# Role of Surface-Active Element Sulfur on Thermal Behavior, Driving Forces, Fluid Flow and Solute Dilution in Laser Linear Welding of Dissimilar Metals

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}concentration in the shielding gas results in the change of the width and depth of the weld. Lienert et al. [26] observed a significant centerline shift in the molten pool during Gas Tungsten Arc (GTA) welding when two stainless steels with greatly different sulfur contents were welded, and they suggested that sulfur-influenced Marangoni convection was one of the reasons. Based on this, Wei et al. [27] analyzed the offset of maximum molten depth and rotation of the molten pool shape, and they concluded that the spatial gradient of temperature and sulfur caused the centerline shift and the rotation of the molten pool. Bahrami et al. [28] studied sulfur-induced driving forces at the free surface in GTA spot welding of 1018 steel and nickel 200, and they indicated that the driving forces induced by the concentration gradient of sulfur mainly affected Marangoni convection when the molten pool was just formed.

## 2. Numerical Model

- The liquid metal in the molten pool is an incompressible, Newtonian, and laminar flow.
- The laser power distribution is Gaussian.
- The free surface is set as a flat plane. The role of buoyancy is described by the Boussinesq approximation.
- Material properties are temperature-independent.

#### 2.1. Governing Equations

**u**is the velocity, μ is the viscosity, p is the pressure, T is the temperature, k is the thermal conductivity, C

_{P}is the specific heat, and D

_{i}and C

_{i}are the ith component of the diffusion factor and the concentration, respectively.

_{mush}represents the resistance of the mushy zone, which is set to 10

^{7}kg/m

^{3}·s in this study, M is a small number to avoid the division by zero, and f

_{l}is the liquid fraction expressed as:

_{l}and T

_{s}are the liquidus and solidus temperatures, respectively.

_{T}and β

_{C}represent the volumetric expansion coefficients caused by temperature and composition, respectively. T

_{ref}is the ambient temperature, C is the local concentration, and C

_{ref}is the reference concentration. ΔH in Equation (3) represents the latent heat of phase change, which is described in Equation (8):

#### 2.2. Sub-Model of Surface Tension

_{p}is the surface tension of the pure melting metal, A is the negative of TCST, Γ

_{S}is the surface excess at saturation, R is the universal gas constant, K is the adsorption coefficient, k

_{l}is the constant corresponding to the segregation entropy, ΔH

^{0}is the standard heat of adsorption, and α

_{s}is the activity of the surface-active element, which could be approximated by the weight % of sulfur in the molten pool. When the surface-active element is negligible, the value of α

_{s}is 0, and the TCST is a negative constant. The parameters used in the sub-model of surface tension are given in Table 3. In this study, the value of the TCST varies with the spatial distribution of sulfur concentration and the local temperature.

#### 2.3. Boundary Conditions

_{laser}is the laser power, η is the absorptivity of laser energy, r

_{e}is the effective radius of the laser spot, and r is the distance from the laser center. The second and third terms on the right side represent the heat loss by convection and radiation, respectively. T

_{0}is the ambient temperature, h

_{c}and σ

_{b}are the convection heat transfer coefficient and Stefan-Boltzmann constant, respectively, and ε is the emissivity. The welding parameters used in the simulation are listed in Table 4, and the center of the laser beam is located at the contact position of 304SS and Ni.

_{s}is the concentration of sulfur.

_{Ci}is the coefficient of diffusivity and

**u**is the velocity of the mass flux for one certain element.

_{Ci}#### 2.4. Model Verification

## 3. Results and Discussion

#### 3.1. Thermal Behavior

_{max}is the maximum fluid flow velocity, L is the characteristic length, which is equal to the molten pool depth in this study, and α is the thermal diffusivity, which is defined as k/(C

_{P}·ρ). At 5 ms, Pe

_{T}on the 304SS side is 20 and 4 on the Ni side. This indicates that the dominant mechanism of heat transfer on the 304SS side is already thermal convection during the initial stage of molten pool formation, while the contribution of heat conduction on the Ni side cannot be neglected. As plotted in Figure 2B, the molten pool dimensions increase rapidly before 20 ms, and the aspect ratio, which is defined by the ratio of the maximum width to the maximum depth, amounts to 0.24. Subsequently, the growth rates of pool depth and pool width slow down, and the aspect ratio is stabilized around 0.3 after 45 ms. At this time, the molten pool has been fully developed, and the Pe

_{T}number is 400 for the 304SS side and 60 for the Ni side, which indicates that thermal convection determines heat transfer in the molten pool. The simulated and experimental cross-sectional profiles [17] are compared in Figure 2C, which shows good agreement in terms of size and morphology.

#### 3.2. Dilution of Sulfur and Driving Forces

^{2}, and the magnitude of the temperature-gradient term is up to 1800 N/m

^{2}after the molten pool reaches a quasi-steady stage. On the Ni side, the surface shear stress is mainly influenced by the concentration gradient in the early stage due to the difference in concentration between the middle of the molten pool where sulfur is diluted and the edge where the Ni is just melted, with a temperature-gradient term of about 500 N/m

^{2}and a concentration-gradient term of about 2000 N/m

^{2}, as illustrated in Figure 6A. After 50 ms, due to a mixing dilution of the solute, the surface shear stress is determined by the temperature gradient, except for the front, where a large concentration difference between the base metal and the molten pool exists. The isotherm shown in Figure 3D on the Ni side is sparser than that of the 304SS side in the quasi-steady state. This means that the temperature gradient is smaller, so the temperature-gradient term and, thus, the surface shear stress inside the molten pool are smaller.

^{2}, which is three times the peak of the temperature-gradient term, due to the significant difference in sulfur concentration between Ni and 304SS. The surface shear stress on the 304SS side, where the sulfur content in the molten pool is close to that of the base metal, is dominated by the temperature-gradient term. With the continuous dilution of sulfur, the main driving force inside the molten pool becomes the temperature gradient. When the molten pool is solidified, the concentration-gradient term and the temperature-gradient term inside the molten pool are in the same order of magnitude. Under their joint action, the inward convection is deflected toward the centerline of the molten pool, as plotted in Figure 3D.

#### 3.3. Fluid Flow

#### 3.4. Mass Transfer

## 4. Conclusions

- The molten pool is fully developed after 45 ms under the influence of sulfur, and the aspect ratio is stabilized at about 0.3. The maximum flow velocity is 1.7 m/s, and the Peclet number reaches 400 on the 304SS side and 60 on the Ni side, indicating the predominance of convective heat transfer.
- After the molten pool reaches a quasi-steady state, sulfur is uniformly mixed in the front of the molten pool, and eventually there is a gradient distribution at the rear. The temperature-gradient term of surface shear stress plays a major role in welding direction. In the transverse direction, the temperature-gradient term of the surface shear stress is in the same order of magnitude as the concentration-gradient term, and they jointly determine the direction of inward convection. The spatial distribution of the surface-active element and temperature leads to differences in the TCST distribution. For the Ni side, the sign of the TCST shifts at 2100 K, and for the 304SS side, the sulfur element in the base metal is much higher than Ni, making the sign of the TCST shift at 2200 K. These differences further affect the fluid flow.
- When considering the role of elemental sulfur, the velocity of inward convection is significantly higher at the rear than the other positions of the molten pool. Inward convection collisions with outward convection inside the molten pool, along with the presence of complex vortices, are conducive to solute dilution. From the front part of the molten pool to the rear, the mixing of the solute gradually becomes homogeneous, and the rear of the molten pool is an important area for sufficient dilution of solute elements, e.g., Ni, Fe, and Cr.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Sun, Z.; Ion, J.C. Laser-welding of dissimilar metal combinations. J. Mater. Sci.
**1995**, 30, 4205–4214. [Google Scholar] [CrossRef] - Oliveira, J.P.; Ponder, K.; Brizes, E.; Abke, T.; Edwards, P.; Ramirez, A.J. Combining resistance spot welding and friction element welding for dissimilar joining of aluminum to high strength steels. J. Mater. Process. Technol.
**2019**, 273, 116192. [Google Scholar] [CrossRef] - Hejripour, F.; Helenbrook, B.T.; Valentine, D.T.; Aidun, D.K. Mass transport and solidification phenomenon in dissimilar metals arc welding. Int. J. Heat Mass Transf.
**2019**, 144, 118703. [Google Scholar] [CrossRef] - Bahrami, A.; Helenbrook, B.T.; Valentine, D.T.; Aidun, D.K. Fluid flow and mixing in linear GTA welding of dissimilar ferrous alloys. Int. J. Heat Mass Transf.
**2016**, 93, 729–741. [Google Scholar] [CrossRef] - Zang, C.W.; Liu, J.G.; Tan, C.W.; Zhang, K.; Song, X.; Chen, B.; Li, L.; Feng, J. Laser conduction welding characteristics of dissimilar metals Mg/Ti with Al interlayer. J. Manuf. Process.
**2018**, 32, 595–605. [Google Scholar] [CrossRef] - Oliveira, J.P.; Zeng, Z.; Andrei, C.; Fernandes, F.B.; Miranda, R.M.; Ramirez, A.J.; Omoti, T.; Zhou, N. Dissimilar laser welding of superelastic NiTi and CuAlMn shape memory alloys. Mater. Des.
**2017**, 128, 166–175. [Google Scholar] [CrossRef] - Li, Z.; Yu, G.; He, X.; Tian, C.; Li, S.; Li, H. Probing thermocapillary convection and multisolute dilution in laser welding of dissimilar miscible metals. Int. J. Therm. Sci.
**2022**, 172, 107242. [Google Scholar] [CrossRef] - Hu, Y.; He, X.; Yu, G.; Ge, Z.; Zheng, C.; Ning, W. Heat and mass transfer in laser dissimilar welding of stainless steel and nickel. Appl. Surf. Sci.
**2012**, 258, 5914–5922. [Google Scholar] [CrossRef] [Green Version] - Cao, X.; Jahazi, M.; Immarigeon, J.P.; Wallace, W. A review of laser welding techniques for magnesium alloys. J. Mater. Process. Technol.
**2006**, 171, 188–204. [Google Scholar] [CrossRef] - Mai, T.A.; Spowage, A.C. Characterisation of dissimilar joints in laser welding of steel-kovar, copper-steel and copper-aluminium. Mater. Sci. Eng. A
**2004**, 374, 224–233. [Google Scholar] [CrossRef] - Mukherjee, S.; Chakraborty, S.; Galun, R.; Estrin, Y.; Manna, I. Transport phenomena in conduction mode laser beam welding of Fe-Al dissimilar couple with Ta diffusion barrier. Int. J. Heat Mass Transf.
**2010**, 53, 5274–5282. [Google Scholar] [CrossRef] - Schubert, E.; Klassen, M.; Zerner, I.; Walz, C.; Sepold, G. Light-weight structures produced by laser beam joining for future applications in automobile and aerospace industry. J. Mater. Process. Technol.
**2001**, 115, 2–8. [Google Scholar] [CrossRef] - Meijer, J. Laser beam machining (LBM), state of the art and new opportunities. J. Mater. Process. Technol.
**2004**, 149, 2–17. [Google Scholar] [CrossRef] - He, X.; Fuerschbach, P.W.; DebRoy, T. Heat transfer and fluid flow during laser spot welding of 304 stainless steel. J. Phys. D Appl. Phys.
**2003**, 36, 1388–1398. [Google Scholar] [CrossRef] - Wang, R.; Lei, Y.; Shi, Y. Numerical simulation of transient temperature field during laser keyhole welding of 304 stainless steel sheet. Opt. Laser Technol.
**2011**, 43, 870–873. [Google Scholar] [CrossRef] - Saldi, Z.S.; Kidess, A.; Kenjeres, S.; Zhao, C.; Richardson, I.M.; Kleijn, C.R. Effect of enhanced heat and mass transport and flow reversal during cool down on weld pool shapes in laser spot welding of steel. Int. J. Heat Mass Transf.
**2013**, 66, 879–888. [Google Scholar] [CrossRef] - Li, Z.; Yu, G.; He, X.; Li, S.; Li, Z. Fluid flow and solute dilution in laser linear butt joining of 304SS and Ni. Int. J. Heat Mass Transf.
**2020**, 161, 120233. [Google Scholar] [CrossRef] - Zhang, R.; Tang, X.; Xu, L.; Lu, F.; Cui, H. Study of molten pool dynamics and porosity formation mechanism in full penetration fiber laser welding of Al-alloy. Int. J. Heat Mass Transf.
**2020**, 148, 119089. [Google Scholar] [CrossRef] - Duggirala, A.; Kalvettukaran, P.; Acherjee, B.; Mitra, S. Numerical simulation of the temperature field, weld profile, and weld pool dynamics in laser welding of aluminium alloy. Optik
**2021**, 247, 167990. [Google Scholar] [CrossRef] - Hu, Y.; He, X.; Yu, G.; Zhao, S. Capillary convection in pulsed-butt welding of miscible dissimilar couple. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**2017**, 231, 2429–2440. [Google Scholar] [CrossRef] - Shen, H.; Pan, Y.; Zhou, J.; Yao, Z. Forming Mechanism of Bump Shape in Pulsed Laser Melting of Stainless Steel. J. Heat Transf.
**2017**, 139, 062301. [Google Scholar] [CrossRef] - Gan, Z.; Yu, G.; He, X.; Li, S. Surface-active element transport and its effect on liquid metal flow in laser-assisted additive manufacturing. Int. Commun. Heat Mass Transf.
**2017**, 86, 206–214. [Google Scholar] [CrossRef] [Green Version] - Sahoo, P.; Debroy, T.; McNallan, M.J. Surface-tension of binary metal—Surface-active solute systems under conditions relevant to welding metallurgy. Metall. Trans. B
**1988**, 19, 483–491. [Google Scholar] [CrossRef] - Zhao, C.X.; Kwakernaak, C.; Pan, Y.; Richardson, I.M.; Saldi, Z.; Kenjeres, S.; Kleijn, C.R. The effect of oxygen on transitional Marangoni flow in laser spot welding. Acta Mater.
**2010**, 58, 6345–6357. [Google Scholar] [CrossRef] - Ribic, B.; Tsukamoto, S.; Rai, R.; DebRoy, T. Role of surface-active elements during keyhole-mode laser welding. J. Phys. D Appl. Phys.
**2011**, 44, 485203. [Google Scholar] [CrossRef] - Lienert, T.J.; Burgardt, P.; Harada, K.L.; Forsyth, R.T.; DebRoy, T. Weld bead center line shift during laser welding of austenitic stainless steels with different sulfur content. Scr. Mater.
**2014**, 71, 37–40. [Google Scholar] [CrossRef] - Wei, H.L.; Pal, S.; Manvatkar, V.; Lienert, T.J.; DebRoy, T. Asymmetry in steel welds with dissimilar amounts of sulfur. Scr. Mater.
**2015**, 108, 88–91. [Google Scholar] [CrossRef] - Bahrami, A.; Valentine, D.T.; Helenbrook, B.T.; Aidun, D. Study of mass transport in autogenous GTA welding of dissimilar metals. Int. J. Heat Mass Transf.
**2015**, 85, 41–53. [Google Scholar] [CrossRef]

**Figure 2.**Evolution of the temperature field, the velocity field, and the dimensions and morphology of the molten pool. (

**A**) Evolution of the temperature field and velocity field; (

**B**) Dimensions of the molten pool; (

**C**) Comparison between the simulated and experimental [17] cross-sectional profiles. Parameters: laser radius of 0.57 mm, welding speed of 20 mm/s, and laser power of 800 W.

**Figure 3.**Dilution of sulfur on the free surface at different times. (

**A**) 10 ms; (

**B**) 20 ms; (

**C**) 30 ms; (

**D**) 50 ms.

**Figure 5.**Surface shear stress in the longitudinal section with y = −0.2 mm on the 304SS side at different times. (

**A**) 10 ms; (

**B**) 20 ms; (

**C**) 30 ms; (

**D**) 50 ms.

**Figure 6.**Surface shear stress in the longitudinal section with y = 0.2 mm on the Ni side at different times. (

**A**) 10 ms; (

**B**) 20 ms; (

**C**) 30 ms; (

**D**) 50 ms.

**Figure 7.**Surface shear stress with x = 1.5 mm at different times. (

**A**) 10 ms; (

**B**) 20 ms; (

**C**) 30 ms; (

**D**) 50 ms.

**Figure 9.**Fluid flow at the yz cross section. (

**A**) 3D view; (

**B**) x = 2.3 mm; (

**C**) x = 2 mm; (

**D**) x = 1.6 mm.

**Figure 10.**Fluid flow in the xz cross section. (

**A**) 3D view; (

**B**) y = −0.3 mm; (

**C**) y = 0 mm; (

**D**) y = 0.25 mm.

**Figure 11.**Fluid flow in the xy cross section. (

**A**) 3D view; (

**B**) z = 1 mm; (

**C**) z = 0.9 mm; (

**D**) z = 0.8 mm.

**Figure 12.**Ni concentration on yz sections. (

**A**) 3D view; (

**B**) x = 2.3 mm; (

**C**) x = 2 mm; (

**D**) x = 1.6 mm.

**Figure 13.**Ni concentration on xz sections. (

**A**) 3D view; (

**B**) y = −0.3 mm; (

**C**) y = 0 mm; (

**D**) y = 0.25 mm.

**Figure 14.**Ni concentration on xy sections. (

**A**) 3D view; (

**B**) z = 1 mm; (

**C**) z = 0.9 mm; (

**D**) z = 0.8 mm.

**Figure 15.**Comparison between simulated and experimentally measured [7] concentration distributions. Parameters: laser radius of 0.57 mm, welding speed of 30 mm/s, and laser power of 800 W.

Cr | Ni | Mn | Si | C | Fe |
---|---|---|---|---|---|

20 | 10 | 1.32 | 0.83 | 0.08 | Bal. |

**Table 2.**Thermophysical properties of 304SS and Ni [17].

Parameter | 304SS | Ni |
---|---|---|

Solidus temperature (K) | 1672 | 1730 |

Density of solid metal (kg/m^{3}) | 7450 | 8900 |

Thermal conductivity of solid (W/m·K) | 19.2 | 60.7 |

Specific heat of solid (J/kg·K) | 711.28 | 515 |

Liquidus temperature (K) | 1727 | 1735 |

Density of liquid metal (kg/m^{3}) | 6910 | 8880 |

Thermal conductivity of liquid (W/m·K) | 50 | 150 |

Specific heat of liquid (J/kg·K) | 836.8 | 595 |

Heat of fusion (kJ/kg) | 272 | 290 |

Dynamic viscosity (kg/m·s) | 6.70 $\times $ 10^{−3} | 3.68 $\times $ 10^{−3} |

Liquid volume thermal expansion (K^{−1}) | 1.96 $\times $ 10^{−5} | 4.50 $\times $ 10^{−5} |

Liquid volume concentration expansion (K^{−1}) | 0.078 | 0.078 |

Effective mass diffusivity (m^{2}/s) | 7 $\times $ 10^{−7} | 7 $\times $ 10^{−7} |

Parameter | Fe-S | Ni-S |
---|---|---|

γ_{p} (N/m) | 1.943 | 1.845 |

A (N/m·K) | 4.3 $\times $ ${10}^{-4}$ | 4.3 $\times $ ${10}^{-4}$ |

Γ_{S} (mol/m^{2}) | 1.3 $\times $ ${10}^{-5}$ | 1.5 $\times $ ${10}^{-5}$ |

k_{l} | 0.00318 | 0.00318 |

ΔH^{0} (J/mol) | −1.88 $\times $ ${10}^{5}$ | −1.47 $\times $ ${10}^{5}$ |

Parameter | Value |
---|---|

Welding speed (mm/s) | 20, 30 |

Laser power (W) | 800 |

Laser spot (mm) | 0.57 |

Ambient temperature (K) | 300 |

Laser absorption efficiency | 0.26 |

Stefan-Boltzmann constant (W/${\mathrm{m}}^{2}{\mathrm{K}}^{4}$) | 5.67 $\times $ ${10}^{-8}$ |

Emissivity | 0.2 |

Convective heat transfer coefficient at top surface (W/${\mathrm{m}}^{2}\mathrm{K}$) | 100 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shu, Z.; Yu, G.; Dong, B.; He, X.; Li, Z.; Li, S.
Role of Surface-Active Element Sulfur on Thermal Behavior, Driving Forces, Fluid Flow and Solute Dilution in Laser Linear Welding of Dissimilar Metals. *Materials* **2023**, *16*, 2609.
https://doi.org/10.3390/ma16072609

**AMA Style**

Shu Z, Yu G, Dong B, He X, Li Z, Li S.
Role of Surface-Active Element Sulfur on Thermal Behavior, Driving Forces, Fluid Flow and Solute Dilution in Laser Linear Welding of Dissimilar Metals. *Materials*. 2023; 16(7):2609.
https://doi.org/10.3390/ma16072609

**Chicago/Turabian Style**

Shu, Zhuang, Gang Yu, Binxin Dong, Xiuli He, Zhiyong Li, and Shaoxia Li.
2023. "Role of Surface-Active Element Sulfur on Thermal Behavior, Driving Forces, Fluid Flow and Solute Dilution in Laser Linear Welding of Dissimilar Metals" *Materials* 16, no. 7: 2609.
https://doi.org/10.3390/ma16072609