the cylinder and verified through the experimental program. The geometric imperfections measured from the test specimen were mapped into the FE model and incorporation of the residual stresses into the model was done by applying a distributed fictitious temperature loading that produced the initial strains necessary to set up the required residual stresses in the cylinder and stiffeners. Kiymaz et al. [33] examined the structural response of seam-welded stainless steel circular hollow section (CHS) flexural members incorporating residual stresses produced by the seam welding. For the residual stress analysis, they proposed a simpler stress-block model based on the measurements taken by Chen and Ross [34]. Nevertheless, as described, they did not implement direct simulation of the welding process due to the truly complex analysis procedure. Moreover, in their works, girth welding of the tubes was not considered.
C.-H. Lee et al. / Journal of Constructional Steel Research 75 (2012) 142–151
As for the bending behavior of girth-welded circular steel tubes, to the knowledge of the authors, very little attention has been received to date and therefore deserves special attention. Actually, Lee and Chang [2] assessed the behavior of girth-welded steel CHS members exposed to bending by a FE method taking weld-induced residual stresses into account. They simulated four-point bending tests of the CHS members. However, they focused on the effects of welding residual stresses and loading positions on the flexural behavior, and thus the bending strength and buckling mode depending on the diameter to thickness (D/t) ratio are still unknown. This paper deals with the numerical investigation on the buckling behavior of girth-welded circular steel tubes subjected to bending by a sequentially coupled thermo-mechanical analysis followed by a buckling analysis. FE simulation of the girth welding process was first performed to obtain weld-induced residual stress and deformation. Elastoplastic large-deformation analysis in which the failure modes, the limiting bending moments and the moment versus end-rotation behavior of the tube models with varying D/t ratios were explored incorporating weld-induced geometric imperfection and residual stress was next carried out. Finally, the paper concludes from the discussion of the numerical results. 2. FE simulation of the girth welding process In this section, FE methodologies for the simulation of the girth welding process are briefly described as similar approaches proposed in previous publications [2,15] were adopted to identify welding residual stress and deformation. The process of welding was simulated using 3-D thermo-mechanical FE formulation based on the in-house FE-code [35], which has been extensively verified against numerical results found in the literature and experiments [15,36]. The formulation consists of two stages, i.e. a transient thermal analysis followed by a transient mechanical (structural) analysis and considers temperature-dependent thermo-physical and mechanical properties of the materials. Because of the weak structural to thermal field couplings, these two analyses can be carried out in sequence. First, a thermal analysis solves for the transient temperature field and its history associated with the heat flow of welding. The resulting temperature history solutions are further utilized as the thermal loading in the subsequent mechanical analysis to obtain the transient and residual stress and deformation.
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2.1. Thermal and mechanical analysis The transient, non linear thermal solution is based on the heat conduction with the moving heat source, the convective and radiative boundary conditions. The combined heat source model in which the heat of the welding arc is modeled by a surface heat source with a Gaussian distribution, and that of the melt droplets is modeled by a volumetric heat source with uniform density was employed [37] in conjunction with the boundary conditions where radiation heat losses and convection heat losses are both taken into account employing the total temperature-dependent heat transfer coefficient [38]. As for the heat effects relevant to the molten metal of the weld pool, two methodologies were used: (1) the liquid-to-solid phase transformation effects of the weld pool are modeled by taking into account the latent heat of fusion, and (2) the thermal conductivity for molten metal is assumed to increase linearly between the solidus temperature and 3000 K by a factor of three, to allow for its convective stirring effect, as suggested in [1]. The latent heat, solidus and liquidus temperatures are 270 J/g, 1450 °C and 1500 °C, respectively. The subsequent mechanical analysis involves the use of the temperature histories computed by the preceding thermal analysis for each time increment as an input (thermal loading) for the calculation of transient thermal stress and deformation. In this analysis, rateindependent elastic–plastic constitutive equation was considered with the Von Mises yield criterion, temperature-dependent mechanical properties and linear isotropic hardening rule. The metallurgical and mechanical consequences of solid-state phase transformation were not considered because the influence that the metallurgical phase transformation [1] has on welding residual stress and deformation is negligible in mild carbon steels [37]. In the thermal and mechanical analyses, the process of sequential weld filler deposition is simulated using a consistent filler activation/ deactivation scheme [6]. A full Newton–Raphson (NR) iterative solution technique [39,40] was employed for obtaining a solution. During the thermal cycle, temperature and temperature-dependent material properties change very rapidly. Thus, full NR, which uses modified material properties and reformulates the stiffness matrix at every iteration step, was believed to give more accurate results [38]. Reduced integration scheme was implemented to facilitate convergence, and to avoid excessive locking during structural analysis.
Fig. 1. Dimensions of analysis model and welding direction.
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Table 1 Structural parameters of the analyzed models. Model
Diameter D (mm)
Thickness t (mm)
Length L (mm)
D/t
L/D
1 2 3 4 5
120 240 360 480 600
6 6 6 6 6
600 1200 1800 2400 3000
20 40 60 80 100
5 5 5 5 5
2.2. 3-D FE model FE simulation of the girth welding process was performed on a circular steel tube with a wall thickness (t) of 6 mm. Two circular tubes with “V” groove were assumed to be joined by single pass welding. Fig. 1 schematically shows the geometry and dimensions of the girth-welded tube. The nominal length (L) of the welded tube was assumed to be five times the outer diameter (D) of the cross-section. The figure also illustrates welding arc travel direction and welding start/stop position (θ = 0°). The type of welding process modeled using the aforementioned FE technique was FCA (Flux Cored Arc) welding process, for which the heat input and the welding velocity were chosen as 1300 J/mm and 5 mm/s, respectively. The welding procedures used are typical of industrial practice. In this work, the bending behavior of girth-welded circular steel tubes taking weld-induced residual stress and deformation into consideration was explored for five models with the structural parameters listed in Table 1. The D/t ratio was adopted as the main structural parameter because the most crucial geometric parameter of a girth-welded circular tube in flexure is the ratio of D/t by which the failure mode and the load capacity of the tube is strongly influenced. The ratios were generated by changing the diameter of the tubes only, keeping the identical thickness and cover typical thin and thick shells including the transition range [29]. The mesh refinement scheme for the FE model with D/t ratio of 20 is shown in Fig. 2. Because of the symmetry with respect to the weld centerline, only half of the tube needs to be modeled with 8-noded isoparametric solid elements and four layers. The adopted mesh design is a result of the considerations regarding weld-induced residual stress and deformation and the behavior of girth-welded circular steel tubes in bending. For the analysis of welding residual stress and deformation,
a fine mesh is used in the weld region and its vicinity due to the anticipated high temperature and stress gradients there. A few preliminary mesh sensitivity tests lead to using the present FE mesh with the smallest element size of 0.9 mm (axial) × 1.5 mm (thickness) × 12.1 mm (circumference). In order to facilitate nodal data mapping between thermal and mechanical analyses, the same FE mesh refinement was used with respective element types. The element type in thermal analysis is one which has a single degree of freedom, temperature, on each node, whilst in structural analysis the element type is the other with three translational degrees of freedom at each node. The mechanical boundary conditions were prescribed for preventing rigid body motion of the weld piece. The detailed boundary conditions used in the FE model are shown in Fig. 2 by the arrows. Mesh convergence study was also implemented to select suitable mesh density far from the welded zone for investigating the flexural behavior of the girth-welded tubes. The specific description on the mesh scheme is made next (Section 3.1). The other models with different D/t ratios have the same mesh density in and around the weld region except for that along the circumference considering computer power requirements and computational time. The material used here is a mild carbon steel tube (KS SPPS 420) complying with KS specifications [41]. Material modeling has always been a critical issue in the simulation of welding because of the lack of material information at high temperatures. Some simplifications and approximations are usually introduced to cope with this problem. These simplifications are necessary due to both scarcity of data and numerical problems when trying to duplicate the actual hightemperature behavior of the material [6]. In this work, due to the lack of material data especially at elevated temperatures, deterioration of its physical and mechanical properties with increasing temperature was assumed to be the same as the mild carbon steel with similar yield and tensile strength [36]. Fig. 3(a) and (b) shows the temperature-dependent thermo-physical and mechanical properties, respectively. Note that units in Fig. 3(a) are organized so that they can be shown on one graph for clarity. In Fig. 3(b), both the yield stress and elastic modulus are reduced to 5.0 MPa and 5.0 GPa, respectively, at the melting temperature to simulate low strength at high temperatures [1]. For the weld metal, autogenous weldment was assumed. This means that weld metal, heat affected zone and base metal share the same thermal and mechanical properties [42]. It must be recognized that in the FE modeling, residual stresses introduced by the fabrication process (seam welding) of the steel
Symmetry Plane
Z
90º 270º X
Fig. 2. 3-D FE model.
Y
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(a)
145
(a)
10
600
Residual Stress (MPa)
Density
8 Specific heat
6 4 Heat conductivity
2 0
0
200
400
600
800
1000
1200
Axial_90º Axial_180º Axial_270º Axial_0º
450 300 150 0 -150 0
1400
50
100
150
200
250
300
Distance from the weld centerline (mm)
(b)
(b)
400
300
150
200
100 E
100 0
0
200
400
600
800
50
1000
1200
1400
Residual Stress (MPa)
300
Young's modulus, E (GPa)
200
0
Axial_90º Axial_180º Axial_270º Axial_0º
150 0 -150 -300 -450 -600 0
50
100
150
200
250
300
Distance from the weld centerline (mm)
tube prior to the girth welding were ignored since the stresses have little influence on the bending resistance of circular steel tubes [33]. Moreover, the initial residual stresses in and around the girth weld are annealed during the welding process, and thus hardly affecting the evolution of final welding residual stress and deformation there. 2.3. Results and discussion Results are first presented for the investigation of weld-induced residual stresses in girth-welded circular steel tubes. Four different positions along the circumference are selected to portray welding residual stress distributions. The four positions have different circumferential angles from the welding start/stop position, which are 0°, 90°, 180° and 270°, respectively. Residual stresses in girth-welded thinwalled circular tubes are produced mainly from the circumferential shrinkage during the welding process. Fig. 4(a) and (b) depicts the axial residual stresses which act normal to the weld line at the four locations of the FE model with D/t ratio of 20 on the inside and outside surfaces, respectively, with respect to axial distance from the weld centerline. From the simulated results, it can be found that within and near the weld region, the predicted axial residual stresses are tensile on the inside surface and compressive on the outside surface. Fig. 5 shows a representative plot of the radial displacement distribution of the tube model on the outside surface after the welding. The weld depressions are presented at the locations where the circumferential angles are 0° and 90°, respectively. These results reveal that the diameter of the tube in the weld region and its neighborhood becomes smaller due to the circumferential shrinkage after welding; hence a bending moment through the thickness is generated there. This results in tensile axial residual stresses on the inside surface balanced by compressive stresses
Fig. 4. Axial residual stresses at the four locations: (a) inside surface, and (b) outside surface.
on the outside surface. A stress reversal from compressive to tensile on the outside surface away from the weld centerline is observed and vice versa on the inside surface. Moreover, the figure indicates that the diameter changes (weld depressions) are not uniform in the circumferential direction. It should also be mentioned that the axial residual stresses vary spatially. This is attributed to both the traveling arc along the circumference and the welding start/stop effects at the overlapping region [15]. Stresses acting parallel to the weld line are known as hoop stresses. Fig. 6 portrays the hoop residual stress distributions at the four locations. Regarding the hoop residual stresses, their magnitude is influenced by the axial residual stresses. This explains why on the outside surface, which is experiencing axial compression, the hoop
Displacement (mm)
Fig. 3. Temperature-dependent thermo-physical and mechanical properties of the material: (a) physical constants, and (b) mechanical properties.
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2
Radial_0º Radial_90º
0
50
100
150
200
250
Axial coordinate Fig. 5. Radial displacement distribution on the outside surface.
300
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(a) Residual Stress (MPa)
600
Hoop_90º Hoop_180º Hoop_270º Hoop_0º
450 300 150 0
3. Bending behavior of girth-welded circular steel tubes
-150 -300 0
50
100
150
200
250
300
Distance from the weld centerline (mm)
(b) Residual Stress (MPa)
600
Hoop_90º Hoop_180º Hoop_270º Hoop_0º
450 300
In this paper, the flexural responses of girth-welded circular steel tubes were examined by a nonlinear FE analysis using the in-house FE code [43] which employs layered shell elements based on the improved degenerated shell element [44,45] that is free of shear/ membrane locking problems and is suitable for thin or thick shell applications. Problems of flexure involving buckling are typically related to both of the following nonlinear types of behavior, namely: • geometric nonlinearity associated with buckling or large deflection, • material nonlinearity due to yielding or plastic deformation. This means that both geometric and material nonlinearities should always be taken into account in assessment of the bending behavior. In the present analysis, to describe the large deformation behavior and the material nonlinearity, the second Piola–Kirchhoff stress and the Green–Lagrange strain tensors [39] were used in the context of an incremental total Lagrangian formulation.
150 0 -150 -300 0
the preceding axial residual stresses, spatial variations are present along the circumference. Similar results were yielded through the other FE models with different D/t ratios except that with increasing D/t ratio, the region in and around the weld area subjected to plastic deformation becomes larger and the welding start/stop effects become more pronounced, which is consistent with the previous study [15] and not presented here.
50
100
150
200
250
300
3.1. Nonlinear FE model
Distance from the weld centerline (mm) Fig. 6. Hoop residual stresses at the four locations: (a) inside surface, and (b) outside surface.
residual stresses are less tensile at the weld region and its vicinity compared to those on the inside surface. Similar trends of stress reversal to the axial residual stresses are observed. Furthermore, through careful observation of the results, it can be known that like
The girth-welded circular steel tubes in bending were modeled using the layered shell elements which are shear deformable and have four nodes with five independent degrees of freedom per node (three for translation and two for flexural rotaion). The same mesh density as in the analysis of weld-induced residual stress and deformation was employed to make data mapping between the two structural FE models easy. A uniform mesh configuration away from the weld region except for the loading edges was carefully determined by carrying out a mesh
Rigid shell connecting end section nodes with reference node
Reference node
Z
X
Y
Bending moment applied at reference node along the Y-axis Fig. 7. Nodal constraints at the ends of the tube model.
C.-H. Lee et al. / Journal of Constructional Steel Research 75 (2012) 142–151
600.0
(a)
147
Z
Stress (MPa)
500.0 400.0
X
Y
300.0 200.0 100.0 0.0 0.00
0.05
0.10
0.1
0.20
0.25
0.30
Strain
(b)
Fig. 8. Piecewise linear stress–strain model.
convergence study with the aim of achieving accurate results whilst minimizing computational requirements, e.g., the suitable mesh size was found to be a uniform mesh of 7.0 mm (axial) × 12.1 mm (circumference) for the model with D/t ratio of 20. The longer side of the element lies in the circumferential direction, as the number of waves of the deformations along the circumference is generally small [46]. The through-thickness modeling was performed by the layers toward thickness in the element, i.e. four layers were used to discretize the computational domain through the thickness. It is worth noting that full FE model was constructed here due to the dissymmetry of boundary conditions adopted during the application of external loading (discussed afterward). In the analysis, in order to capture the bending behavior of girthwelded circular steel tubes realistically, three kinds of initial imperfections, i.e. global geometric imperfection along with weld-induced local geometric impefrection (weld depression) and residual stress were included in the numerical models. The global imperfection pattern was assumed to be a half-sine wave given by wg sin(πx/L), where x is the distance along the specimen, L is the specimen length and wg is the global imperfection amplitude which was consistently taken as L/500 [47]. The weld depressions were superimposed on the FE model seeded with the initial global deviations from the perfect circular tube associated with fabrication tolerances and minor damage during handling, i.e. the nodal displacements of each solid element on the outside surface caused by the shrinkage of the girth weld were passed to the corresponding nodal points in the shell element. The axial and hoop residual stresses of magnitude and distribution as given by the FE simulation of the welding process were introduced as initial conditions into the model, i.e. the residual stresses of each solid element were mapped into the integration points of corresponding layer through the thickness in the shell element.
No_Weld With_Weld
1.2
Moment (M/Mp)
1 0.8 0.6 0.4 0.2 0
0
0.05
0.1
0.15
0.2
0.25
Rotaion (θ) Fig. 9. Moment versus end-rotation response of the FE model with D/t ratio of 20.
Z
X
Y
Fig. 10. Deformed shape of the FE model with D/t ratio of 20 at the ultimate load: (a) tube model without girth weld (b) tube model with girth weld.
Positive pure bending moment was applied to the specimen with the weld start/stop position where the stress variation along the circumference becomes severe located at the top, thus exposing the specimen to the most unfavorable loading condition so as to obtain a conservative estimate of bending capacity. When preparing a FE model intended to replicate the bending behavior, special attention must be paid to the end constraints. From an extreme standpoint, the ends of the tube can be considered either to be prevented or free to ovalise. The restrained ovalisation of the ends can be easily simulated by constraining the displacements of the tube end nodes to those of a single node, which is placed at the centroid of the end section and acts as the reference node [31]. For the achievement of this condition, in the present study, a network of rigidly connected shell elements was placed at the end cross section. Large stiffness was assigned to these shell elements so that they provide much higher rigidity. The bending action was obtained by applying rotation increments directly to the reference nodes as concentrated couples as shown in Fig. 7. All nodes on the rigid plane were kinematically coupled for rotation in the same direction of the applied end moment. The boundary conditions adopted for the two ends of the tube were chosen such that the tube is simply supported, i.e. one reference node at either end of the tube was pinned and the other was left free to translate along the axial direction, thus avoiding interaction of axial strains. The endrotation under pure bending was monitored throughout the analysis. In this study, as indicated earlier, autogenous weldment was employed during the girth welding. Therefore, the representative true stress–strain relations for the girth-welded circular steel tubes were generated from the engineering stress–strain curves obtained from the tensile coupon tests [48] and material nonlinearity was incorporated into the numerical models by means of a piecewise linear stress–strain model with the Von Mises yield criterion to mimic, in particular, the strainhardening region, which is shown in Fig. 8. It is significant to note that, in the stress–strain model, the increase of yield stress in the weld metal and the heat affected zone induced by plastic deformations during the
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(a) No_Weld With_Weld
1.2
(a)1.2
No_Weld With_Weld
1
Moment (M/Mp)
Moment (M/Mp)
1 0.8 0.6 0.4
0.8 0.6 0.4 0.2
0.2 0 0
0
0.05
0.1
0.15
0.2
0
0.25
0.05
0.1
0.15
0.2
Rotaion (θ)
Rotaion (θ)
(b)
(b)
Z
X
X
Y
(c)
(c)
Z
X
Z
Y
Fig. 11. Bending behavior of the FE model with D/t ratio of 40: (a) moment versus endrotation response, (b) failure mode without girth weld, and (c) failure mode with girth weld.
welding process was not considered due to the lack of experimental data. This assumption seems to be reasonable, and justified for parametric comparative studies because material behavior contributes equally in the results of all cases and differences in structural response can be attributed to changes in the parameters. Incremental-solution strategies are required to trace the proper nonlinear equilibrium path in the analysis. Riks [49] introduced an incremental approach to the solution of snapping and collapse problems. In Riks's algorithm, it is assumed that loading is proportional and all load magnitudes vary with a single scalar parameter that is called ‘arc length’. In this study, the nonlinear load-deformation path was followed by the arc-length method combined with the Newton–Raphson iteration scheme [39].
Y
Z
X
Y
Fig. 12. Bending behavior of the FE model with D/t ratio of 60: (a) moment versus endrotation response, (b) failure mode without girth weld, and (c) failure mode with girth weld.
under pure bending, compared with the nonlinear prediction of the model without girth weld. The bending moments attained in the analysis have been normalized against the plastic moment capacity, Mp, defined by: Mp ¼ σ y Z
ð1Þ
where σy is the material yield stress and Z is the plastic section modulus, calculated as Eq. (2) in the case of circular hollow section.
Z¼
D32 −D31 6
ð2Þ
3.2. Results and discussion Results are first prepared for the model with D/t ratio of 20. Fig. 9 shows the predicted moment versus end-rotation response curve
where D2 is the outer diameter and D1 is the inner diameter. It is immediately apparent that these two responses are very similar except the extent of strain-hardening and show the typical bending
C.-H. Lee et al. / Journal of Constructional Steel Research 75 (2012) 142–151
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(a)
(a)
No_Weld
1.2
With_Weld
No_Weld With_Weld
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1
Moment (M/Mp)
Moment (M/Mp)
1 0.8 0.6 0.4
0.6 0.4 0.2
0.2 0
0.8
0 0
0.05
0.1
0
0.025
0.05
0.15
0.075
0.1
Rotaion (θ)
Rotaion (θ)
(b)
(b)
Z Z X X
Y
Y
(c)
(c)
Z
Z X X
Y
Y
Fig. 13. Bending behavior of the FE model with D/t ratio of 80: (a) moment versus endrotation response, (b) failure mode without girth weld, and (c) failure mode with girth weld.
behavior of circular steel tubes with low D/t ratio, i.e. a significant load increase exists between the onset of yielding and the limiting buckling moment induced by the material strain-hardening, resulting in ultimate moment capacity greater than the full plastic moment. In addition, before and after the ultimate moment, the rising and descending rates are relatively mild. The numerical failure mode of the tube model which does not contain girth weld is given in Fig. 10 and compared with the deformed girth-welded tube model at the ultimate load, where displacements are amplified with a coefficient of 1.5 in order to allow a better visualization of the deformations. The former model buckles by the Brazier ovalization mode [50], whereas the latter model exhibits a combined failure mode of flattening and local buckling near the girth weld on the compression side induced by the circumferential shrinkage during welding. This local buckling
Fig. 14. Bending behavior of the FE model with D/t ratio of 100: (a) moment versus end-rotation response, (b) failure mode without girth weld, and (c) failure mode with girth weld.
prevents the attainment of larger extent of strain-hardening in the moment versus end-rotation relationship, leading to lower ductility and ultimate moment capacity. The other moment versus end-rotation predictions are presented in Figs. 11–14 for the models with D/t ratios of 40, 60, 80 and 100 in that order, followed by the corresponding deformed shapes at the limiting buckling moment in which displacements are magnified by a factor of 1.5. It can be found that the moment ratio achieved by the FE model without girth weld becomes lower with the failure being less ductile as the D/t ratio increases. The D/t ratio reflects the resistance of circular tubes to local buckling. With an increase in D/t, which is equivalent to a decrease of the curvature, the out-of-plane stiffness of a curved panel of a given circumferential width is reduced [32]. Moreover, a large D/t ratio induces a nearly uniform distribution of compressive stress in the most highly stressed panels. This leads to a
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1.2
M/Mp
1.1
1
0.9
0.8
0
20
40
60
80
100
120
D/t Fig. 15. Ultimate bending capacity of circular steel tubes with and without girth weld depending on the D/t ratio.
lower level of buckling stress than would occur in a tube with a higher stress gradient resulting from a smaller D/t ratio [32,47]. The normalized moment capacity of the FE models with girth weld shows similar trends to their counterparts without girth weld. In addition, careful observation of the results unveils that the larger the ratio of D/t, the more significant the influence of weld-induced residual stress and deformation on the bending capacity becomes. The main possible reason for this phenomenon is believed to be the fact that as described earlier, plastic region near the girth weld becomes larger, whilst the local wavelength becomes smaller with the increase of D/t ratio. It should be noted that the flexural behavior of the tube models with girth weld always involves local buckling near the girth weld on the compression side accompanied by the tube center ovalization reflecting the D/t ratio, whereas the failure modes of the tubes with no girth weld are divided into three categories depending on the bending capacity that they achieve: (1) the Brazier ovalization, (2) combined mode of ovalization and local buckling and (3) local buckling. This local buckling alters the nature of moment versus end-rotation response and diminishes the limiting buckling moment of girth-welded circular steel tubes. Fig. 15 compares the effect of D/t ratio on the ultimate bending capacity of circular steel tubes with and without girth weld. This result corroborates the previous finding, i.e. the normalized moment capacity obviously decreases with the increasing ratio of D/t in both cases. Furthermore, it is clear that the influence of girth weld on the ultimate moment capacity becomes more pronounced as the ratio of D/t increases. 4. Conclusions This paper investigated the buckling behavior of girth-welded circular steel tubes subjected to pure bending by FE method. Sequentially coupled 3-D thermo-mechanical FE analysis for predicting residual stress and deformation induced by the girth welding of circular steel tubes with different D/t ratios was first performed. Nonlinear FE analysis which can identify the failure mode, the ultimate moment capacity and the moment versus end-rotation behavior of the girth-welded circular steel tubes taking weld-induced geometric imperfection and residual stress into account was next carried out. Based on the results in this work, the following conclusions can be made. a) 3-D FE model is essential to accurately simulate the girth welding of circular steel tubes because the weld-induced residual stress and deformation are by no means axisymmetric, which is induced by the traveling arc and welding start/stop effects. In addition, the region near the girth weld subjected to plastic deformation becomes larger and the welding start/stop effects become more pronounced with increasing the D/t ratio.
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