Transient distortion behavior during TIG welding of thin steel plate

Transient distortion behavior during TIG welding of thin steel plate

Accepted Manuscript Title: Transient distortion behavior during TIG welding of thin steel plate Author: Shigetaka Okano Masahito Mochizuki PII: DOI: R...

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Accepted Manuscript Title: Transient distortion behavior during TIG welding of thin steel plate Author: Shigetaka Okano Masahito Mochizuki PII: DOI: Reference:

S0924-0136(16)30380-6 http://dx.doi.org/doi:10.1016/j.jmatprotec.2016.11.006 PROTEC 15007

To appear in:

Journal of Materials Processing Technology

Received date: Revised date: Accepted date:

13-5-2016 7-11-2016 7-11-2016

Please cite this article as: Okano, Shigetaka, Mochizuki, Masahito, Transient distortion behavior during TIG welding of thin steel plate.Journal of Materials Processing Technology http://dx.doi.org/10.1016/j.jmatprotec.2016.11.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

–Title– Transient distortion behavior during TIG welding of thin steel plate

–Author names (given names and family names)– Shigetaka OKANO* Masahito MOCHIZUKI*

–Affiliations (including postal address)– *Graduate School of Engineering, Osaka University 2-1 Yamada-oka, Suita, Osaka 565-0871 Japan

–Corresponding Author– Shigetaka OKANO ([email protected])

–Abstract– To examine the generation characteristics of excessive distortions involved with the welding-induced buckling of a thin steel plate, the temperature profiles and distortion behaviors of welded plates during tungsten inert gas (TIG) welding were experimentally measured. Large-deformation thermal elastic–plastic analysis based on arc physics-based heat source modeling was utilized to accurately simulate the thermomechanical behavior of the plate during welding. The calculated and measured temperature profiles and distortion behaviors were compared to validate the developed numerical analysis technique. On the basis of the developed analysis technique, the effect of geometric imperfections on the thermomechanical behavior of welded thin steel plates was further investigated. Both angular and longitudinal bending distortions were found to monotonically increase with increasing heat input because of excessive longitudinal bending distortion and the secondary generation of angular distortion during the cooling process when buckling occurred. The through-thickness gradient of the plastic strain that developed with the transient distortion behavior during welding resulted in excessive angular distortion in the welded thin steel plate. It was concluded that the transient distortion behavior during welding should be taken into consideration to accurately predict and control large welding-induced distortions in thin steel plates. –Keywords– Welding, Thin steel plate, Buckling distortion, Angular distortion, Real-time measurement, Computational simulation

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–Text– 1. Introduction Welding technology is widely used in the construction of lightweight structures comprising thin plates; however, excessive residual distortions easily occur and are extremely difficult to correct. The geometric imperfections induced by welding deteriorate the performance of structures and influence the appearance of finished products. Therefore, in lightweight structures comprising thin plates, the highly accurate predictions and control of weld distortions are gaining increasingly important because large welding-induced distortions often result in critical problems. Classical welding mechanics provides the theoretical framework to understand and quantify various types of shrinkage and distortion based on simplified models and empirical formulae. White et al. (1977, 1980) proposed the tendon force concept as a driving force for longitudinal shrinkage and bending distortion. The value of the tendon force can be estimated as a function of the net heat input per unit welding length, Qnet. Terasaki et al. (2000) theoretically verified the welding heat input dependence of the welding-induced tendon force. Okano and Mochizuki (2015) recently clarified the details of the dependence of the tendon force on the welding conditions, focusing on the interaction between the welding heat input and the dimensions of the welded joint. To coordinately quantify the transverse shrinkage and bending (angular) distortion, Satoh and Terasaki (1976) proposed the heat input parameter, Qnet/h2, where h is the thickness of the material to be welded, based on the similarity rule of the temperature distribution on the plate thickness section. It is well known that welding-induced angular distortion yields a convex curve when plotted against the heat input parameter. For the occurrence of welding-induced buckling distortions in thin plates, Watanabe and Satoh (1957, 1958) first proposed the critical plate length based on I/h√vh, where I is the welding current and v is the welding speed; this term represents the transient temperature profiles around the weld pool. Fujita and Nomoto (1977) proposed an expression for the critical welding heat input based on Qnet/h that represents the distribution of residual longitudinal stress after welding. Subsequently, Nomoto et al. (1997) derived other dominant factors (Qnet/h2, L/h, and B/h, where L and B are the length and width, respectively, of the material to be welded) based on the inherent strain theory. On the basis of these parameters, Terasaki et al. (1998) quantified the critical conditions for the occurrence of welding-induced buckling distortions in thin plates. Thus, on the basis of classical welding mechanics, it has been proposed that various types of shrinkage and distortion induced by welding can be controlled by the net heat input per unit welding length. Meanwhile, Okano and Mochizuki (2016) recently conducted an experimental investigation on the effect of welding conditions on welding-induced buckling and angular distortions in thin steel plates, focusing on the heat input parameter. The results clarified the limits of applying the heat input parameter to

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accurately quantify angular distortion, especially when buckling distortion has occurred. Therefore, a more detailed understanding of the angular distortion generation mechanism in conjunction with the occurrence of buckling distortion is required to accurately predict and control large welding-induced distortions in thin steel plates. The popularity of modern computational welding mechanics has increased since Ueda and Yamakawa (1971) applied thermal elastic–plastic analysis using the finite element method to welding thermomechanical problems. Computational methods that can be used to calculate the time evolution of thermomechanical behavior during welding are expected to be useful tools to understand the generation characteristics of buckling distortions induced by welding. Michaleris et al. (2006) and Deng and Murakawa (2007) have provided the computational framework to evaluate buckling welding distortions, focusing on three-dimensional modeling and large deformation analysis. Deng et al. (2008, 2012) introduced the interface element to simulate the joining process and correction of the gap between the welded parts in the assembly process of a curved plate structure and a thin-plate panel structure, respectively. Schenk et al. (2009) reported that the mesh density used to model the buckling distortion significantly influences the simulation results. Wang et al. (2013) showed that initial deflection and inherent bending deformation are disturbances that trigger buckling. Furthermore, the importance of welding heat source modeling for welding thermomechanical analysis has been widely discussed. For arc welding, Long and Maropoulos (2009) and Tchoumi et al. (2016) investigated the effect of the parameters in the double-ellipsoid Gaussian heat source model, which was proposed by Goldak (1984), on the numerical width and depth of the welds. Zain-ul-Abdein et al. (2009) and Chukan et al. (2015) conducted similar investigations for laser welding in stainless steel and aluminum alloy sheets, respectively. Okano et al. (2011) proposed an arc physics-based heat source model for more accurate distortion analysis in tungsten inert gas (TIG) welding. Thus, computational methods in welding mechanics have already shown significant potential to accurately simulate distortions in thin plate structures. However, very few studies, such as those by Dhingra et al. (2005) and Heinze et al. (2012), have discussed the transient distortion behavior during the welding of thin steel plates through a coupled experimental–numerical approach. For a more detailed understanding of the generation characteristics of buckling distortions induced by the welding of thin steel plates, further discussions of the transient distortion behavior during welding are necessary. This paper examines the generation characteristics of excessive distortions involved with buckling induced by the welding of thin steel plates through a coupled experimental–numerical approach. To accurately simulate the temperature distribution during welding, arc physics-based heat source modeling was adopted for welding thermal conduction analysis. The obtained temperature distributions were used for the large-deformation

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thermal elastic–plastic analysis of the weld distortion. The transient temperature profiles and distortion behaviors of the welded material during welding were experimentally measured and computationally calculated to obtain a more detailed understanding of the generation characteristics of the buckling distortions induced by the welding of thin steel plates. Additionally, the experimental and computational results were compared to validate the developed analysis model. With the developed analysis technique, the effect of geometric imperfections on the generation characteristics of the buckling distortions and plastic strain that develop during the welding of thin steel plates were further investigated. Based on the results of these investigations, the generation mechanism of large welding-induced distortions that easily occur in thin steel plates is discussed.

2. Experimental setup and computational modeling 2.1 Experimental setup The thin steel plates to be welded in the experiment were made of 570 MPa class high-tensile strength SPHC (Steel Plate Hot Commercial). The chemical composition and mechanical properties of the steel are given in Table 1. Fig. 1 shows the configuration of the steel plate to be welded. The thin plate has a length of 200 mm, a width of 200 mm, and a thickness of 2.3 mm. The weld length was 180 mm, leaving unwelded sections of 10 mm at either end of the welds on each plate. The bead-on-plate welded joints were produced by TIG welding. Three different welding currents of 50, 100, and 150 A were employed in the TIG welding experiment. A welding speed of 7.5 mm/s and an arc length of 3 mm were used. The shielding gas was 100% argon (Ar) with a flow rate of 3.3 × 105 mm3/s. The thin steel plates to be welded were placed on sill plates to allow heat transfer from the bottom of the plate to the air. No restraints preventing welding-induced thermal deformation were used.

In the welding experiment, the temperature profiles and vertical deflection variations were measured during welding. The temperature profiles were measured using K-type thermocouples whose contacts, or “channels” (ch.), were located on the bottom surface at three different positions, as shown in Fig. 2. The measurement position of ch. 1 was just below the weld bead, whereas ch. 2 and 3 were located at positions with transverse distances of 20 and 100 mm, respectively, from the weld center line. The vertical displacements of the bottom surface of the welded thin steel plates were measured using laser displacement sensors at three different positions along the transverse axis at the longitudinal center of the plate, as shown in Fig. 2. The longitudinal bending and angular distortions were estimated from the measured vertical displacements using the equations given in Fig. 2.

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2.2 Computational modeling The Abaqus ver. 6.12-3 general purpose finite element (FE) code was used to compute the sequential thermal conduction and elastic–plastic analyses to calculate the thermomechanical behavior of the material during TIG welding. Fig. 3 shows the FE model of a bead-on-plate welded joint used in the present numerical analysis. The dimensions of the simulated welded thin plate are exactly the same as those used in the welding experiment. A half-symmetric model was used for the welding thermomechanical analysis for the sake of numerical calculation efficiency. A fine mesh was used around the melted zone to accurately simulate the temperature distribution that determines the thermomechanical behavior of the material during welding. The dimensions of the minimum mesh size were 1.33 mm in both the longitudinal and transverse directions and 0.46 mm in the thickness direction. In the FE analysis, reduced integration elements were adopted to prevent or reduce membrane and volume locking. The reduced integration elements occasionally showed hourglassing (zero-energy modes); however, hourglassing did not occur in the analysis technique developed in the present study.

The material properties determined for the high-tensile strength SPHC are shown in Fig. 4. Fig. 4(a) shows the temperature dependence of the density, specific heat, and thermal conductivity; these data were used in the welding thermal conduction analysis. The initial temperature of the material to be welded and atmospheric temperature were estimated to be 20 °C. Heat transfer and thermal emission from the surface of the material to air were introduced as boundary conditions. The heat transfer coefficient and thermal emissivity were set to 12.5 × 10-6 W mm-2 K-1 and 0.3, respectively, by referring to a previous study by Okano et al. (2016). Fig. 4(b) shows the temperature dependence of the Young’s modulus, yield stress, thermal expansion coefficient, and Poisson’s ratio; these data were used in the welding thermomechanical analysis as well. The work hardening of the material was also taken into account, as shown in Fig. 4(c). No restraints preventing welding-induced thermal deformation were implemented in the welding thermomechanical analysis.

It is well known that welding simulation results strongly depend on the accuracy of the heat source model. An arc physics-based heat source modeling method proposed by Okano et al. (2011) to accurately simulate the temperature distribution during welding was adopted in the present model. For TIG welding, the radial distribution of the heat w transferred from the arc plasma to a welded plate is expressed as w = (q/R2) exp{-(x-vt) 2/R2} exp{-y2/R2},

(1)

where q is the heat input per unit welding time, R is the radius of the Gaussian distribution, v is the welding speed, and t is the time from the start of welding. Both q and R can be quantified according to the welding heat input

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conditions, including the welding current, arc length, and shielding gas. The values of these parameters used in the present model are given in Table 2. Both q and R increase monotonically with the welding current.

3. Results and discussion 3.1 Comparison of measurements and calculations Figs. 5(a) and (b) show the simulation results for an illustrative example with a welding current of 50 A. This figure shows the two-dimensional (2D) distributions of temperature fields and the vertical displacement of the welded thin steel plate at the time when a welding torch reached the longitudinal center of the plate. From the numerical simulation results, the temperature profile and vertical deflection variation obtained during welding were compared with the measured values to validate the developed welding thermomechanical analysis model.

Figs. 6(a), 7(a), and 8(a) show the measured and calculated temperature profiles along the welds for welding currents of 50, 100, and 150 A, respectively. Similarly, Figs. 6(b), 7(b), and 8(b) show the measured and calculated transient distortion behaviors during the welding of a thin steel plate for welding currents of 50, 100, and 150 A, respectively. In these figures, the points and lines show the measured and the calculated results, respectively.

For all welding currents, the results show that the calculated and measured temperature profiles are in very good agreement. At the measurement position of ch. 1, the temperature suddenly increased during welding, and the peak temperature was the highest among the three measurement positions. The temperature gradually increased as a result of the welding, and the peak value decreased with increasing transverse distance from the weld line. At all measurement positions, the peak temperature increased with increasing welding current. Thus, the differences in the temperature profiles at different welding currents and measurement positions were successfully obtained using both measurements and calculations. Small differences between the calculated and measured transient distortion behavior were observed for welding currents of 100 and 150 A; however, the calculated and measured transient behaviors during welding were still in fair agreement. In both cases, both longitudinal bending and angular distortions were temporarily concave upward during welding. However, the distortion behaviors during the cooling process after welding varied depending on the welding current. The concave upward longitudinal bending distortion returned to approximately zero, and the angular distortion remained constant only when the welding current was 50 A. In

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contrast, when the welding current was 100 and 150 A, an excessive return in the longitudinal bending distortion from concave upward to convex upward was observed during the cooling process. A longitudinal shrinkage force that resulted in buckling increased with increasing welding heat input when the plate thickness was kept constant. Additionally, the V-shaped eccentric cross section involved with angular distortion, which was suddenly generated during welding, may have increased the longitudinal convex deflection, resulting in buckling caused by the longitudinal shrinkage force. Furthermore, a secondary generation of angular distortion was observed during this process. Through these processes, the angular distortion also likely increased when buckling occurred. Therefore, both the longitudinal bending and angular distortions monotonically increased with increasing welding current. This differs from the traditional view that angular distortion yields a convex curve when plotted against the heat input parameter. Okano and Mochizuki (2016) have found that the convex upward curve representing the relationship between the angular distortion and the welding heat input is not obtained when welding-induced buckling distortion occurs in thin plate. On the basis of a nearly linear relationship between the welding heat input and the welding current, a probable cause for the monotonic increase in the angular distortion with welding current is the secondary generation of angular distortion involved with welding-induced buckling that occurs during the cooling process. A more detailed investigation of the transient thermomechanical behavior during welding is essential to understand the generation mechanism of the distortions in bead-on-plate welded thin steel plates.

3.2 Numerical discussion of distortion mechanism To further discuss the generation mechanism of excessive distortions induced by the welding of thin steel plates, the effect of geometric imperfections on the transient thermomechanical behavior during welding was investigated. As previously stated, it is well known that one cause of angular distortion is the presence of a temperature gradient along the thickness of the welded materials. A through-thickness welding heat source does not generate a temperature gradient along the thickness; thus, angular distortion is not generated by welding using such a heat source. Here, to eliminate angular distortion caused by a thickness-directional temperature gradient, a through-thickness welding heat source with three different heat input values was adopted for the welding thermomechanical analysis of a thin steel plate. The welding heat input values used in this analysis correspond to welding currents of 50, 75, and 100 A. The Gaussian radii were also exactly the same as the previously obtained values given in Table 2. For the intermediate condition, 75 A, the values of heat input and Gaussian radius were linearly interpolated from the values of 50 and 100 A. Some geometric imperfections were also introduced to study their effect on the transient thermomechanical behavior during welding. A transverse deflection, which

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represents a welding-induced angular distortion, was considered as an initial geometric imperfection, as shown in Fig. 9. The magnitude of the transverse deflection initial was set to 0 (no geometric imperfections), 0.001875, 0.00375, 0.0075, 0.015, 0.025, and 0.030 rad. These seven geometric imperfections were combined with each of the three welding heat inputs, yielding a total of 21 considered conditions in the welding thermomechanical analysis. All other analytical conditions except the heat source model were the same as in the previously described analysis.

Fig. 10(a) and (b) show the calculation results for the residual longitudinal bending and angular distortions, respectively, focusing on the effects of the welding heat input and geometric imperfection. The vertical axis in Fig. 10(b) represents only the angular distortion induced by welding and excludes the angular distortion primarily introduced by the geometric imperfections. The results show that both longitudinal bending and angular distortions increase with increasing welding heat input and geometric imperfection magnitude. A V-shaped eccentric cross section increases the magnitudes of longitudinal bending and angular distortions induced by welding in comparison with a flat cross section. Without geometric imperfections, neither longitudinal bending nor angular distortions occurred even at the highest considered welding heat input. Thus, it was confirmed that geometric imperfections induce drastic increases in the magnitudes of both longitudinal bending and angular distortions in bead-on-plate welded thin plates.

For a more detailed investigation of the effect of geometric imperfections on angular distortion induced by the welding of thin steel plates, the time evolution of the temperature and distortions during welding was estimated at the longitudinal center of the welded thin plate. Fig. 11 shows the results for the case where the welding heat input and the initial magnitude of the geometric imperfection were 840 J/s and 0.015 rad, respectively. As shown in Fig. 11(a), the temperature profiles were exactly the same on the upper and lower sides of the welded thin steel plate because a through-thickness welding heat source was applied. However, angular distortion suddenly occurred during welding, as shown in Fig. 11(b), even though no through-thickness temperature gradient was present within the welded material. This indicates that a factor other than the through-thickness temperature gradient induced angular distortion in this case.

The transient thermal stress and plastic strain behaviors during welding were then estimated, as shown in Figs. 12(a) and (b), respectively, to clarify the details of the generation mechanism of angular distortion induced by the welding of thin steel plates with geometric imperfections. The estimation positions were the same as those

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for the temperature profiles (see Fig. 11(a)). The results show that thermal stress and plastic strain behaviors of the upper and lower sides of the welded thin steel plate differed, even though the temperature profiles were equivalent. As shown in Fig. 12(a), both the upper and lower sides experienced tensile thermal stress at the start of welding, but the magnitude of the stress differed. It was considered that concave upward deflection during welding (Fig. 11(b)) enabled the material to stretch on the lower side of the thin steel plate and caused it to shrink on the upper side. As a result, higher tensile stress was generated on the lower side approximately 10 s before the arrival of the welding torch. The primary tensile thermal stress may delay the evolution of the compressive thermal stress, which induces a compressive plastic strain during welding. Fig. 12(b) shows that the evolution of the welding-induced compressive plastic strain differs between the upper and lower sides of the welded thin steel plate.

For an alternative perspective, the temperature–plastic strain relation during welding was also estimated on both the upper and lower sides of the thin steel plate. Fig. 13 shows the temperature–plastic strain relations during welding with and without geometric imperfections. As shown in this figure, the temperature–plastic strain relations on the upper and lower sides of the thin steel plate without geometric imperfections are equivalent. However, for the plate with geometric imperfections, the development of compressive plastic strain during the heating process was encouraged and discouraged on the upper and lower sides of the thin steel plate, respectively. As a results, the difference between the compressive plastic strains of the upper and lower sides reached approximately 0.0039 at the peak temperature. At room temperature after welding, the difference between the compressive plastic strains of the upper and lower sides increased to approximately 0.0066 via the cooling process. This may have been caused by the excessive longitudinal convex deflection involved with the buckling induced by the welding. The through-thickness gradient of the plastic strain that developed during welding resulted in excessive angular distortion in the welded thin steel plate. Thus, a more detailed understanding of the generation mechanism of excessive distortions induced by the welding of thin steel plates was successfully obtained by focusing on the transient thermomechanical behavior of the plates during welding.

Consequently, the generation and evolution of compressive plastic strain that developed during welding can be influenced by not only the temperature distribution but also the transient distortion behavior when a thin plate structure with low rigidity is considered. To accurately predict and control welding-induced distortions in thin plate structures, the transient distortion behavior during welding should be taken into consideration.

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Computer methods that can calculate the time evolution of thermomechanical behavior during welding and have been further enhanced by the inclusion of arc physics-based heat source modeling are expected to be a useful tool to understand and quantify the generation characteristics of welding-induced distortions in thin steel plate structures.

4. Conclusions (1) Both longitudinal bending and angular distortions monotonically increased with welding heat input when buckling occurred. Excessive longitudinal bending distortion and the secondary generation of angular distortion involved with buckling were experimentally observed during the cooling process.

(2) The temperature profiles and transient distortion behaviors calculated using a distortion analysis method developed based on arc physics-based heat source modeling were in good agreement with the measured profiles and behaviors.

(3) Both longitudinal bending and angular distortions were greater in plates with initial geometric imperfections than in plates without imperfections, even when the welding heat input was equivalent for the two plates and no through-thickness temperature gradient was present within the material welded.

(4) In a welded thin steel plate, the generation and evolution of the plastic strain that developed during welding were influenced not only by the temperature distribution but also by the transient distortion behavior during welding. A through-thickness gradient of the plastic strain developed because of the transient distortion behavior despite there being no temperature gradient along the thickness.

Acknowledgements This research did not receive any specific grants from funding agencies in the public, commercial, or not-for-profit sectors.

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References Chukkan, J. R., Vasudevan, M., Muthukumaran, S., Kumar, R. R., Chandrasekhar, N., 2015. Simulation of laser butt welding of AISI 316L stainless steel sheet using various heat sources and experimental validation. J. Mater. Process. Technol. 219, 48-59. Dhingra, A. K., Murphy, C. L., 2005. Numerical simulation of welding-induced distortion in thin-walled structure. Sci. Technol. Weld. Joining 10 (5), 528–536. Deng, D., Murakawa, H., 2008. Prediction of welding distortion and residual stress in a thin plate butt-welded joint. Comput. Mater. Sci. 43, 353-365. Deng, D., Murakawa, H., Liang, W., 2008. Prediction of welding distortion in a curved plane structure by means of elastic finite element method. J. Mater. Process. Technol. 203, 252-266. Deng, D., Murakawa, H., Ma, N., 2012. Predicting welding deformation in thin plate panel structure by means of inherent strain and interface element. Sci. Technol. Weld. Joining 17(1), 13-21. Fujita, Y., Nomoto, T., Terai, K., Matsui, S., Kinoshita, T., 1977. Studies on welding deformation in thin-skin plates structures (1st report : on the analysis of lateral deformation due to welding). J. Soc. Nav. Archit. Jpn. 142, 182–189. Goldak, J., Chakravarti, A., Bibby, M., 1984. A new finite element model for welding heat source. Metall. Trans. B 15B, 299-305. Heinze, C., Schwenk, C., Rethmeier, M., 2012. The effect of tack welding on numerically calculated welding-induced distortion. J. Mater. Process. Technol. 212, 308-314. Long, H., Maropoulos, P. G., 2009. Prediction of welding distortion in butt joint of thin plates. Mater. Design 30, 4126-4135. Michaleris, P., Zhang, L., Bhide, S. R., Marugabandhu, P., 2006. Evaluation of 2D, 3D and applied plastic strain methods for predicting buckling welding distortion and residual stress. Sci. Technol. Weld. Joining 11(6), 707-716. Nomoto, T., Terasaki, T., Maeda, K., 1997. Study of parameters controlling weld buckling. Trans. JSME Series A 63(609), 1063–1068. Okano, S., Tanaka, M., Mochizuki, M., 2011. Arc physics-based heat source modelling for numerical simulation of weld residual stress and distortion. Sci. Technol. Weld. Joining 16 (3), 209–214. Okano, S., Mochizuki, M., 2015. Dominant factors and quantification of Tendon Force in welded structural materials (Development of accuracy management system for high quality construction in welded structures on the basis of advance theory of inherent strain). Trans. JSME 81 (830), 15-00277 [DOI:10:1299/transjsme.15-00277].

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Okano, S., Mochizuki, M., 2016. Experimental study on generation characteristics of weld buckling distortion in thin plate. Trans. JSME 82 (834), 15-00314 [DOI:10:1299/transjsme.15-00314]. Okano, S., Tsuji, H., Mochizuki, M., 2017. Temperature distribution effect on relation between welding heat input and angular distortion. Sci. Technol. Weld. Joining 22 (1), 59–65. [DOI:10:1080/13621718.2016.1185313]. Satoh, K., Terasaki, T., 1976. Effect of welding conditions on welding deformations in welded structural materials. J. Jpn. Weld. Soc. 45 (4), 302–308. Schenk, T., Richardson, I. M., Krask, M., Ohnimus, S., 2009. Modeling buckling distortion of DP600 overlap joints due to gas metal arc welding and the influence of the mesh density. Comput. Mater. Sci. 46, 977-986. Terasaki, T., Maeda, K., Murakawa, H., Nomoto, T., 1998. Critical conditions of plate buckling generated by welding. Trans. JSME Series A 64(625), 2239–2244. Terasaki, T., Nakatani, M., Ishimura, T., 2000. Study on tendon force generating in welded joint. Q. J. Jpn. Weld. Soc. 18 (3), 479–486. Tchoumi, T., Peyraut, F., Bolot, R., 2016. Influence of the welding speed on the distortion of thin stainless steel plates –Numerical and experimental investigations in the framework of the food industry machines. J. Mater. Process. Technol. 229, 216-229. Ueda. Y., Yamakawa, T., 1971. Analysis of thermal elastic-plastic stress and strain during welding by finite element method. Trans. Jpn. Weld. Soc. 2(2), 186-196. Watanabe, M., Satoh, K., 1957. On the type of distortion in various welded joints –shrinkage distortion in welded joint (report 5)–. J. Jpn. Weld. Soc. 26 (6), 399–405. Watanabe, M., Satoh, K., 1958. Fundamental study on buckling of thin steel plate due to bead-welding. J. Jpn. Weld. Soc. 27 (6), 313–320. White, J. D., 1977. Longitudinal shrinkage of a single pass weld. CUED/C-StRUCT/TR. 57, 587–596. White, J. D., Leggat, R. H., Deight, J. B., 1980. Weld shrinkage prediction. Weld. Met. Fabr. 11, 587–596. Wang, J., Yin, X., Murakawa, H., 2013. Experimental and computational analysis of residual buckling distortion of bead-on-plate welded joint. J. Mater. Process. Technol. 213, 1447-1458. Zain–ul–Abdein, M., Nelias, D., Jullien, J. F., 2009. Prediction of laser beam welding-induced distortions and residual stress by numerical simulation for aeronautic application. J. Mater. Process. Technol. 209, 2907-2917.

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Figures caption listFig. 1

Configuration of the thin steel plate to be welded.

Fig. 2

Procedure for measuring the temperature profiles and the longitudinal bending and angular distortions

caused by welding. Fig. 3

Half-symmetric FE model used in the numerical analysis.

Fig. 4

Material properties used in the numerical analysis.

(a) Thermo-physical properties (b) Mechanical properties (c) Work hardening behavior Fig. 5

Two-dimensional distribution of temperature and vertical displacement distributions obtained by

numerical analysis. (a) Temperature (b) Vertical displacement Fig. 6

Measured and calculated transient temperature profiles and distortion behaviors during welding for a

welding current of 50 A. (a) Temperature profiles (b) Distortion behaviors Fig. 7

Measured and calculated transient temperature profiles and distortion behaviors during welding for a

welding current of100 A. (a) Temperature profiles (b) Distortion behaviors Fig. 8

Measured and calculated transient temperature profiles and distortion behaviors during welding for a

welding current of 150 A. (a) Temperature profiles (b) Distortion behaviors Fig. 9

Definition of geometric imperfection (V-shaped cross section).

Fig. 10

Effects of welding heat input and geometric imperfections on residual welding-induced distortions.

(a) Longitudinal bending distortion (b) Angular distortion Fig. 11

Effect of geometric imperfections on the time evolution of temperature and distortions during

welding.

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(a) Temperature profiles (b) Distortion behaviors Fig. 12

Comparison of the time evolution of thermal stress and plastic strain of the upper and lower sides of

the welded thin steel plate with geometric imperfections. (a) Thermal stress (b) Plastic strain Fig. 13

Temperature–plastic strain relation during welding on the upper and lower sides of the thin steel plates

with and without geometric imperfections.

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Fig. 1

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Fig. 2

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Fig. 3

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(a) Thermo-physical properties

(b) Mechanical properties

(c) Work hardening behavior Fig. 4

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(a) Temperature

(b) Vertical displacement Fig. 5

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(a) Temperature profiles

(b) Distortion behaviors Fig. 6

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(a) Temperature profiles

(b) Distortion behaviors Fig. 7

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(a) Temperature profiles

(b) Distortion behaviors Fig. 8

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Fig. 9

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(a) Longitudinal bending distortion

(b) Angular distortion Fig. 10

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(a) Temperature profiles

(b) Distortion behaviors Fig. 11

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(a) Thermal stress

(b) Plastic strain Fig. 12

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Fig. 13

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Table 1

Chemical composition and mechanical properties of the steel used in the welding experiments. Chemical composition (mass%) C 0.08

Si 0.06

Mn 1.30

P 0.014

Mechanical properties S 0.003

Mo 0

Ti 0.06

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Fe Bal.

Yield

Tensile

Tensile

strength

strength

strength

(MPa)

(MPa)

(MPa)

565

642

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Table 2

Welding heat input conditions of the welding current-based heat source model used for TIG welding. Welding current, I (A)

Heat input per unit welding time, q (J/s)

Gaussian radius, R (mm)

50

415

2.40

100

840

2.70

150

1235

2.95

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