CALCULATION OF THE SECONDARY BENDING MOMENT EFFECT IN THE SINGLE-SIDED FILLET-WELDED JOINTS.
Lappeenranta–Lahti University of Technology LUT
Master’s Programme in Mechanical Engineering, Master’s Thesis.
2021
Vladislav Bobylev
Examiner(s): Prof. Timo Björk
D.Sc. (Tech) Antti Ahola
ABSTRACT
Lappeenranta–Lahti University of Technology LUT LUT School of Energy Systems
Mechanical Engineering
Vladislav Bobylev
Calculation of the secondary bending moment effect in the single-sided welded joints.
Master’s thesis 2021
50 pages, 31 figures, 7 tables and 7 appendices Examiner(s): Prof. Timo Björk
D.Sc. (Tech.) Antti Ahola
Keywords: secondary bending moment, eccentricity, single-sided welds.
In this study, the effect of the secondary bending moment in the single-sided welds is investigated. The research was based on comparison analysis of analytical and experimental results. The current EN 1993-1-8. 2005 code does not provide explicit guidance for design calculation of the single-sided welds; therefore, the main focus is made on the alternative design verification guide described in Teräsnormikortti № 24/2018.
The analytical results strength capacities were calculated according to EN 1993-1-8:2005 and Teräsnormikortti № 24/2018. Experimental tests consist of the tensile tests of single- sided welded plate connections made of S355 and S700 with total amount of 8 specimens.
Four weld geometries with different eccentricity values are designed for laboratory tests.
Explicit analysis of laboratory tests is conducted by means of Finite element analysis in FEMAP software.
Comparison of strength capacities obtained by directional method provided in EN 1993-1- 8: 2005 and actual capacities, indicated that EN 1993-1-8:2005 was not capable of making safe predictions for welds with relatively high eccentricity. On the contrary, results obtained with Teräsnormikortti № 24/2018 verified the ability of modified calculation model toproduce safe prediction for single-sided fillet welds. Although, Teräsnormikortti strength predictions for welds with relatively small eccentricity (0,5 mm) correlated well with test
results, in case of specimens possessing larger eccentricity (>2 mm), obtained prediction were overconservative. Further, finite element analysis facilitated identification of results variation cause, which was clamping conditions of the test specimens which prevented development of maximum bending moment amplitude. According to the results, it can be concluded that design calculation of single-sided welded joints considering eccentricity is challenging due to major dependence on local structure rigidity.
ACKNOWLEDGEMENTS
I would like to express my gratitude to Prof. Timo Björk and D.Sc. (Tech.) Antti Ahola for for their assistance and guidance at every stage of the research. Their immense knowledge and novel thinking have encouraged me to strive for progressing in this project. I also have to thank employees of the Laboratory of Steel Structures for planning and conducting experimental part of the thesis. I would like to extend my sincere thanks to my groupmates Ahmed Yusuf and Riku Turkia for giving me valuable tips and motivation throughout this work.
Additionally, I would like to express my deepest gratitude to my both families for tremendous understanding and invaluable support which were indispensable for me all through my studies.
Vladislav Bobylev
In Lappeenranta, 1st of December 2021
SYMBOLS AND ABBREVIATIONS
a Critical throat thickness [mm]
b Plate width [mm]
e Eccentricity [mm]
E Young’s modulus [MPa]
F Load [kN]
fu nominal tensile strength [MPa]
fy Yield strength [MPa]
Hv Vickers Hardness value [-]
I Current [A]
k Stress distribution factor [-]
M Moment [kNmm]
U Voltage [V]
z1 Butt weld penetration depth [mm]
z2 Fillet weld leg length [mm]
α Angle [degree]
βw Correlation factor for tensile strength of base material and weld material [-]
γM2 partial material safety factor [-]
ν Poisson’s ratio [-]
σ Stress [MPa]
σ|| Normal stress parallel to the throat [MPa]
σ⊥ Normal stress perpendicular to the throat [MPa]
σb Bending stress [MPa]
σm Membrane stress [MPa]
σx Normal stress [MPa]
τ|| Shear stress parallel to the axis of the weld [MPa]
τ⊥ Shear stress perpendicular to the axis of the weld [MPa]
DOB Degree of bending EC3 Eurocode 3
FEA Finite element analysis FW Fillet weld
HAZ Heat affected zone SBW Single side bevel weld
Table of contents
Abstract
Acknowledgements
Symbols and abbreviations
1. Introduction ... 8
1.1 Background of the study ... 8
1.2 Objectives ... 9
1.3 Structure and limitations of the study ... 10
2. Theory ... 11
2.1 Eurocode 3 ... 13
2.2 Calculation model for single sided filled welds ... 15
3. Research Methods ... 19
3.1 Experimental tests ... 19
3.2 Test specimens ... 20
3.4 Test set-up and instrumentation ... 23
3.5 Finite Element Analysis ... 24
4. Results ... 27
4.1 Tested weld geometries ... 27
4.2 Comparison of analytical and test results. ... 31
4.3 FEA results ... 34
5 Discussion ... 44
5.1 Further research ... 46
6 Summary ... 48
References ... 49
Appendices
Appendix 1. Welding Parameters of Test Specimens.
Appendix 2. Test Welds’ Geometries.
Appendix 3. Welds’ Failure Planes.
Appendix 4. Hardness Measurements Points and Values, Evaluation of tensile strength along potential failure lines according to Equation 12.
Appendix 5. Fracture surfaces of test specimens.
Appendix 6. Force displacement curves FE versus test data.
Appendix 7. Verification of the weld according to Teräsnormikortti №24/2018.
1. Introduction
The history of arc welding as we know it nowadays counts more than 100 years. For many decades engineers invested many efforts in research targeted on development of numerical models for prediction of welded structures’ behavior in various service conditions. As a result of many researcher projects, engineering community got universal technical standards which allowed to unify requirements to the design of welded connections. For decades, set of technical standards such as EC3 have being fulfilled needs of major industrial applications. However, recent increase of high strength and ultra-high strength steels utilization in combination with trends in modern design require revision and amendment of current design rules. Lack of standard design instructions created the need for research projects in field of metal structures. One of the current topics for research pointed out by Björk et al. (2018) is development of design rules for welds subjected to bending moment.
1.1 Background of the study
In many applications, where fillet weld joints are under tensile loading, due to asymmetric geometry of weld or structural misalignments, a secondary or primary bending moment occur. Figure 1 represents joints where bending moment occurs at the root of weld. Such joints can be represented by single-sided butt welds, single-sided fillet welds, beveled groove single-sided weld where eccentricity appears due to position of weld legs or defects of insufficient penetration of weld root. (Bjork et al., 2018, p.10.) In practice, single-sided weld joints are used in connections between hollow sections and manufacturing of welded box sections.
The EC3 standard does not provide clear instructions for considering of tensile stresses occurring in welds due to bending. However, it has been already indicated by Tuominen et al. (2017) that tensile stresses in the root side of the weld due to bending and tension loads is the combination which decreases capacity of the joint. Furthermore, Teräsrakenneyhdistys (Finnish Constructional Steelwork Association) issued supplementary design guidance
Teräsnormikortti № 24/2018 to EC3 which contained updated regulation for considering of design resistance of single sided welds. Even though Teräsnormikortti № 24/2018 has been already adopted for use, there is still demand for verification of guidance by experimental results.
Figure 1. Bending moment occurring in joints due to: a) weld eccentricity, b) external bending, c) chord flange deformation (Tuominen et al. 2017, p. 1).
1.2 Objectives
The core objective of this research is to determine the effect of asymmetric geometry and loading on the static strength of load-carrying single-sided welded joints. The magnitude of effect is predicted by computational analysis based on Teräsnormikortti №24/2018 and FE models. Obtained results are compared with data from experimental tests. Tests are conducted to examine influence of weld geometry variables e.g., throat thickness, eccentricity of critical weld throat in relation to load direction. Eventually, this study is designed in conformity with following research questions:
• How does eccentricity of weld influence the static strength of load-carrying one- sided fillet weld joints?
• Are the numerically obtained capacities by use of Teräsnormikortti №24/2018 reliable?
• When weld eccentricity is essential to consideration for strength capacity calculation?
1.3 Structure and limitations of the study
The research is based on comparison analysis between laboratory tests of single-sided welds and their capacities obtained by utilization of Teräsnormikortti №24/2018 and FE models.
The examined weld geometries are prepared in Laboratory of Steel Structures where they are subsequently tested for evaluation of static strength. Software used for building and analyzing of FE models is Femap with NX Nastran.
Only load-carrying joints are selected for being studied in this research. For simplification of modelling and compliance to selected range of variable geometry parameters, welds are assumed to possess ideal geometry which means that welds have equal leg lengths and flank angle is 45 °. In order to reach planned weld geometry without over penetration in laboratory tests, infusible tungsten strip is used at the weld root.
2. Theory
Metal structures in service often designed to withstand complex loadings in tension, compression, bending, etc., so that at any given point material might be subjected to combined stresses acting in several directions. If magnitude of these stresses reaches a critical value, the material starts to yield or fracture. In order to predict behavior of material under combined loading and determine the safe limits, it is necessary to apply failure criterion. In other words, it is needed to correlate material’s strength properties with stresses occurring in structure. (Dowling 2013, p. 275.)
Failure criteria can be divided according to predicted failure mechanism: yielding or brittle/cleavage fracture. Since, the focus of this research made on structural steels which dominantly have ductile behavior, it is worth to further extend yield criteria. Moreover, design of fillet according to EC3 is also based on von Mises yield criterion.
𝜎ℎ = 𝜎1+ 𝜎2 + 𝜎3
3 (1)
𝜏ℎ =1
3√(𝜎1− 𝜎2)2+ (𝜎2− 𝜎3)2 + (𝜎3− 𝜎1)2 (2)
The von Mises yield criterion predicts a failure to occur when shear stress reaches critical value on octahedral plane which is plane oriented with principal axes making angles α=β=γ as represented on Figure 2 (a). Thus, the octahedral normal stress σh and octahedral shear stress τh can be expressed in terms of principal stresses by Equation 1 and 2.
In general, eight octahedral planes have similar stresses σh and τh. Together these planes form an octahedron, as shown on Figure 2 (b). Since the opposite face of the octahedron are parallel, the octahedral stresses are acting in four different directions.
Figure 2. Octahedral planes relatively to the principal axes (a), and the octahedron formed by the similar planes (Dowling 2013, p. 261).
𝜏ℎ =√2
3 𝜎 1 (3)
Applying Equation 2 to uniaxial loading case as illustrated by Figure 3, so that σ2= σ3=0 and substituting σ1 by yield strength of material obtained from tensile test σo, resulting in Equation 3.
As can be observed from Figure 2 and Figure 3, the plane on which the uniaxial stress acts is situated at the angle α = 57° relatively to octahedral plane.
Figure 3. The plane of octahedral shear in uniaxial tension test. (Dowling 2013, p. 289).
𝜎o= 1
√2√(𝜎1− 𝜎2)2+ (𝜎2− 𝜎3)2+ (𝜎3− 𝜎1)2 (4)
Combination of Equation 2 and 3 is resulting in general form of von Mises yield criterion Equation 4 expressed in terms of yielding strength obtained from uniaxial tensile test. The von Mises yield criterion served as the basis for evaluation of fillet welds resistance described in Eurocode 3.
2.1 Eurocode 3
The EC3 provides two methods for evaluation of design resistance of fillet welds. The one used in this work is called Directional method which resolves the force carried by a unit length of weld into four components which presented in Figure 4:
• σ⊥ is the normal stress perpendicular to the weld throat.
• σ|| is the normal stress parallel to the weld axis which is not considered in resistance verification
• τ⊥ is the shear stress (in the plane of the throat) perpendicular to the axis of the weld
• τ|| is the shear stress (in the plane of the throat) parallel to the axis of the weld (SFS-EN 1993-1-8 2005, p. 43.)
Figure 4. Stresses in the throat section of fillet weld. (SFS-EN 1993-1-8 2005, p. 43).
The directional method’s weld resistance verification model is based on the modified octahedral shear stress yield criterion, where only perpendicular normal stress and shear are considered in the critical plane due to transverse loading. The critical plane location is assumed to be 45 degrees in the case of symmetric fillet welds under transverse axial loading.
However, as it was shown by Björk et al. (2018), 45 degrees as not correct either theoretically or in practice, but overall influence on ultimate capacity was not remarkable. Modified for fillet weld geometry, EC3 calculation model looks as follows:
[𝜎⊥2+ 3(𝜏⊥2 + 𝜏||2)]0,5 ≤ 𝑓𝑢 𝛽𝑤 ∙ 𝛾𝑀2
(5) and 𝜎⊥ ≤ 0.9𝑓𝑢
𝛾𝑀2 (6)
where:
• fu is the nominal tensile strength of the weaker part of the joint so that in case of welded connections between steels with different strength value, for calculation the lowest strength property should be determined.
• γM2 is a partial material safety factor.
• βw is the appropriate correlation factor which represents strength relation between base and filler materials. Proper value should be selected from the standard according to steel grade used. (SFS-EN 1993-1-8 2005, p. 43,44.)
The EC3 includes the paragraph 4.12 giving recommendations for cases where eccentrically loaded single fillet or single-sided partial penetration butt welds could not be avoided in design. The standard pointed out two cases where local eccentricity should be considered.
Firstly, welded joints where bending moment conducted about the longitudinal axis of the weld causes tension at the root as presented in Figure 5 (a). Secondly, when tensile force directed perpendicularly to the longitudinal axis of the weld induces bending moment, resulting in tension force at the root of the weld, as could be observed from Figure 5 (b).
(SFS-EN 1993-1-8 2005, p. 48.)
Figure 5. Single fillet welds and single-sided partial penetration butt welds. (SFS-EN 1993- 1-8 2005, p. 48).
2.2 Calculation model for single sided filled welds
As it was firstly indicated by Tuominen et al. (2017), EC3 instructions referred to single fillet or single-sided partial penetration butt welds do not provide explicit guide for numerical evaluation of welds design resistance. Conducted research was focused on investigation of secondary moment effect on the static strength of the welds. Analytical calculation model was based on extended von Mises yield criterion as follows:
√(𝜎𝑚+ 𝜎𝑏)2+ 3𝜏2 = 𝑓𝑢
𝛽𝑤𝛾𝑀2 (7)
where all stress components are calculated for the critical plane of the weld as can be observed from Figure 6. The stress induced due to presence of bending moment and secondary bending moment occurring due to weld eccentricity is:
𝜎𝑏 =𝑘(𝑀 ± 𝐹𝑒)
𝑎2𝑏 (8)
where k = 6 is used for elastic and k = 4 for fully plastic stress distribution; M is the constant primary or secondary bending moment affecting the adjacent member; F is tension force applied axially in weld; e is eccentricity measured as the perpendicular from the force action line to the center line of assumed critical weld throat; a is the throat thickness of the critical weld plane; and b is the effective length of the weld. (Tuominen et al. 2017, p. 2.)
The membrane and shear stress components depend on the angle α between axes of acting force F and the normal to the critical plane.
𝜎𝑚 = 𝐹 cos 𝛼
𝑎𝑏 (9)
𝜏 =𝐹 sin 𝛼
𝑎𝑏 (10)
Test results obtained in the research confirmed the ability of analytical model to predict a load-carrying capacity of one-sided welds. Therefore, this model was adopted as a main tool for stress analysis in this thesis.
Figure 6. Eccentricity of weld and load components (Tuominen et al. 2017, p. 2).
Teräsnormikortti №24/2018 is currently available guidance for calculation of design resistance for one-sided welds. The core of the recommendation is based on the directional method presented in EN 1993-1-8: 2005 since the method considers in details stress components applied to weld. The first step in the calculation of design resistance is identifying of the critical weld throat and its orientation in the joint. There are three highlighted weld geometries in the guidance, those are partial penetration butt weld, single fillet weld and partial penetration butt weld with reinforcing fillet weld. For each of these, the critical throat parameters are defined in Table 1. (Teräsnormikortti №24/2018, p. 2-5.)
Table 1. Identification of critical weld throat width and orientation (Teräsnormikortti
№24/2018, p. 5).
Weld Geometry Critical weld throat angle (β) Critical throat width (a)
Fillet Weld with leg length z2 45 degs 𝑎 = 𝑧2
√2 Partial Penetration butt weld with
penetration depth z1
0 degs 𝑎 = 𝑧1
Partial penetration butt welds with penetration z1 with reinforcing fillet weld with leg length z2
If z2 > z1 45 degs 𝑎 = 𝑧1√2 +(𝑧2− 𝑧1)
√2
If z2 = z1 45 degs 𝑎 = 𝑧1√2
If z2 < z1 𝛽 = atan𝑧2
𝑧1 𝑎 = √𝑧22+ 𝑧12
The analytical model for calculation of stress components which are membrane, bending and shear stresses, is identical to presented by Tuominen et al. 2017. The explicit part of the guidance suggests verifying the resistance of weld against two cases of stress states developed in critical weld throat plane line 1-1 and across the fusion line perpendicular to applied load, line 2-2 as shown in Figure 7.
Figure 7. Weld Dimension Labels (Modified Teräsnormikortti №24/2018, p. 6).
Eventually, evaluation of weld’s resistance is going according following procedure:
• Firstly, identification of critical weld throat and its position relatively to loading according to Table 1.
• Secondly, expressing Fw critical loading magnitude from equation 7 by substuting stress components with equations 8, 9 and 10 which will consequently lead to equation 11.
𝐹𝑤 = 𝑎2𝑏𝑓𝑢
√(𝑎 cos 𝛼 + 𝑘𝑒)2+ 3𝑎2sin2𝛼 (11)
It should be note that βw correlation factor and γM2 are both assumed to be 1, since the goal is to obtain the magnitude of load at failure. The value fu is based on the filler material ultimate strength, normally calculation is based on the base material as βw is used for consideration of potential strength difference contributing to the result safety.
In addition, it is worth noticing that Teräsnormikortti does not consider the case where failure occurs along vertical or inclined fusion line depending on fillet weld penetration as shown in Figure 7 by orange dash line. Failure along this line happens mainly by shear, which magnitude reaches maximum in comparison with other presumable failure paths as illustrated in Figure 8. In case of joints made of high strength steels which are more prone to fail around fusion lines as was described by Björk et al. (2018), shear mode failure along the inclined fusion line is more probabilistic than along path 2-2.
Figure 8. Stress components on the single-sided fillet weld’s legs with linear elastic bending moment distribution.
3. Research Methods
This thesis project employs both analytical and experimental approaches. The core of the research is comparison of welded joints’ strength performance obtained by analytical calculation with laboratory test results.
3.1 Experimental tests
Experimental part of the research is required for verification and calibration of analytical computation model. Specimens’ preparation and subsequent tests were conducted in the Laboratory of Steel Structures at LUT University.
Since the main variable parameter considered in this research is geometry of weld, therefore the goal of laboratory tests was covering the range of single-sided welds’ geometries. The summary of dimensions for laboratory specimens are presented in test matrix, Table 2.
Table 2. Established test matrix for laboratory tests specimens.
ID Steel
Grade t* [mm]
z1
[mm]
z2
[mm]
e [mm]
SBW_S355_7 S355 8 7 - 0,5
SBW&FW_S355_4&4 S355 8 4 4 2 SBW&FW_S355_2&6 S355 8 2 6 4
FW_S355_8 S355 8 - 8 6
SBW_S700_7 S700 8 7 0,5
SBW&FW_S700_4&4 S700 8 4 4 2 SBW&FW_S700_2&6 S700 8 2 6 4
FW_S700_8 S700 8 - 8 6
* plate thickness t
3.2 Test specimens
Four specimens of the test set were made of SSAB DOMEX 355MC D with minimum yield strength of 355 MPa and ultimate tensile strength of 430-550 MPa. The rest of the set were made of STRENX 700 MC PLUS with nominal yield strength of 700 MPa and ultimate tensile strength of 750-950 MPa. The chemical composition and mechanical properties of both filler and base materials are available from Table 3.
Table 3. Nominal Mechanical properties and chemical compositions of the base and filler materials (SSAB, 2019; Böhler, 2019, p. 243; Elga, 2019, p. 80).
Mechanical Properties Material
Yield Strength fy [MPa]
Ultimate Strength fu [MPa]
Elongation A5
[%]
Charpy V-Notch CVN [J]
CE (IIW)
SSAB 355MC 355 430-550 23 27 0.39
Elgamatic 100 470 550 26 50 0.32
STRENX 700 700 750-950 13 40 0.51
Union NiMoCr 720 780 16 47 0.60
Chemical composition [weight-%]
Material C Si Mn P S Altot Nb V Ti Ni Cr Mo
SSAB 355MC 0.10 0.03 1.50 0.025 0.010 0.015 0.09 0.2 0.15 - - -
Elgamatic 100 0.08 0.82 1.45 - - - - - - - - -
STRENX 700 0.12 0.25 2.10 0.020 0.010 0.015 0.09 0.2 0.15 - - -
Union NiMoCr 0.08 0.6 1.70 - - - - - - 1.50 0.2 0.5
The dimensions of test specimens are presented in Figure 9. The identical test specimens were used for both tested steel grades S355 and S700. The thickness of plates was 8 mm for both materials. Prior to welding, test plates were bevelled according to desired weld geometries, in total, three bevel types were utilized as could be found from Figure 10.
Furthermore, in order to control weld root penetration, infusible tungsten strip was placed in the weld zone.
Figure 9. Dimensions of tensile test specimen.
Figure 10. Type of bevels used in preparation of test welds and placement of tungsten strip for root penetration control.
Preassembly process consisted of possession of tungsten strip at the weld root and tack welding of plates. Alignment of vertical plates was ensured by utilization of custom-made support Figure 11. Start and end welds’ sections were moved outside actual specimen as could be seen in Figure 11. After welding these sections were sawed and machined to avoid possible imperfections. Cut sections, further, were used for hardness measurements and inspection of weld geometry.
Tungsten
Figure 11. Tack welded specimen and positioning of plates with tungsten strip in custom made support prior tack welding.
Welding of specimens was conducted by robotized GMAW process. Robot welding was selected in order to minimize the variation in throat thickness and penetration along welds’
length. Welding sequence and passes are designated in Figure 12. Welding parameters for each pass are given in Appendix I.
Figure 12. Welding sequence. Welding position is PB (horizontal vertical).
3.3 Measurements
Start and end sections of welds were cut and polished so that leg length of fillet weld and penetration depth of butt weld could be evaluated. Examples of polished sections are shown in Figure 13. All polished section figures are seen in Appendix II. Examination of welds revealed deviation of weld dimensions from planned ones. Actual parameters were used for
analytical evaluation of weld load capacities in Equation 11. Employment of robotic welding provides substantial ground for assuming constant weld dimensions throughout total length.
Even though, precision of tungsten strip positioning is problematic, utilization of tungsten strips proved its effectiveness in controlling of root penetration. Therefore, obtained welds possessed sufficient ability for root opening under tensile loading.
Figure 13. Polished sections of FW_S700_8 and SBW_FW_S700_4_4 specimens.
3.4 Test set-up and instrumentation
All specimens were tested under uniaxial tensile loading at the room temperature till failure.
The test rig used in the experiment had maximum loading capacity equal to 1200 kN.
Schematic representation of the test setup introduced in Figure 14. The speed of applied displacement by rigs was equal to 0.01 m/s. Strain values was recorded from extensometer and initial measuring length was 80 mm.
Figure 14. Schematic tensile test setup.
3.5 Finite Element Analysis
The finite element method (FEM) is a computational tool which can be used for solving complex engineering problems. In general, FEM is based on principal of substitution the complicated problem by simpler one. Since the actual problem is replaced by simplified model, it is possible to obtain an approximated solution rather than exact one. In the finite element method, the solution region is divided into small, interconnected subregions which are called finite elements. In whole structure, an approximate response solution is assumed for each element, then, based on overall equilibrium, these local solutions are summarized into overall system behavior. In combination with high-speed digital computers, FEM found wide application in field of structural mechanics. (Rao 2005, p. 3.) Nowadays, there are many software packages that employ FEM for solving various engineering problems. The one of them is Simcenter Femap 12.0 which was used in this research.
A finite element model consists of many points, called nodes, which form a geometry of the tested part. Nodes create a grid known as finite element mesh which divides a material into finite elements. Each element contains material properties and defines a reaction of model to various loading conditions. The density of mesh may vary throughout the model, depending on anticipated stress level fluctuation in certain regions. Thus, areas experiencing significant gradients changes usually requires high mesh density while areas of minor stress changes can be modeled by larger elements without compromising results. Points of interest might be represented by stress-concentration points such as weld root or determined from failure paths of previously tested specimens.
For this research, each specimen was represented by simplified model. For simplification of analysis and obtaining proper meshing, welds were represented by idealized triangular shapes. In order to optimize the time required for obtaining FEA solution, each model constituted a half symmetry. The nonlinear static analysis mode was selected for this research since it was desired to observe the joint behavior after initial yield of material.
Bi-linear Elasto-Plastic material models were defined for plate and weld materials. Table 4 presents the true stress-strain material models used in FE models. Poisson’s ratio ν was similar for all materials and was equal to 0.3. The Young’s modulus, E for S700 was obtained from research conducted by Shakil et al. (2020) and its value was 216 GPa. For the rest of materials, the conventional value of 210 GPa for E was used. Isotropic hardening was employed for analysis since this model sufficiently reflected material behavior in case of monotonic loading since it sufficiently reflected material behavior in case of monotonic loading and more preferable for saving computational time.
Table 4. Bi-linear material models used in FEA.
Material
Plastic Strain 1st point [mm/mm]
Stress 1st point [MPa]
Plastic Strain 2nd point [mm/mm]
Stress 2nd point [MPa]
SSAB 355MC 0 415 0.33 481
Elgamatic 100 0 470 0.26 550
STRENX 700 0 725 0.16 850
Union NiMoCr 0 720 0.16 780
Tensile specimens were modeled by solid elements in FEMAP. Since the focus of interest was weld joint, so more refined mesh was selected for weld representation. The element size in the weld area varied from 0.6 to 1 mm. Element size was gradually increased with accordance to distance from the weld.
Figure 15. Meshing of the fillet weld model.
Nodal set of constraints were applied to FE models in order to reproduce the conditions of laboratory tests. The set of constraints was assumed to be completely rigid which might cause some challenges in comparison with test results. A symmetry constraint was applied to the bottom of middle plate in order to compensate another half of the specimen. The second constraint set was used for reproduction of the clamping condition of specimen in the test rig. Importance of clamping constraint was considerable because it had major effect on test specimen deformation and development of the secondary bending moment. In Figure 16, constraint setup can be seen. In the analysis, loading was applied in form of nodal displacement.
Figure 16. Applied constraints and loading used in FEA.
4. Results
The target of this study was to determine the effect of secondary bending moment on strength capacity of single-sided fillet welds. Desired outcome of tests was obtaining weld failure.
Welded specimens with different degree of bending (DOB) were manufactured and tested under similar loading conditions.
𝐷𝑂𝐵 = 𝜎𝑏
|𝜎𝑚| + |𝜎𝑏| (12)
Equation 12 defines DOB value where σm is the membrane stress and σb is the bending moment in the weld critical throat thickness. DOB for tested weld geometries is presented in Table 5. Critical throat thickness was identified according to Teräsnormikortti №24/2018 and actual weld geometries illustrated in Appendix II. Locations of failure planes for all specimen beside specimen SBW_S355_7 are available from Appendix III. Unfortunately, the specimen SBW_S355_7 failed from base material.
Table 5. Test Matrix with DOB at assumed critical throat and actual failure location.
Test Specimen
DOB
Assumed critical throat angle
α [deg]
Eccentricity e[mm]
Location of failure*
SBW_S355_7 0.34 18.7 1.10 BMF
SBW&FW_S355_4&4 0.68 45 2.32 FLF&WF
SBW&FW_S355_2&6 0.79 45 4.13 FLF
FW_S355_8 0.86 45 6.05 WF
SBW_S700_7 0.28 13.4 0.86 FLF
SBW&FW_S700_4&4 0.67 45 2.10 FLF
SBW&FW_S700_2&6 0.78 45 3.73 FLW
FW_S700_8 0.85 45 6.23 WF
*BMF=base material, FLF=fusion line failure, WF=weld failure
4.1 Tested weld geometries
The first tested weld geometry was fillet weld without root penetration insured by tungsten strip. Two specimens FW_S355_8 and FW_S700_8 were prepared. These welds were in
particular interest since they possessed the maximum eccentricity and the major effect of secondary bending moment was expected during tensile test. Both specimens failed from the weld. The failure plane of the S355 specimen inclined at an angle 48° which is in conformity with failure path predicted by Eurocode 3 and maximum shear stress e.g., the Tresca criterion. The failure ligament of S700 specimen was located at an angle 30° which is typical for transversely loaded fillet welds as was noticed by Björk et al. (2017).
Following specimens were designed with an idea, while keeping perpendicular weld leg length equal, to increase weld penetration. Thus, it was planned to gradually decrease an effect of eccentricity on weld’s strength. Next geometry for specimens SBW_FW_S355&S700_2&6 was designed so that partial penetration butt weld was expected to have 2 mm penetration and reinforcing fillet weld to have leg length of 6 mm.
Failure location of S355 is parallel fusion line. Further examination of failure plane surface Figure 17 revealed porosity of a filler material at the weld root. This weld defect caused the crack development along the fusion line. The specimen made of S700 failed along the parallel fusion line even though assumed magnitude of the secondary bending moment in this plane is less than in the weld metal and perpendicular fusion line. However, proneness of high strength steel joints to fail around fusion was previously described by Björk et al.
(2018). The research revealed that due to the softening and other metallurgical effects, the areas around fusion lines might become the weakest zone in a joint (Björk, Ahola &
Tuominen, 2018, p. 8). Furthermore, more supporting evidences can be derived from hardness measurement results along the fusion lines presented in Appendix IV.
𝑓𝑢 𝑎𝑣𝑔 = −93,8 + 3,295𝐻𝑣 (13)
Dependence of hardness and strength can be described by Equation 13 (Pavlina & Van Tyne, 2008). Equation 13 was used for evaluation of metal strength along fusion lines and weld metal. Results obtained from specimen SBW_FW_S700_2&6 (Appendix IV) displayed that parallel fusion line was the weakest from examined potential failure paths.
Figure 17. Fracture surface of SBW_FW_S355_2_6.
Subsequent couple of specimens SBW_FW_S355&S700_4&4 was beveled in a way to reach 4 mm penetration for butt weld and reinforced by fillet weld with leg length 4 mm.
Obtained weld geometries slightly deviated from the plan, especially in the butt weld penetration, but nevertheless, the eccentricity parameter kept decreasing. The failure path of S355 specimen had two directions as could be seen from Appendix III. The failure crack started to propagate from the weld root along the perpendicular fusion line. Then the crack reached the fillet part of the weld, it changed it direction towards a plane making 46° angle with load action line. The cause for such failure crack propagation became lack of fusion at the weld root as can be seen from Figure 18. Thus, once the failure crack had overcome plane weakened by lack of fusion, the crack continued to propagate along maximum shear criterion plane.
Figure 18. Fracture surface of SBW_FW_S355_4_4.
The specimen S700 failed from perpendicular fusion line. Force-displacement curve Figure 19 obtained from the movement of test cylinder, revealed the lack of deformation capacity.
As it was written by Guo et al. (2016), welding of high strength steels is very challenging due to their high hardenability and tendency to form the martensite below the fusion boundary. Such area of HSS joint has low toughness value which might lead to brittle fracture or lack of deformation capacity of the joint under loading. This is also supported by relatively high carbon equivalent CE of STRENX 700 and Union NiMoCr from table 3.
Photos of fracture surfaces are available in Appendix V.
Figure 19. Load-displacement curve for SBW_FW_S700_4_4.
Design of the last two specimens SBW_S355&S700_7 was made in conformity with goal to investigate the effect of 1 mm under-penetration in single sided butt weld loaded in tension.
Under-penetration was successfully achieved; however, the welds’ size was excessive due to fillet portion. There was an option to grind the excessive fillet weld, but modification of welds’ geometry might cause other uncertainties such as creation of additional stress risers.
Therefore, it was decided to test specimens in as welded condition. The S355 joint performed well in the test because the weld strength exceeded the base material strength so failure occurred outside the weld area. The result with S700 joint was different since the weld failed in the perpendicular failure line. This type of failure might result from softening of the adjacent heat affected zone in similar manner with specimen SBW_FW_S700_2&6.
4.2 Comparison of analytical and test results.
In the first column of Table 6, theoretical capacities of joints were calculated according to design guide presented in Teräsnormikortti №24/2018 equation 11. Measured test welds’ leg lengths z1 and z2 were used for evaluation and are seen in Table 7. The second column represents capacities calculated with use of equation 11 according to actual location and length of failure path as presented in Appendix III. Even though, current Eurocode 3 doesn’t have clear guide for design of single-sided fillet welds, it was interesting to utilize directional method Equation 5 for comparison. Therefore, the third column contains capacity values evaluated in respect to critical throat thicknesses which are marked by yellow lines in the Appendix II. Actual welds’ strength capacities obtained from tensile tests are shown in the last column.
Table 6. Comparison of analytical and tested weld capacities.
ID
Fw
(Teräsnormikortti) k = 4 [kN]
*
Fa
(Actual failure
path) k = 4 [kN]
**
FEC
(Eurocode 3) [kN]
***
Ft
(Test) [kN]
SBW_S355_7 195,57 1,18 193,37 1,21 249,77 0,94 233,87
SBW&FW_S355_4&4 83,10 2,13 83,10 2,13 170,89 1,03 176,8 SBW&FW_S355_2&6 54,32 3,08 57,79 2,89 129,55 1,29 167,12
FW_S355_8 38,02 3,00 45,11 2,53 135,19 0,84 114,04
SBW_S700_7 329,67 1,15 334,85 1,13 441,86 0,86 378,64
SBW&FW_S700_4&4 123,67 1,75 141,10 1,53 247,01 0,87 215,85 SBW&FW_S700_2&6 85,02 2,66 125,91 1,79 203,73 1,11 225,74
FW_S700_8 66,79 2,65 73,47 2,4 351,01 0,5 176,69
*Ft / Fw ** Ft / Fa ***Ft / FEC
Main calculation variables used for calculation capacities Fw and Fa are presented in the Table 7. It was problematic to calculate the Fa for specimen SBW&FW_S355_4&4 since actual failure path didn’t follow single direction, therefore Fw and Fa are the same. The ultimate tensile strength fu for materials was taken from Table 2. Ultimate strength used for S355 was 550 MPa and 850 MPa for S700. Selection of reduced value for S700 is explained by determination of various weld defects associated with welding HSS.
Table 7. Calculation Parameters used for analytical model.
ID z1 [mm] z2 [mm] a [mm] α [deg] e [mm]
SBW_S355_7 FW
7,26 2,45 9,20 18,65 1,10
FA 9,71 0,00 1,60
FEC 8,26 18,00 -
SBW&FW_S355_4&4 FW
3,91 4,99 6,29 45,00 2,32
FA 6,29 45,00 2,32
FEC 6,80 37,00 -
SBW&FW_S355_2&6 FW
2,00 6,52 6,02 45,00 4,13
FA 7,20 0,00 5,60
FEC 5,60 46,00 -
FW_S355_8 FW
0,00 8,20 5,80 45,00 6,05
FA 6,57 42,00 6,44
FEC 5,64 42,00 -
SBW_S700_7 FW
7,57 1,80 9,12 13,38 0,86
FA 8,05 0,00 0,46
FEC 9,12 13,38 -
SBW&FW_S700_4&4 FW
4,00 4,40 5,94 45,00 2,10
FA 8,30 0,00 4,15
FEC 6,36 37,00 -
SBW&FW_S700_2&6 FW
2,33 5,90 5,82 45,00 3,73
FA 6,84 64,00 3,17
FEC 5,55 43,00 -
FW_S700_8 FW
0,00 8,92 6,31 45,00 6,23
FA 7,10 60,00 5,78
FEC 7,94 24,00 -
The results in Table 6 show that traditional calculation guidance provided in EC3 does not provide safe strength capacities for pure fillet welds where the effect of the secondary moment is maximum. However, for other S355 geometries EC3 produces safe predictions.
The specimen SBW_S355_7 should not imply any uncertainties, since the Ft for this specimen is obtained from base material failure. Predicted nominal strengths for S700 can be compared with test results for all geometries beside S700_4&4 specimen since the full joint strength was not developed due to weld defect. Strength prediction with sufficient safety margins was obtained only for S700_2&6.
Nominal strength predictions by Teräsnormikortti can be best analyzed on the example of S355 set of specimens due to absence of severe weld defects. Representation of results comparison is illustrated in Figure 20. The results obtained for S355 joints proved the
functionality of the concept about capacity reduction. Calculated values obtained for welds with minimal eccentricity SBW_7 corresponds to actual values and provides safer results than EC3. However, with increasing eccentricity parameter, deviation of calculated results is significantly progressing. While test results possess linear regression behavior, calculated capacities regression is more exponential. So that, if generally compared to EC3, Teräsnormikortti provides more conservative results. Example of Teräsnormikortti design check calculation can be found from Appendix VII.
Teräsnormikortti:
𝐹𝑤= 𝑎2𝑏𝑓𝑢
√(𝑎 cos 𝛼 + 𝑘𝑒)2+ 3𝑎2sin2𝛼
EC3:
𝐹𝑤= 𝑎𝑏𝑓𝑢
√cos2𝛼 + 3 sin2𝛼
Figure 20. Comparison of actual strengths and design strengths per Teräsnormikortti
№24/2018 and EC3 for S355 joints.
Comparison of calculated and theoretical capacities for S700 joints (Figure 21) is revealing the same pattern as for S355. However, the certain assumption should be made for specimen S700_4&4, since flawless joint was expected to develop equal or surpassing strength as specimen S700_2&6. It can be also noticed that EC capacity prediction for pure fillet is absolutely unconservative.
233,87 176,8 167,12
114,04 198,57
83,10
54,32
38,02 0
50 100 150 200 250 300
1,60 2,32 5,60 6,44
Strength (kN)
eccentricity (mm)
Test Results Teräsnormikortti Results
EC3
Teräsnormikortti:
𝐹𝑤= 𝑎2𝑏𝑓𝑢
√(𝑎 cos 𝛼 + 𝑘𝑒)2+ 3𝑎2sin2𝛼
EC3:
𝐹𝑤= 𝑎𝑏𝑓𝑢
√cos2𝛼 + 3 sin2𝛼
Figure 21. Comparison of actual strengths and design strengths per Teräsnormikortti
№24/2018 and EC3 for S700 joints.
In summary, Teräsnormikortti strength capacity predictions are considerably lower than experimentally obtained weld strengths. Deviation from the actual failure loads is progressing with the eccentricity factor and consequently with growth of secondary bending moment. It seems that the influence of the secondary moment on strength capacity reduction was over estimated for tested specimens. The variation of calculated strengths from actual failure loads is not similar for both materials. Thus, test results obtained with S700 specimens are closer to predictions by Teräsnormikortti. Therefore, it might be concluded that the secondary bending moment is more critical is HSS joints than in conventional structural steels e.g., S355.
4.3 FEA results
Welding analysis is an important field of research, since welding is the main metal joining process employed in modern fabrication. Computer modelling is one of the modern, effective tools used in design and research. In particular, FEA is the most important tool used in simulation of welding process and determination of welded joints strength capacities (Lindgren, 2001. p.144). However, FEA of welds is associated with many different phenomena, consideration of which is a challenging task. The major obstacle is material properties and their distribution within welded joint. (Lindgren, 2001. pp.144-145.) Moreover, welded joints might have various imperfections such as porosity, lack of fusion, cracks, HAZ softening etc. Consideration of all possible variables in FEA does not seem
378,64
215,85 225,74
176,69 329,67
123,67
85,02 66,79 0
100 200 300 400 500
0,86 2,10 3,73 6,23
Strength (kN)
eccentricity (mm)
Test Results Teräsnormikortti Results
EC3
possible and in many cases is not even necessary, hence, simplified models are utilized.
However, it is worth mentioning, that every FE model requires a validation by actual test results.
Approach selected for creation of FE models for this research was going along with an intention to build simplified representation of test specimens which would perform in a way close to actual testing data. Each model consisted of two material properties: base plate and filler wire. Material behavior function was defined by two linear functions representing elastic and plastic regions. Validation of FEA conformity with test results was executed by comparison of force-displacement curves.
Figure 22. Freebody location in FE models.
During laboratory tests, displacement was measured from movement of the force cylinder.
Displacement and loading of FE models was obtained from Freebody selection located close to the end of the model presented on Figure 22. Displacement was taken from summation node of the Freebody. Loading values were derived by means of Force Balance Interface Load Summary tool from the same location.
An example of force displacement curve is presented in Figure 23. Results obtained by FEA for S355 specimens showed sufficient correspondence with test results in both plastic and elastic regions which allowed to assume that overall behavior of FE models and test
specimens had been comparable. Thus, it was possible to receive reasonable FEA data from weld area. FEA for S700 fillet weld specimen indicated a good correspondence with test results, however for partial penetration welds the behavior of the weld distinguished from the test data as could be seen from Appendix VI.
Figure 23. Load Displacement curve (FW_S355_8).
As it was mentioned previously, Teräsnormikortti weld strength capacity predictions for fillet welds significantly distinguished from test capacities. The reason of such deviation might be misestimation of the secondary bending moment effect. Calculation of stress induced by secondary bending moment in given in Equation 8. Beside weld length b and throat thickness a, magnitude of the secondary bending moment depends of the eccentricity parameter e, which is assumed to stay constant. However, e could change throughout loading due to deformation of the test specimens. It can be seen on the example of FW_S355_8.
Figure 24 presents deformation of the joint during FEA. Blue lines show profile of the model before loading. The specimen deformed in a way that the weld moved towards the load application line, thus, decreasing the eccentricity parameter and consequently the bending moment. In order to compare prediction of the secondary bending moment magnitude by Teräsnormikortti and FE, case of the perpendicular fusion line of the specimen S355_8 was selected.
0 20 40 60 80 100 120 140
0 1 2 3 4
Load [kN]
Displacement [mm]
Test Data FE-data
Figure 24. Deformation of FE model (FW_S355_8).
The secondary bending moment FE data was obtained by utilization of Freebody tool.
Location of selected elements and nodes representing perpendicular fusion line can be observed from Figure 25. According to Teräsnormikortti, the secondary bending moment is calculated as a product of tensile load F and eccentricity e. For perpendicular fusion line of specimen S355_8, eccentricity is equal to 8 mm. Summary of two data sets is presented in Figure 26.
Figure 25. Freebody representing perpendicular fusion line FW_S355_8.
My
Figure 26. Comparison of FEA and Teräsnormikortti tensile loading versus bending moment occurring in the perpendicular fusion line (FW_S355_8).
According to FEA data, the secondary bending moment growth is linearly depended from the load up to yielding point, after which increase in load doesn’t affect significant gain in the moment magnitude. In contrast, Teräsnormikortti prediction of the secondary bending moment is a continuously rising function throughout loading history and dependent just on the tensile load magnitude. Thus, the moment’s values obtained by the design code are higher than FE results due to omitting variation of eccentricity and formation of plastic hinges.
The closest matching between predicted and actual strengths was obtained in case of specimens SBW_7, which was initially planned as butt welds with 1 mm of under penetration, however during welding some fillet portion of welds was formed. The fillet part of the welds was neglected in FE models. Stress contour for SBW_S355_7 is presented in Figure 27.
0 100 200 300 400 500 600 700 800 900 1000
0 50 100 150
My [kNmm]
Fx [kN]
FE
Teräsnormikortti
Figure 27. Deformation of FE model (SBW_S355_7).
The same procedure was conducted for derivation of the bending moment values as for pure fillet weld. The resultant curves could be seen in Figure 27. The comparison of the maximum secondary bending moment magnitudes predicted by design code and obtained from FE revealed, as expected, smaller difference than in case of the fillet weld joint.
Figure 28. Comparison of FEA and Teräsnormikortti tensile loading versus bending moment occurring in the perpendicular fusion line (SBW_S355_7).
Further, closer matching of Teräsnormikortti load capacity prediction with test results of S700 welds, can be explained by lower ductility of S700. Therefore, S700 test specimens experience relatively smaller deformation. Consequently, diminishing of the secondary bending moment effect had less influence on S700 specimens than on ones made from S355
0 10 20 30 40 50 60 70 80 90 100
0 50 100 150 200 250
My [kNmm]
Fx [kN]
FE
Teräsnormikortti
steel. So, inherently, high strength steels welded joints are more vulnerable to the secondary moment impact.
In order to further investigate the influence of deformation pattern of weld capacity, it was decided to modify the FEA conditions for S355 fillet weld. As it could be seen from Figure 24, overall deformation of the specimen consisted of middle plate translation to the negative z-direction and bending of the web. New set of nodal constraints was implemented with purpose to restrict any translation of the vertical plate in z direction. The final view of the model presented in Figure 29.
Figure 29. Deformation of FE model with additional TZ constraints (FW_S355_8).
Maximum stress level obtained from constraint model was slightly higher than during simulation of laboratory test conditions. However, due to locking of bending moment deformations in the middle plate and web, overall joint performance possessed better strength capacity as could be seen from Figure 30. Applied additional constraints set simulate the stress-strain conditions similar to that occurring in fillet welds to hollow structural sections which had been earlier investigated by Packer et al. (2016). Actual strength capacities obtained by Packer et al. (2016) were on average 2.04 higher than EC3 predictions, which proved validity of the directional method for design of hollow section joints.
Figure 30. Force displacement curves obtained for specimen FW_S355_8.
In order to further research the effect of constraining web deformation on the welded joint performance, it was decided to investigate stress distribution along the perpendicular fusion line in case of FE model representing laboratory test conditions and FE model with constrained deformation of the web. For the comparison, geometry of FW_S355_8 specimen was utilized. Stress distribution values were obtained from the nodes in the middle section of the weld model in form of non-linear solid normal stress σx.
𝜎𝑚 =1
𝑙∫ 𝜎(𝑥)𝑑𝑥
𝑙
0 (14)
𝜎𝑏 = 6
𝑙2∫(𝜎(𝑥) − 𝜎𝑚) ∙ (𝑙
2− 𝑥) 𝑑𝑥
𝑙
0
(15)
Membrane stress was calculated according to equation 14, where l is the length of the perpendicular fusion line. Bending stress was obtained from Equation 15.
Summary for stress distributions is presented in Figure 31. Visual representation of stresses allows to see how significant is the effect of web deformation freedom on the magnitude of the bending stress. Furthermore, interesting detail can be noticed from contour von Mises
0 20 40 60 80 100 120 140 160 180
0 1 2 3 4
Load Fx [kN]
Displacement Tx [mm]
Test Data FE-data
FE (TZ deformation constraints)
