# The Influence of Welding Heat Source Inclination on the Melted Zone Shape, Deformations and Stress State of Laser Welded T-Joints

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Experiment

_{2}laser. A welded joint and its cross-section are presented in Figure 1 and Figure 2, respectively.

## 3. Mathematical Model

^{3}), q

_{v}is volumetric heat source (W/m

^{3}), q

_{s}is a surface heat flux (W/m

^{2}).

_{o}, taking into account convection and radiation:

_{0}is an ambient temperature, α

_{k}is convective coefficient (W/m

^{2}K), ε is radiation, σ is the Stefan-Boltzman constant.

_{L}= 260 × 10

^{3}(J/kg) is assumed in numerical simulations in the solidus-liquidus temperatures range (T

_{S}= 1673 K; T

_{L}= 1728 K).

_{0}is a laser beam radius (m), η is efficiency of welding processes, d is material penetration depth (m), r is actual radius (m), where $r=\sqrt{{x}^{2}+{y}^{2}}$, r

_{t}and r

_{b}is beam radius, respectively for z = 0 and z = h

_{1}, h

_{1}is a height of heat source penetration and z is actual depth of penetration (m) [32].

_{1}, y

_{1}, z

_{1}):

**σ**=

**σ**(σ

_{ij}) is Cauchy stress tensor, x

_{α}is location of considered point,

**D**=

**D**(T) is a stiffness matrix. The total strain rate is decomposed by its constituents: elastic strain ε

^{e}, plastic strain ε

^{p}and thermal strain ε

^{Th}.

## 4. Numerical Simulation

^{2}. The thermomechanical properties of the welded T-joint presented in Figure 8 are assumed in numerical simulations for austenitic steel X5CrNi18-10 [32]. Chemical composition: 0.06 C, 17–19 Cr, 11–13 Ni, N < 0.11 [%].

_{L}≈ 1455 °C) is marked with a solid line. The numerically estimated shape of the weld is marked on the macroscopic picture of the joint. The comparison of FZ geometry with macroscopic view shows that a good representation of the weld shape is obtained. Good compliance of the calculation results with the experiment is obtained for the following source parameters: source penetration depth d = 2.8 mm, beam radius r

_{t}= 0.2 mm (for z = 0), beam radius r

_{b}= 0.08 mm (for z = h

_{1}), h

_{1}= 4 mm.

_{y}for the source inclinations α = 20°, 30° and 40°, respectively. Figure 21a, Figure 22a and Figure 23a show the results for lines (lines 1, 2, 3) perpendicular to the weld line of the joint. Whereas Figure 21b, Figure 22b and Figure 23b describe the results for lines parallel to the welding lines (measuring lines 4–9).

_{y}occur in the direction perpendicular to the welding line. The differences in the obtained results are slight. Obtained simulation results are compared in Figure 24 in order to visualize the differences between displacement U

_{y}.

_{y}displacements. For the analyzed model difference between slope α = 20° and 30° is about 0.03 mm.

## 5. Conclusions

- Changing the inclination of the heat source changes the shape and size of the melted zone. As the angle of inclination increases, the depth of fusion into the base of T-joint increases, and the width of the fusion zone decreases at the same time. A further increase in the angle of inclination of the source may lead to a reduction of the quality of the joint (see Figure 16).
- Changing the inclination of the heat source changes the deformation of the joint. Increasing the angle of inclination reduces the amount of deformation (Figure 24). For the analyzed joint, the differences are at the level of 0.03 mm.
- Changing the inclination of the heat source has no significant effect on the stress state (see Figure 18, Figure 19 and Figure 20). In general, increasing the angle of inclination of the heat source slightly increases residual stress. The predicted magnitudes and distributions of are determined only by numerical simulations, according to the model adopted in the Abaqus FEA software. Detailed analysis of the stress state in single-side welded T-joint requires experimental verification. Stress measurement in T-joints is complex, requires special equipment and will be the subject of further research.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Huang, H.; Wang, J.; Li, L.; Ma, N. Prediction of laser welding induced deformation in thin sheets by effcient numerical modeling. J. Mater. Process. Technol.
**2016**, 227, 117–128. [Google Scholar] [CrossRef] - Li, Y.; Wang, K.; Jin, Y.; Xu, M.; Lu, H. Prediction of welding deformation in stiffened structure by intro ducing thermo-mechanical interface element. J. Mater. Process. Technol.
**2015**, 216, 440–446. [Google Scholar] - Torkamany, M.J.; Sabbaghzadeh, J.; Hamedi, M.J. Effect of laser welding mode on the microstructure and mechanical performance of dissimilar laser spot welds between low carbon and austenitic stainless steels. Mater. Des.
**2012**, 34, 666–672. [Google Scholar] [CrossRef] - Danielewski, H.; Skrzypczyk, A. Steel Sheets Laser Lap Joint Welding—Process Analysis. Materials
**2020**, 13, 2258. [Google Scholar] [CrossRef] - Khan, M.M.A.; Romoli, L.; Dini, G. Laser beam welding of dissimilar ferritic/martensitic stainless steels in a butt joint configuration. Opt. Laser Technol.
**2013**, 49, 125–136. [Google Scholar] [CrossRef] - Francis, J.A.; Holtum, N.; Olschok, S.; Roy, M.J.; Vasileiou, A.N.; Jakobs, S.; Reisgen, U.; Smith, M.C. Vacuum laser welding of SA508 steel. J. Mater. Process. Technol.
**2019**, 274, 116269. [Google Scholar] [CrossRef] - Danielewski, H.; Skrzypczyk, A.; Hebda, M.; Tofil, S.; Witkowski, G.; Długosz, P.; Nigrovic, R. Numerical and metallurgical analysis of laser welded, sealed lap joints of S355J2 and 316L steels under different configurations. Materials
**2020**, 13, 5819. [Google Scholar] [CrossRef] [PubMed] - Zhang, C.; Li, S.; Hu, L.; Deng, D. Effects of pass arrangement on angular distortion, residual stresses and lamellar tearing tendency in thick-plate T-joints of low alloy steel. J. Mater. Process. Technol.
**2019**, 274, 116293. [Google Scholar] [CrossRef] - Zhang, Y.; Tao, W.; Chen, Y.; Nan, T. Effects of heat treatment on microstructure and mechanical properties of double-sided laser-welded AA2060/AA2099 T-Joint. J. Mater. Process. Technol.
**2020**, 285, 116777. [Google Scholar] [CrossRef] - Hammada, A.; Churiaqueb, C.; Sanchez-Amayab, J.; Abdel-Nasser, Y. Experimental and numerical investigation of hybrid laser arc welding process and the influence of welding sequence on the manufacture of stiffened flat panels. J. Manu Process.
**2021**, 61, 527–538. [Google Scholar] [CrossRef] - Shanmugam, N.S.; Buvanashekaran, G.; Sankaranarayanasamy, K.; Kumar, S.R. A transient finite element simulation of the temperature and bead profiles of T-joint laser welds. Mater. Design.
**2010**, 31, 4528–4542. [Google Scholar] [CrossRef] - Unt, A.; Poutiainen, I.; Salminen, A. Effects of sealing run welding with defocused laser beam on the quality of T-joint fillet weld. Phys. Procedia
**2014**, 56, 497–506. [Google Scholar] [CrossRef] [Green Version] - Kujala, P.; Klanac, A. Steel Sandwich Panels in Marine Applications. BrodoGradnja
**2005**, 56, 305–314. [Google Scholar] - Kozak, J. All steel sandwich panels—New possibilities introduced by laser welding techniques. Weld. Technol. Rev.
**2007**, 10, 53–59. [Google Scholar] - Piekarska, W.; Kubiak, M.; Saternus, Z. Numerical Simulation of Deformations in T-Joint Welded by the Laser Beam. Arch. Metall. Mater.
**2013**, 58, 1391–1396. [Google Scholar] [CrossRef] [Green Version] - Macckwood, A.P.; Cafer, R.C. Thermal modeling of laser of laser welding and related processes: A literature review. Opt. Laser Technol.
**2009**, 37, 99–115. [Google Scholar] [CrossRef] - Banik, S.; Kumar, S.; Kumar Singh, P.; Bhattacharya, S.; Mahapatra, M.M. Distortion and residual stresses in thick plate weld joint of austenitic stainless steel: Experiments and analysis. J. Mater. Process. Technol.
**2021**, 289, 116944. [Google Scholar] [CrossRef] - Zhang, Y.; Wang, Y. The infuence of welding mechanical boundary condition on the residual stress and distortion of a stiffened-panel. Mar. Struct.
**2019**, 65, 259–270. [Google Scholar] [CrossRef] - Geng, S.; Jiang, P.; Shao, X.; Guo, L.; Gao, X. Heat transfer and fluid flow and their effects on the solidification microstructure in full-penetration laser welding of aluminum sheet. J. Mater. Sci. Technol.
**2020**, 46, 50–63. [Google Scholar] [CrossRef] - Svenungssona, J.; Choqueta, I.; Kaplan, A.F.H. Laser welding process—a review of keyhole welding modeling. Phys. Procedia
**2015**, 78, 182–191. [Google Scholar] [CrossRef] [Green Version] - De, A.; Maiti, S.K.; Walsh, C.A.; Bhadesia, K.D.H. Finite element simulation of laser spot welding. Sci. Technol. Weld. Join.
**2003**, 8, 377–384. [Google Scholar] [CrossRef] - Oliveira, A.C.; Siqueira, R.H.M.; Riva, R.; Lima, M.S.F. One-sided laser beam welding of autogenous T-joints for 6013-T4 aluminium alloy. Mater. Des.
**2015**, 65, 726–736. [Google Scholar] [CrossRef] - Deng, D.; Murakawa, H. Prediction of welding distortion and residual stress in a thin plate butt-welded joint. Comput. Mater. Sci.
**2008**, 43, 353–365. [Google Scholar] [CrossRef] - Deng, D.; Liang, W.; Murakawa, H. Determination of welding deformation in fillet-welded joint by means of numerical simulation and comparison with experimental measurements, J. Mater. Process. Technol.
**2007**, 183, 219–225. [Google Scholar] [CrossRef] - Dowden, J.M. The Mathematics of Thermal Modeling; Taylor & Francis Group: New York, NY, USA, 2001. [Google Scholar]
- Moumni, Z.; Roger, F.; Thuy Trinh, N. Theoretical and numerical modeling of the thermomechanical and metallurgical behavior of steel. Int. J. Plast.
**2011**, 27, 414–439. [Google Scholar] [CrossRef] - Rong, Y.; Huang, Y.; Wang, L. Evolution mechanism of transient strain and residual stress distribution in al 6061 laser welding. Crystals
**2021**, 11, 205. [Google Scholar] [CrossRef] - Rong, Y.; Xu, J.; Lei, T.; Huang, Y.; Shao, X.; Wang, C. Magnetism aided mitigation of deformation and residual stress in dissimilar joint 316L with EH36. J. Mater. Process. Technol.
**2018**, 259, 23–32. [Google Scholar] [CrossRef] - Rong, Y.; Lei, T.; Xu, J.; Huang, Y.; Wang, C. Residual stress modelling in laser welding marine steel EH36 considering a thermodynamics-based solid phase transformation. Int. J. Mech. Sci.
**2018**, 146–147, 180–190. [Google Scholar] [CrossRef] - Dassault System. Abaqus Theory Manual; Version 6.7; SIMULIA: Johnston, RI, USA, 2007. [Google Scholar]
- Tsirkas, S.A.; Papanikos, P.; Kermanidis, T. Numerical simulation of the laser welding process in butt-joint specimens. J. Mater. Process. Technol.
**2003**, 134, 59–69. [Google Scholar] [CrossRef] - Piekarska, W.; Kubiak, M.; Saternus, Z.; Stano, D.T. Numerical prediction of deformations in laser welded sheets made of X5CrNi18-10 steel. Arch. Metall. Mater.
**2015**, 60, 1965–1972. [Google Scholar] [CrossRef] - Ahn, J.; Davies, C.M.; He, E.; Wimpory, R.C.; Chen, L.; Dear, J.P. Prediction and measurement of residual stresses and distortions in fibre laser welded Ti-6Al-4V considering phase transformation. Mater. Des.
**2017**, 117, 441–457. [Google Scholar] [CrossRef] - Guoxiang, X.; Chuansong, W.; Xuezhou, M.; Xuyou, W. Numerical analysis of welding residual stress and distortion in laser+GMAW hybrid welding of aluminum alloy T-joint. Acta Metall. Sin.
**2013**, 26, 352–360. [Google Scholar] - Zienkiewicz, O.C.; Taylor, R.L. The Finite Element Method, 5th ed.; Butterworth-Heinemann: Oxford, UK, 2000. [Google Scholar]
- Rohde, J.; Jeppsson, A. Literature review of heat treatment simulations with respect to phase transformation, residual stresses and distortion. Scand. J. Metall.
**2000**, 29, 47–62. [Google Scholar] [CrossRef]

**Figure 8.**Thermomechanical properties assumed in calculations [32].

**Figure 10.**Temperature distribution in welded joint (

**a**) t = 3 s, (

**b**) t = 5 s (inclination angle α = 20°).

**Figure 12.**Residual temporary reduced stress (

**a**) and reduced residual stress (

**b**) of laser welded joint.

**Figure 16.**Comparison of the simulation results of thermal phenomena for different slopes of the heating source.

**Figure 18.**Reduced residual stress σ for slope α = 20°. (

**a**) transverse direction to the welding line (

**b**) along the welding line.

**Figure 19.**Reduced residual stress σ for slope α = 30°. (

**a**) transverse direction to the welding line (

**b**) along the welding line.

**Figure 20.**Reduced residual stress σ for slope α = 40°. (

**a**) transverse direction to the welding line (

**b**) along the welding line.

**Figure 21.**Numerically estimated displacement U

_{y}in laser welded T-joint for slope α = 20°. (

**a**) transverse direction to the welding line (

**b**) along the welding line.

**Figure 22.**Numerically estimated displacement U

_{y}in laser welded T-joint for slope α = 30°. (

**a**) transverse direction to the welding line (

**b**) along the welding line.

**Figure 23.**Numerically estimated displacement U

_{y}in laser welded T-joint for slope α = 40°. (

**a**) transverse direction to the welding line (

**b**) along the welding line.

**Figure 24.**Comparison of numerically predicted displacement U

_{y}for three different slopes α = 20°, 30° and 40°.

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**MDPI and ACS Style**

Saternus, Z.; Piekarska, W.; Kubiak, M.; Domański, T.
The Influence of Welding Heat Source Inclination on the Melted Zone Shape, Deformations and Stress State of Laser Welded T-Joints. *Materials* **2021**, *14*, 5303.
https://doi.org/10.3390/ma14185303

**AMA Style**

Saternus Z, Piekarska W, Kubiak M, Domański T.
The Influence of Welding Heat Source Inclination on the Melted Zone Shape, Deformations and Stress State of Laser Welded T-Joints. *Materials*. 2021; 14(18):5303.
https://doi.org/10.3390/ma14185303

**Chicago/Turabian Style**

Saternus, Zbigniew, Wiesława Piekarska, Marcin Kubiak, and Tomasz Domański.
2021. "The Influence of Welding Heat Source Inclination on the Melted Zone Shape, Deformations and Stress State of Laser Welded T-Joints" *Materials* 14, no. 18: 5303.
https://doi.org/10.3390/ma14185303