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In this paper, a traction stress based shear strength definition is presented for correlating weldment test data obtained from standard specimens such as those stipulated by AWS B4.0 as well as for applications in general structural design applications when finite element methods are used. With this proposed approach, well-documented discrepancies...

## Contexts in source publication

**Context 1**

... while longitudinal shear specimens typically fail at an angle of about 45°, consistent with the assumption in equation (1). The two typical failure paths observed from transverse and longitudinal shear tests are illustrated in Figure 3, as documented extensively for weldments made of mild steel, 4-7 high strength steel, 4,8 aluminum alloys, 9 as well as titanium alloys recently by the authors. 10 It should be noted that from an engineering application point of view, such a difference in failure angle alone may not introduce any significant error in shear strength determination. ...

**Context 2**

... The nodal force method is an equilibrium based (or generalized free-body cut) and therefore offers a significant degree of mesh-type and mesh-size insensitivity. 20,21 3. The method directly provide shear traction stresses in the form of membrane and bending along any hypothetical cut, which offer a direct comparison with the simple stress definition given in equation (1) if a cut plane is chosen to coincide with a 45° failure angle or 22.5° as observed in Figure 3(b). ...

**Context 3**

... a cursory review of existing test data (e.g. Figure 3), as discussed the previous sections, should eliminate some of the possibilities, such as by the consideration of failure angles observed, either around 22.5° in transverse shear or 45° in longitudinal shear. ...

**Context 4**

... necessary conditions for validating any failure criteria are to show that they predict a failure angle of about 22.5° for transverse shear and about 45° for longitudinal shear tests, such as those in Figure 3. As an example, based on the test specimen geometry and test conditions reported in McClellan, 4 two plane strain finite element models with 1/4" (6 mm) and 3/8" Figure 9. Transformation of nodal forces to equilibrium-equivalent nodal forces and moments acting on a weld throat plane at angle u with respect to horizontal base plate. ...

**Context 5**

... the traction stress components calculated according to equations (2) to (4), the effective stresses according to equations (6) to (8) on five angular planes are plotted in Figure 11(b) as a function of angle with respect to the main plate. Among the three effective stress definitions, Figure 11(b) shows that only s e2 and s e3 attain their respective maximum values at exactly 22.5°, consistent with experimental observations (Figure 3) under transverse shear conditions. The same trend is also found for the case with weld leg size of 3/8". ...

**Context 6**

... addition to transverse shear conditions, the same two criteria, e.g. equations (7) and (8), must also predict a correct failure angle in longitudinal shear specimens, which is about 45° measured from base plate (see Figure 3 as reported in McClellan 4 ). To examine this, two 3D solid finite element models with 1/4" and 3/8" leg sizes were used. ...

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## Citations

... Moreover, the steel design standards consider the theoretical throat dimension with an angle of 45° for the fillet welds with equal leg sizes as the critical failure angle. Many studies and experimental tests have shown that it is not a correct assumption when the load is not parallel to the weld length (angle loading conditions) (Lu et al. 2015;Miazga et al. 1989;Nie et al. 2012) AWS B4.0:2016 standard (American Welding Society 2016) introduces two different specimen types for weld shear testing, including longitudinal and transverse specimens. Figure 3 illustrates the position of welds versus the load direction in each specimen type. ...

... According to the experimental tests, the average angle of fracture in welds was 52 and 18 degrees for longitudinal and transverse samples, respectively (see Fig. 4). This result was consistent with the findings of other studies (Lu et al. 2015;Miazga et al. 1989;Nie et al. 2012). The study recommended using transverse samples with real weld fracture angles to calculate the shear strength of welds and to investigate more closely the effect of the actual weld size compared with the idealised weld size. ...

Fillet and partial (incomplete) penetration butt welds are often the most cost-effective weld details for structural steel connections in seismic-resisting systems. Appropriately sized and executed, double-sided, balanced fillet welds and partial penetration butt welds can offer the same performance as complete penetration butt welds under both semi-static and low cycle fatigue (seismic) loadings. The weld sizing criteria are explained in NZS 3404 standard, including for use in seismic connections between members in ductile responding systems. Despite this, there is a misperception among design engineers about the performance of fillet welds under seismic load. Most overseas design specifications still call for complete penetration butt welds to be used in seismic full-capacity connections. This paper presents literature review and test results achieved as a part of HERA Seismic Research Programme in partnership with the Universities of Auckland and Waikato, Auckland University of Technology and the University of Michigan. It demonstrates that the sizing criterion for fillet welds used in the seismic connections currently included in NZS 3404 is conservative, especially the use of the overstrength factor in determining the demand from the principal load path elements in connections results in oversized fillet welds. It also discusses the performance of partial penetration welds as an alternative to fillet welds. Paper 24-Seismic application of fillet and partial penetration butt welds NZSEE 2023 Annual Conference

... Ameri et al., based on the basic concept of critical theory (TCD), verified the practicability of using local linear elastic stress to estim static strength of steel arc-welded joints by testing various welding geometries ac to experimental results obtained in different documents [11]. Varbai et al. focuse shear strength of welded structures [15], while Nie et al. [16] and Lu et al. [17] m to apply the structural stress method to static stress analysis and developed th strength theory of fillet welds. Current research is still in the stage of theoretical tion, and the analyses and tests of complex engineering structures are relatively l This study focuses on the load-carrying capacity of welded joints for rocke frames. ...

... There are three typical methods of defining the effective stress as shown in Equations (8)-(10) for the analysis of static strength, which have also been mentioned in reference [16]. Among them, Equation (8) is based on the assumption that when the vector sum of the normal and shear traction components reaches its limit value, static failure will occur along the cutting plane, while Equation (9) is based on the assumption that when the Von Mises stress of the traction stress component reaches its limit value, failure will occur. ...

The load-carrying capacities of welded joints need to be paid attention to in the design of the frame, which transfers the thrust generated by the rocket engine to the rocket body. A load-carrying capacity evaluation method of welded joints based on the structural stress method is proposed in this study. Both the ultimate load-carrying capacity and fracture section angle are precisely obtained by the evaluation method. At the same time, a definition of weld-failure stress is given based on the evaluation method and tests. The load-carrying capacity of welded joints in the rocket engine frame is analyzed through the finite element model, including the overall structure and local weld details. The weld-failure stress of welded joints is obtained based on the analysis of three types of welded structures—standard shear specimen, U-shaped fillet welded specimen and pipe-plate fillet welded specimen. The safety factors of the transverse rod and longitudinal bearing rod welded joints of the frame are 8.6 and 13.4, respectively.

... The traction stress method is a stress analysis method capable of accurately extracting the stress parameters correlated to the static shear failures, which is needed in order to avoid discrepancies in failure path and shear strengths [3,49]. The traction stress method has been proven effective in determining the shear strength of fillet welded joints compared to the conventional shear stress method [3]. ...

... The traction stress method has been proven effective in determining the shear strength of fillet welded joints compared to the conventional shear stress method [3]. Nie and Dong [49] introduced a new traction shear stress definition and calculation procedure to evaluate the static shear strength of the fillet welded joints. Therefore, this study developed finite element (FE) models of transverse and longitudinal fillet welded joints and validated against the test results of McClellan [50] in terms of shear stress and failure angles. ...

... 3D and 2D modelling techniques were adopted to investigate the static strength of fillet welded joints using various software packages such as ABAQUS [3,24,25,35,53,55], ANSYS [6,30] and FEMAP [23]. Nie and Dong [49] and Lu et al. [3] conducted a numerical simulation to perform the traction stress-based analysis. They recommended a 3D solid element with a reduced integration model and a 2D model under plane strain conditions for longitudinal and transverse fillet welded joints, respectively. ...

Fillet welded joints are commonly used in steel structures for various engineering applications such as buildings, bridges, railways, ships, and marine structures. Fillet welded joints are generally subjected to static and fatigue loading, resulting in failures of such welded joints. A number of experimental and numerical investigations on the strength and failure behaviour of fillet welded joints have been published. This paper presents a comprehensive review of research results on the static strength, fatigue life, and thermal performance of fillet welded joints. The review covers the various influential factors, such as loading direction, weld geometry, grades of steel, filler materials, welding process, weld penetration, strength mismatch of weld metal, and post-welded treatment. In total, 100 papers were critically reviewed, which were published from 1970 till date. The key findings and research developments on fillet welded joints are summarised. It was found that the transverse fillet welded joints have a higher static strength than the longitudinal fillet welded joints. Filler materials, post-welded treatment, and penetration of weld metal can offer significant strength enhancements in terms of their static and fatigue strength. Lastly, research gaps have been found in the existing body of knowledge, which will help guide future research.

... It is worth noting that in engineering applications, the traction stress is computed through the "nodal force" output by the FE model (see Ref. [51] for details). The equivalent traction stress (ΔS s ) parameter is determined based on the traction stress, which further takes the thickness effect and the bending ratio effect into account and can be utilized to evaluate the fatigue life of welded structures combined with the Master S-N curve [10,44,[52][53][54]. The definition of ΔS s is given in Eq. (6) [55][56][57]. ...

Understanding the weld-root-based fatigue failure of welded cast steel joints is critical, and the fatigue stress parameter corresponding to the S-N curve for the fatigue-derived design of welded cast steel joints still needs to be addressed. In this paper, we compared three widely used fatigue stress parameters, namely, the structural hot spot stress, the traction stress, and the 1-mm stress, for the analysis of different types of welded cast steel joints under various loading conditions. The results indicate that: (1) the structural hot spot stress calculated through linear extrapolation is close to the traction stress proposed by Dong (2001) but is easier to compute; (2) the 1-mm stress performs slightly better in correlating the fatigue data of different joint geometries and loading conditions, but its calculation requires more effort; and (3) finally, the equivalent hot spot stress parameter is proposed for fatigue design and data-based analysis of welded cast steel joints as it balances computational efficiency and data correction accuracy. Two S-N curves corresponding to the equivalent hot spot stress and the 1-mm stress are provided for the fatigue-based life evaluation of welded cast steel joints.

... The equivalent traction structural stress ( 8 remote bending and remote tension), so a single S-N curve with relative scatter band can be used to evaluate the fatigue life of different types of welded steel joints, and the Master S-N curve has been verified by many research works [10,[19][20][21]. The s S is calculated according to Eq.(2) [22][23][24] to take account of the plate thickness and bending ratio effect. ...

Cast steel joints (CSJ) are widely used in complex tubular structures to connect different parts of structures. This paper presents a simplified approach for efficient fatigue life estimation of full-scale welded cast steel structures. The proposed approach is applied to analyze a set of fatigue data of a full-scale CSJ thin-walled tubular truss structure. The results indicate that the fatigue lives estimated based on the simplified approach compare well with the experimental data. It is also shown that the simplified approach is much more efficient than the classical three-dimensional finite element-based method.

... In addition, the difference in flexibility or compliance between the connected members can make the stress determination more difficult (Packer & Cassidy, 1995). As a result of lacking an effective means of quantitatively determining the weld stress state, existing weld sizing criteria in current Codes and Standards are empirical and tend to be excessively conservative in nature, which often result in significantly oversizing of fillet welds (Packer et al., 2016;Nie & Dong, 2012). ...

... (1.1) simple to use for processing test data, it has been shown to exhibit some serious limitations in correlating test data as demonstrated by investigations both in the past and recent years. Firstly, it has been well established that failure angle of transver shear specimens tends to occur at an angle much smaller than 45°, but more close to 22.5°, as illustrated in Figure 1.4, for various weldment made of mild steel (Kato & Morita, 1974;McClellan, 1990;Lu et al., 2015), high strength steel (Björk et al., 2012;Khurshid et al., 2012), aluminum alloys (Krumpen & Jordan, 1984;Marsh, 1985Marsh, & 1988, as well as titanium alloys (Dong et al., 2013;Nie & Dong, 2012 McClellan (1990) and Dong et al. (2013) showed that longitudinal shear specimens tend to exhibit weld failure initiated at weld ends (near the machined slot locations in Figure 1.2a). Finite element analysis (FEA) performed by Nie and Dong (2012), as well as by Lu et al. (2015) also demonstrated that severe stress concentration at weld ends of longitudinal shear specimens must be properly taken into account in analyzing the test data. ...

... Firstly, it has been well established that failure angle of transver shear specimens tends to occur at an angle much smaller than 45°, but more close to 22.5°, as illustrated in Figure 1.4, for various weldment made of mild steel (Kato & Morita, 1974;McClellan, 1990;Lu et al., 2015), high strength steel (Björk et al., 2012;Khurshid et al., 2012), aluminum alloys (Krumpen & Jordan, 1984;Marsh, 1985Marsh, & 1988, as well as titanium alloys (Dong et al., 2013;Nie & Dong, 2012 McClellan (1990) and Dong et al. (2013) showed that longitudinal shear specimens tend to exhibit weld failure initiated at weld ends (near the machined slot locations in Figure 1.2a). Finite element analysis (FEA) performed by Nie and Dong (2012), as well as by Lu et al. (2015) also demonstrated that severe stress concentration at weld ends of longitudinal shear specimens must be properly taken into account in analyzing the test data. As a result, it can be concluded that Eq. (1.1) produces significant discrepancies in analyzing weld strengths from the standard fillet-welded shear test specimens, resulting in a shear strength in longitudinal shear specimens, which can be 30% to 80% lower than that in transverse shear specimens. ...

Rampant welding-induced distortions in construction of modern lightweight shipboard structures not only increase production cost, but also cause structural integrity concerns in service. Numerous recent studies have shown that overwelding in complying with the existing empirical-based fillet weld sizing criteria is the key contributor. Fillet-welded connections are widely used in the construction of marine structures. However, due to the complex stress state in fillet-welded connections and the lack of an effective means to relate the stress state at a joint to failure conditions observed in standardized component tests, existing weld sizing criteria in Codes and Standards used today were largely based on design experiences and observations from limited test data, dating back to decades ago. Therefore, a more quantitative mechanics-based weld sizing criterion must be developed for not only enabling the cost-effective construction of lightweight ship structures, but also ensuring structural safety in service. In this study, a traction stress based mesh-insensitive method is introduced for characterizing the complex stress state and its relationship to weld failure conditions in fillet-welded components. The insights gained enable the development of a closed-form solution for relating weld throat shear stress state to remotely applied loading conditions, which in turn leads to an effective traction stress based failure criterion serving as a mechanics basis for achieving quantitative weld sizing. To support and validate the analytical developments, a comprehensive testing program using over 200 standard longitudinal and transverse shear joint specimens was carried out. The test results have proven the effectiveness of the closed-form failure criterion in predicting both failure angle and correlating joint strength test data. A careful observation of the test data obtained in this study suggests that certain nonlinear effects such as plate-to-plate contact can be important in certain type of test configurations. This leads to the development of a new analytical formulation for incorporating the nonlinear effects to further generalize the effective traction stress based weld sizing failure criterion for a broader range of structural applications. To further validate the effectiveness of the developed quantitative weld sizing failure criterion, a large number of well-known full-scale test data available from past and recent literature on hollow structural section (HSS) joints have been analyzed in detail. The results show that the correlations between the predicted failure loads with the proposed failure criterion and the measured loads offer as much as 60% improvement over those predicted by the existing Codes and Standards, confirming the validity of the proposed failure criterion resulted from this study. Finally, within the context of these standard shear test specimens and full-scale HSS connections, it can be shown that the quantitative weld sizing criterion proposed in this study can result in a weld size reduction as much as 40%, compared with the existing empirical-based weld sizing criteria used today, which can be very beneficial for welding-induced distortion control in the construction of lightweight shipboard structures.

... Received 14 April 2020; Received in revised form 26 June 2020; Accepted 28 July 2020 have been proposed to quantify the stress/strain state at the weld and evaluate the fatigue life of the welded structure. These include nominal stress methods [23,24], surface extrapolation based hot spot stress methods [25][26][27], equivalent notch stress method [28][29][30][31][32], critical distance method [33][34][35], traction structural stress method [36][37][38], and most recently structural strain method [39][40][41][42]. Most of these methods are designed for fusion welded structures and have not been shown to be effective in fatigue data analyses of FSW structures. ...

This paper presents a detailed experimental and computational investigation into fatigue behaviors in friction stir welds at both joint and component level for welded assemblies of complex 6005A-T6 aluminum extrusion profiles. A novel fatigue test method was developed for characterizing FSW joint fatigue resistance in a structural context. The fatigue test data obtained in this study were then generalized by using a traction-based structural stress method. The results show that the fatigue test data and their S-N curve representation can be used as a basis for supporting fatigue evaluation of friction stir welds joining complex aluminum extrusions.

... This is because a higher welding speed would be highly desirable for adoption in massproduction environment, e.g., automobile body panel assembly. In addition, joint quality and joint strengths will be characterized through mechanical testing and the resulting test data will be analyzed by advanced mesh-insensitive traction stress method developed by Nie and Dong (2012) which is particularly suited for effectively suppressing stress/strain singularity at stress riser locations in lap joints. More importantly, the use of the mesh-insensitive method also allows generalizing the joint strength properties as well as demonstrating effects of joint details on joint performance in a structural context. ...

... "F/A" approach) in which F and A stand for load at failure and bonded area, respectively. To address this issue, an advanced mesh-insensitive traction stress method developed by Nie and Dong (2012) is applied for the joint strength analysis for gaining insights on the test data shown in Fig. 7. ...

... In all cases, linear elastic analysis using elastic material properties (see Table 2) of the two materials were performed, which can be justified for joint shear strength analysis, as discussed by Lu et al. (2015). The resulting interfacial traction stress distributions (i.e., shear and opening stresses) are shown in Fig. 14, which were computed using nodal forces through a simultaneous equation developed by Nie and Dong (2012). Fig. 14a shows the interfacial shear and opening stress distributions corresponding to the welding speed of 3 m/min. ...

A high-speed friction lap welding (FLW) technique for directly joining of aluminum to polymer is presented in this paper. Experimental results show that a consistent bond quality at the joint interface has been achieved at welding speeds as high as 5 m/min, which can be attributed to the formation of new C-O-Al bonds observed by X-ray photoelectron spectroscopy (XPS), in addition to mechanical interlocking. Lap-shear tests were performed for evaluating joint shear strengths of the welded samples corresponding to different welding conditions. It was found that as long as an interfacial threshold temperature was attained, the actual interface bond strengths are essentially the same regardless of welding temperature and welding speed.

... It is well known that fatigue behaviors of welded joints under time-varying loading conditions are complex [4] and significantly different from those seen in unwelded components [5,6] As a result, different fatigue evaluation procedures have been devised for assessing fatigue of welded joints. These include nominal stress methods [7,8], surface extrapolation based hot spot stress methods [9][10][11], equivalent notch stress method [12][13][14], traction structural stress method [15][16][17], and most recently structural strain method [18][19][20][21]41]. These methods are all intended to determine a relevant stress or strain parameter by avoiding the uncertainties caused by stress or strain singularity at weld toe or weld root due to ill-defined notch geometry at weld toe or at weld root. ...

... Then, the maximum traction stresses acting on the critical weld throat cut plane can be analytically determined. In fact, the mesh-insensitive structural stress method [15,17] can be conveniently used for the robust determination of the internal line forces F T , , and line moment M by postprocessing the FE results, with respect to unit weld width along z direction, as illustrated in Fig. 5d. Then, imposing force balances in x and y, and moment balance with respect to O (see Fig. 5d), we have: ...

... Shear strength on positive surface of an element is positive if it works in the positive direction of one of the positive axes and so it is in the negative direction [7][8] [9] [10]. The shear strength on negative surface of an element is positive if it works in the negative axe and negative if it works in positive direction [11]. ...

Spot welding is a process of connecting two metal components through one or more connection points by using heat from electrical resistance which is carried by two electrodes to the metal to be connected with a certain welding time. The purpose of this study is to determine the effect of voltage and time of pressure used for spot welding on the shear strength and peel strength on the SPCC plate. The variables used in this study are independent variables of electric current variation of 2.30 V, 2.70 V, 3.20 V and time variation of 3 seconds, 4 seconds, and 5 seconds with 1mm plate thickness. The dependent variable in this study is the calculation of shear strength and peel strength in universal testing machine, and the controlled variable in this study is 1mm plate thickness characteristic of SPCC palate work piece. The research method was carried out using the ANOVA Factorial with the null hypothesis that there was no influence of the spot welding time and voltage on spot welding on the shear strength and strength of the SPCC material's peel. The results of the study are for the shear test seen from the calculation using MINITAB, the time variation of the pressure is no effect, while for the voltage and the combination of time suppression and voltage there is influence. For strength testing, the null hypothesis is rejected for all variations, which means that there is an influence on the strength of the peel test.