NEW METHODS FOR STRESS CONCENTRATION FACTOR CALCULATION IN BUTT WELDED JOINTS: A COMPARATIVE STUDY

Surface cracks in butt-welded joints usually occur in places with increased stress concentrations. The stress concentration factor (SCF) can be calculated using an empirical equation, with five geometric parameters of a butt-welded joint (thickness of the base material, toe radius, weld toe angle, weld width, and reinforcement height). However, in an industrial environment, it is impractical and sometimes even impossible to measure all five geometric parameters with sufficient accuracy. In this study, eight experiments on butt-welded joints were performed. All samples were scanned with a 3D scanner, and the geometric sizes of the welded joints were measured using computer software. A modified empirical expression proposed by Ushirokawa and Nakayama was used to calculate the SCF; the expression was adjusted in such a way that the SCF was calculated by knowing only the toe radius. In addition, four new expressions were proposed for the calculation of the SCF by knowing the toe radius in relation to the weld toe angle; the expressions were then compared and analysed. Additionally, the values of the stress concentrations in the butt-welded joints were obtained using a finite element method (FEM). The SCFs calculated using the four methods were compared and further discussed. Our data suggested a new accurate and straightforward approach for calculating the SCF by knowing only the weld toe radius.


Introduction
Welding is the most commonly used method for joining metals and is applied in all types of industries, including bridge construction, shipbuilding, house building, the offshore industry, and the car industry. Welding is a relatively fast and inexpensive process in which the weld joint has the same properties as the base material. There are two main types of welding: manual welding and automated welding. A manually welded joint has an irregular shape. Due to sudden changes in geometry and an increase in stress concentrations, this method can lead to surface cracks and, in turn, cracking of the whole welded joint, after which the whole structure around that welded joint may collapse. Surface cracks often occur when the SCF is high [1]. With an increase in the SCF, the risk of creating surface cracks also increases.
Five geometric parameters affect the SCF, including the thickness of the base material, toe radius, weld toe angle, weld width, and reinforcement height [2]. SCFs can be calculated through empirical expressions [3,4]. However, for this method, it is necessary to measure all five geometric parameters; this process can be slow and sometimes barely even feasible, depending on the weld location. There are several ways to measure the geometric dimensions of a welded joint, ranging from conventional methods of measurement (by using simple measuring instruments) to modern 3D scanning approaches to determine geometric properties using computer software. Since the weld toe radius is the most influential geometric variable for the SCF, particular attention is given to its accurate measurement [5,6]. Measuring the toe radius with simple measuring devices is the fastest and simplest method; however, its accuracy may be questionable [7]. Measuring the geometric dimensions of welded joints with computer software can give the most accurate results; however, this method is complicated and costly and cannot be used to assess welded joints in all locations [8].
After the geometric dimensions of a welded joint have been measured, it is possible to use empirical equations to calculate the SCF in its cross-section. The finite element method (FEM) is used in the modelling of welded joints to analyse the mechanical and geometric characteristics [9]. This is a useful technique for stress analysis in welded joints [10].
Previously, Kiyak et al [11] calculated SCFs using 2D finite elements, after which they compared those results with the results of empirical equations. Moreover, Ninh Nguyen and Wahab discovered that the toe radius has a significant effect on the SCF, which was confirmed using an FEM [12]. Additionally, Tang obtained similar conclusions, with one addition, i.e., that the weld toe angle has a slightly smaller effect on the SCF [13][14][15]. The influence of welding process, parameters, constraints, solid phase transformation and multipass welding for thick plate on the distribution of welding deformation and residual stress was analysed by Rong et al [16].
In this paper, we propose new expressions for calculating the SCF, taking into account only the toe radius, which is the most influential parameter for the SCF. The SCF can be calculated by knowing only the toe radius, which is essential for practical work, where it is often necessary to determine the SCF quickly to avoid possible initiation of surface cracks.
The expressions for calculating the SCF become more accurate if the weld toe angle is known.

Materials and Methods
A total of eight welding experiments were performed, after which three different welding methods were changed. The following welding methods were changed: the number of cover passes was analysed in two levels (one pass and three passes); the electrode stick-out length was also analysed in two levels (5 mm and 15 mm); and experiments were performed with two types of shielding gas (-) mixture of (82% Ar +18% CO 2 ) and (+) 100% CO 2 . The welding methods were modified to obtain different surface shapes of welded joints with different values of the SCF and with different weld toe radii of the welded joints. These welding methods have a significant effect on the surface of a welded joint [17].
Consequently, various forms of welded joints were obtained. Table 1 shows the welding methods that were changed during the experiments, and Table 2 shows the complete test plan.

Measurement of geometrical parameters of welded joints
Welding experiments were performed on samples that were 150 mm long. For each sample, the geometric parameters of the welded joint were measured using three different bands. Each measured band was 10 mm wide. The welding parameters were automatically measured and stored during welding. It was found that the welding parameters stabilized a few millimetres after the start of welding. Based on this result, the first band was measured 20 mm to 30 mm from the beginning of welding; the second band was measured at the middle of the sample, 70 mm to 80 mm from the beginning of welding; and the last band was measured at the end of the sample, 120 mm to 130 mm from the beginning of welding.
In each specified band, the geometric dimensions were measured every 1 mm; measurements were taken in 11 cross sections and in two places (right and left).  The measurements of the geometric parameters of a welded joint by the computer method were divided into two parts: 1) sample scanning and 2) cross-section analysis of the welded joint using computer software. The surface of each sample was scanned by the "ATOS II Triple Scan" (Advanced Topometric Sensor) at the Center for Advanced Computing and Modeling at the University of Rijeka. The computer program "GOM inspect", v.2.0.1, was used to measure the geometric dimensions of the welded joint. Briefly, the data obtained by 3D scanning were loaded into a computer, after which the surface of the welded joint was generated [18]. The measured geometric properties of sample A3 in band A are shown in Table 3.

Stress concentration factor (SCF)
The SCF is defined by the ratio of the maximum and nominal stress. The surface of a welded joint has an irregular shape with a great number of local shape changes; therefore, it is not easy to calculate the SCF for a welded joint [19].
In this expression, the SCF is influenced by the toe radius, weld toe angle, weld width, thickness of the base material, and reinforcement height. These geometric dimensions were obtained by 3D scanning of the welded joint and then measured by "GOM inspect" software.
After the geometric properties were assessed, they were included in expression (1), and the concentration factors for the right and left sides of each section in the observed areas on each sample were calculated. Table 3 shows the values of the SCF obtained by expression (1) for sample A3 in band A in columns 9 and 10.
The experiments were performed with eight samples. The SCF was calculated at 66 places on each of the eight samples, and therefore, the SCF was calculated for 528 points.
These points are plotted in the diagrams shown in Figure 2a and 2b. The diagram in Figure   2a shows the trend line, which is a function of the toe radius and SCF. The diagram in Figure   2b shows four trend lines that are functions of the toe radius and SCF, which depend on the weld toe angle for values from 0° to 20°, from 20° to 30°, from 30° to 40° and for the area over 40°. These expressions are shown in equations (2) and (3a to d), respectively; the values obtained by these expressions are shown in Table 3

Evaluation of stress concentration using the finite element method (FEM)
The FEM is a numerical method that is often used in engineering calculations. In this paper, the values of the stress concentration in butt-welded joints were obtained using the finite element method. The coordinates of the points obtained by 3D scanning of the surface of a welded joint were used to create a numerical model that was then analysed by the finite element method. The values obtained by the previous expressions were compared with the SCFs obtained using the finite element method. Figure 3 shows a flow chart of sequential actions during the finite element analysis [21].

Fig. 3 FEM analysis diagram.
3. Results Figure 4 shows the A3 sample for which an analysis was conducted using the FEM. The areas before 10 mm from where welding was initiated and after 140 mm from the beginning of welding was not analysed due to uneven ends that could affect the results.

Fig. 4 A3 sample shown in GOM inspect.
The mesh obtained by 3D recording (scanning) was loaded into Salome software (Figure 5a). Spry drops were not removed from the surface of the specimen since they did not affect the stress concentration. However, during the finite element method analysis, these spry drops might have an impact in the form of the stress concentration that can form on them; thus, they were cleaned from the finite element model. The cleaned model is shown in  Table   3 in columns 15 and 16. Figure 6 shows a comparison of the SCFs obtained using the four different methods.
Curve (1) indicates the values of the SCFs obtained using the expressions proposed by Ushirokawa and Nakayama; curve (2) represents the values obtained using expression (2), which takes into consideration only the weld toe radius; curve (3) represents the values obtained by expressions (3a to d), which take into account the weld toe radius with respect to the weld toe angle; and curve (4) represents the values obtained using the FEM.

Availability of data and materials
The datasets generated and analysed during the current study are not publicly available because there are lots of datasets collected during experiments. Sample of collected datasets are presented in manuscript table 3 for one sample and one band. All datasets are available from the corresponding author on reasonable request.

Competing interests
The authors declare that they have no competing interests.