# Numerical Study of the Cold Metal Transfer (CMT) Welding of Thin Austenitic Steel Plates with an Equivalent Heat Source Approach

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{w}in the range of 600–720 mm/min ensures low porosity and minimizes the product distortion. The authors also suggested that the optimization of heat input Q between 70 and 110 J/mm ensures adequate joint penetration while minimizing deformations.

## 2. Experimental Conditions

_{0}and TC

_{1}) were positioned at the center of the sheet, with a 20 mm gap with regard to the welding line, as illustrated in Figure 1. This distance ensured that the thermocouples were not exposed to burning during welding, a situation typically encountered in CMT welding, where the width of the weld seam is more substantial compared to other processes such as TIG (tungsten inert gas) welding.

_{w}(mm/min) to provide $Es$ (kJ/mm).

_{eff}and U

_{eff}), as demonstrated in Figure 3.

_{1}and e

_{2}are the sheet thicknesses.

## 3. Numerical Model

#### 3.1. FEM Model

^{−2}·°C

^{−1}were tested. The choice of welding on a copper lath was made in view of the very-low thickness of the sheets to be welded. It is essential to avoid any risk that the weld pool collapses when assembling this type of sheet. Copper was also chosen because it cools the weld pool very quickly, thus avoiding oxidation problems on the reverse side of the weld seam.

_{t}, and yield stress σ

_{e}) on temperature. The plastic strain ε

_{pl}was determined from the literature data [24] obtained from experimental nominal stress-nominal strain curves, see Figure 7.

_{t}, and σ

_{e}. The strain-hardening parameter µ represents the ratio between the E

_{t}and the E.

^{−1});

^{−1});

#### 3.2. Equivalent Heat Source Approach

_{w}in the direction of the seam axis. The cross-section was made up of two disc-segments separated by an intermediate trapezoid; therefore, it was a prismatic type source. The elements were progressively activated during calculations, and the source moved linearly in time; an example is shown in Figure 8. Note that L

_{w}represents the optimum value for element length, for which calculation results close to reality have been obtained.

## 4. Results and Discussions

_{0}and TC

_{1}thermocouples on the assembly shown in Figure 1, i.e., thermocouples placed at 20 mm from the weld seam. The maximal temperatures recorded do not exceed 260 °C for the 1 mm/1 mm configuration and 340 °C for the 1.2 mm/1 mm configuration due to the increase in the conductive thermal resistance between the TC measurement point and the copper lath. Temperatures then dropped progressively to ambient temperature.

^{2}) in comparison with the latter one (17 mm

^{2}).

^{−2}·°C

^{−1}provides a smaller relative difference compared to other values of the heat exchange coefficient (this difference is lower than 3%).

^{−2}·°C

^{−1}, provide a satisfactory comparison for h = 30 W·m

^{−2}·°C

^{−1}, and higher differences for h = 10 and 20 W·m

^{−2}·°C

^{−1}.

^{−2}·°C

^{−1}). Again, the comparison yields to satisfactory conclusions for h = 30 W·m

^{−2}·°C

^{−1}and higher differences for the two other values of h.

^{−2}·°C

^{−1}and greater than this percentage for the other values of h. This can be explained by the loss of contact between the copper lath and the sheet during welding due to induced deformation.

^{−2}·°C

^{−1}. This coefficient is justified by the fact that CMT was performed on metal sheets in direct contact with a copper lath, and also by the fact that it also includes radiative losses.

_{0}along the sheet width direction (X), see Figure 12.

_{0}) and simulations for the vertical displacements (V) along the width (line L

_{0}). The measurements and calculations show similar concave curvatures.

## 5. Conclusions

- Determining angular distortion within the welded structure.
- Analyzing displacement fields of the welded plates.
- Studying the transient evolution of temperature in proximity to the welding zone.
- Determining the maximum temperatures reached on a specific sheet during the welding process.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${E}_{s}$ | Linear welding energy (kJ/mm) |

U | Voltage (V) |

I | Current (A) |

${V}_{w}$ | Welding velocity (mm/min) |

P | Average power (kW) |

t_{arc} | Arc-on time (s) |

L_{w} | Weld length (mm) |

E_{tot} | Cumulative energy (kJ) |

Q | Heat input (kJ/mm) |

η | Process thermal efficiency coefficient |

E | Young’s modulus (GPa) |

E_{t} | Tangent modulus (GPa) |

σ_{e} | Yield stress (MPa) |

µ | Strain hardening |

h | Heat exchange coefficient (W·m^{−2}·°C^{−1}) |

ε_{pl} | Plastic deformation |

ε_{th} | Thermal strain |

T | Current temperature (°C) |

α_{T} | Thermal expansion coefficient (°C^{−1}) |

$\overline{{\alpha}_{T}}$ | Average coefficient of thermal expansion at a current temperature (°C^{−1}) |

$\overline{{\alpha}_{init}}$ | Average coefficient of thermal expansion at an initial temperature (°C^{−1}) |

${T}_{init}$ | Initial temperature (°C) |

${T}_{ref}$ | Metal reference temperature (°C) |

X, Y, Z | Subscripts (Cartesian coordinates) |

## References

- Fronius International. Available online: http://www.fronius.com/en (accessed on 27 July 2023).
- Wesling, V.; Schram, A.; Kessler, M. Low heat joining—Manufacturing and fatigue strength of brazed, locally hardened structures. Adv. Mater. Res.
**2010**, 137, 347–374. [Google Scholar] [CrossRef] - Furukawa, K. New CMT arc welding process—Welding of steel to aluminium dissimilar metals and welding of super-thin aluminium sheets. Weld. Int.
**2010**, 20, 440–445. [Google Scholar] [CrossRef] - Matusiak, J.; Pfeifer, T. The research of technological and environmental conditions during low-energetic gas-shielded metal arc welding of aluminium alloys. Weld. Int.
**2011**, 27, 338–344. [Google Scholar] [CrossRef] - Nishimura, R.; Ma, N.; Liu, Y.; Li, W.; Yasuki, T. Measurement and analysis of welding deformation and residual stress in CMT welded lap joints of 1180 MPa steel sheets. J. Manuf. Process.
**2021**, 72, 515–528. [Google Scholar] [CrossRef] - Talalaev, R.; Veinthal, R.; Laansoo, A.; Sarkans, M. Cold metal transfer (CMT) welding of thin sheet metal products. Est. J. Eng.
**2012**, 18, 243–250. [Google Scholar] [CrossRef] - CMT (Cold Metal Transfer) de FRONIUS, une Nouvelle Technologie de Soudage à L’arc Qui Ouvre de Nouvelles Perspectives. Available online: https://www.machine-outil.com/actualites/t154/a1250-cmt-cold-metal-transfer-de-fronius-une-nouvelle-technologie-de-soudage-a-l-arc-qui-ouvre-de-nouvelles-perspectives.html (accessed on 10 June 2023).
- Azar, A.S. A heat source model for cold metal transfer (CMT) welding. J. Therm. Anal. Calorim.
**2015**, 122, 741–746. [Google Scholar] [CrossRef] - Wu, K.; He, Z.; Dong, Z.; Lan, Y. Numerical simulation of the temperature field of cold metal transfer welding pool. Mechanika
**2016**, 22, 285–290. [Google Scholar] [CrossRef] - Rao, Z.; Li, Y.; Liu, J.; Liao, S.M.; Wang, F. Numerical simulation of heat and mass transfer during CMT welding of aluminum alloy and galvanized mild steel. J. Manuf. Sci. Eng.
**2015**, 136, 108530. [Google Scholar] [CrossRef] - Escribano-García, R.; Rodriguez, N.; Zubiri, O.; Piccini, J.; Setien, I. 3D numerical simulation of GMAW Cold Metal Transfer using response surface methodology. J. Manuf. Process.
**2022**, 76, 656–665. [Google Scholar] [CrossRef] - Cambon, C.; Rouquette, S.; Bendaoud, I.; Bordreuil, C.; Wimpory, R.; Soulie, F. Thermo-mechanical simulation of overlaid layers made with wire + arc additive manufacturing and GMAW-cold metal transfer. Weld. World
**2020**, 64, 1427–1435. [Google Scholar] [CrossRef] - Schreier, H.; Orteu, J.-J.; Sutton, M.A. Image Correlation for Shape, Motion and Deformation Measurement; Springer Science: Berlin/Heidelberg, Germany, 2009; p. 322. [Google Scholar] [CrossRef]
- Mousavi, S.A.; Miresmaeili, R. Experimental and numerical analyses of residual stress distributions in TIG welding process for 304L stainless steel. J. Am. Acad. Dermatol.
**2008**, 208, 383–394. [Google Scholar] [CrossRef] - Brickstad, B.; Josefson, B. A parametric study of residual stresses in multi-pass butt-welded stainless steel pipes. Int. J. Press. Vessel. Pip.
**1998**, 75, 11–25. [Google Scholar] [CrossRef] - Tchoumi, T.; Peyraut, F.; Bolot, R. 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.
**2016**, 229, 216–229. [Google Scholar] [CrossRef] - Huang, H.; Wang, J.; Li, L.; Ma, N. Prediction of laser welding induced deformation in thin sheets by efficient numerical modeling. J. Mater. Process. Technol.
**2016**, 227, 117–128. [Google Scholar] [CrossRef] - Ma, N.; Li, L.; Huang, H.; Chang, S.; Murakawa, H. Residual stresses in laser-arc hybrid welded butt-joint with different energy ratios. J. Mater. Process. Technol.
**2015**, 220, 36–45. [Google Scholar] [CrossRef] - Nagy, M.; Behúlová, M. Design of welding parameters for laser welding of thin-walled stainless steel tubes using numerical simulation. IOP Conf. Ser. Mater. Sci. Eng.
**2017**, 266, 012013. [Google Scholar] [CrossRef] - Javadi, Y.; Akhlaghi, M.; Najafabadi, M.A. Using finite element and ultrasonic method to evaluate welding longitudinal residual stress through the thickness in austenitic stainless steel plates. Mater. Des.
**2013**, 45, 628–642. [Google Scholar] [CrossRef] - Chukkan, J.R.; Vasudevan, M.; Muthukumaran, S.; Kumar, R.R.; Chandrasekhar, N. Simulation of laser butt welding of AISI 316L stainless steel sheet using various heat sources and experimental validation. J. Mater. Process. Technol.
**2015**, 219, 48–59. [Google Scholar] [CrossRef] - Feli, S.; Aaleagha, M.E.A.; Jahanban, M.R. Evaluation Effects of Modeling Parameters on the Tem- perature Fields and Residual Stresses of Butt-Welded Stain- less Steel Pipes. J. Str. Anal.
**2017**, 1, 25–33. [Google Scholar] - Zain-Ul-Abdein, M.; Nelias, D.; Jullien, J.-F.; Deloison, D. Prediction of laser beam welding-induced distortions and residual stresses by numerical simulation for aeronautic application. J. Mater. Process. Technol.
**2009**, 209, 2907–2917. [Google Scholar] [CrossRef] - Li, Y.; Zhao, Y.; Li, Q.; Wu, A.; Zhu, R.; Wang, G. Effects of welding condition on weld shape and distortion in electron beam welded Ti2AlNb alloy joints. Mater. Des.
**2017**, 114, 226–233. [Google Scholar] [CrossRef] - Attarha, M.; Sattari-Far, I. Study on welding temperature distribution in thin welded plates through experimental measurements and finite element simulation. J. Mater. Process. Technol.
**2011**, 211, 688–694. [Google Scholar] [CrossRef] - Xu, J.; Chen, J.; Duan, Y.; Yu, C.; Chen, J.; Lu, H. Comparison of residual stress induced by TIG and LBW in girth weld of AISI 304 stainless steel pipes. J. Mater. Process. Technol.
**2017**, 248, 178–184. [Google Scholar] [CrossRef] - Tchoumi Nyankam, T.C. Multiphysics Modeling of the Welding arc and the Weld Beat during Welding Operation: Prediction of Distorsions ad Residual Stresses. Ph.D. Thesis, University of Technology of Belfort-Montbéliard (UTBM), Belfort, France, 2016. Available online: https://theses.hal.science/tel-01873488 (accessed on 14 December 2022).
- Loose, T.; Klöppel, T. An ls-dyna material model for the consistent simulation of welding, forming and heat treatment. In Proceedings of the 11th International Seminar Numerical Analysis of Weldability, Seggau, Austria, 21–24 September 2015. [Google Scholar]
- Capriccioli, A.; Frosi, P. Multipurpose ANSYS FE procedure for welding processes simulation. Fusion Eng. Des.
**2009**, 84, 546–553. [Google Scholar] [CrossRef] - Fanous, I.F.Z.; Younan, M.Y.A.; Wifi, A.S. 3-D Finite Element Modeling of the Welding Process Using Element Birth and Element Movement Techniques. J. Press. Vessel. Technol.
**2003**, 125, 144–150. [Google Scholar] [CrossRef] - Lindgren, L.E. Finite element modeling and simulation of welding part 1: Increased complexity. J. Therm. Stress.
**2001**, 24, 141–192. [Google Scholar] [CrossRef]

**Figure 1.**Schematic showing the positioning of thermocouples, protection, clamping, and copper lath.

**Figure 7.**Mechanical properties of 304L stainless-steel for the bilinear isotropic strain hardening model [24].

**Figure 10.**Thermal parametric study: temperature at 20 mm from the seam axis for various values of h, case 1 mm/1 mm.

**Figure 11.**Thermal parametric study: temperature at 20 mm from the seam axis for various values of h, case 1.2 mm/1 mm.

**Figure 13.**Comparison between computed results and DIC displacements along line L

_{0}, case 1 mm/1 mm.

**Figure 14.**Comparison between computed results and DIC displacements along line L

_{0}, case 1.2 mm/1 mm.

Configuration | 1 mm/1 mm | 1.2 mm/1 mm |
---|---|---|

$\mathrm{Welding}\mathrm{energy}Es$ (kJ/mm) | 0.242 | 0.235 |

Average power P (kW) | 2.62 | 2.55 |

$\mathrm{Coefficient}\eta $ | 0.8 | 0.8 |

$\mathrm{Heat}\mathrm{input}Q$ (kJ/mm) | 0.194 | 0.188 |

Average real power (kW) | 2.1 | 2.04 |

Configurations | L (mm) | l (mm) | H (mm) | h (mm) | e (mm) = H + h + e_{1} |
---|---|---|---|---|---|

1 mm/1 mm | 8.05 | 7.08 | 1.43 | 0.57 | 3 |

1.2 mm/1 mm | 7.51 | 5.83 | 1.52 | 0.36 | 3.1 |

Configurations | Number of Nodes | Number of Elements |
---|---|---|

1 mm/1 mm | 56,762 | 47,100 |

1.2 mm/1 mm | 58,782 | 48,800 |

Group of Steps | Number of Steps | Time Step (s) |
---|---|---|

1. Initial conditions and clamping | 2 | 10^{−5} |

2. Simulate progressive activation of elements | 25 | 0.37 |

3. Debriding and cooling | 1 | 500 |

Configurations | Thickness (mm) | Maximum Measured Temperature (°C) |
---|---|---|

1 mm/1 mm | 1 | 254 |

1 | ||

1.2 mm/1 mm | 1.2 | 335 |

1 | 272 |

**Table 6.**Relative difference between measured and calculated maximum temperatures for various values of the h, case 1 mm/1 mm.

Convective Heat Transfer Coefficient h (W·m^{−2}·°C^{−1} ) | Relative Difference in the Maximum Temperatures (%) |
---|---|

10 | 22 |

20 | 11.3 |

30 | 2.6 |

**Table 7.**Relative differences between measured and calculated maximum temperatures for different values of h, case 1.2 mm/1 mm.

Convective Heat Transfer Coefficient h (Watt.·m^{−2}·°C^{−1}) | Relative Difference between the Maximum Temperatures (%) | |
---|---|---|

Thickness 1.2 mm | Thickness 1 mm | |

30 | 13.7 | 3.1 |

45 | 22.3 | 8 |

60 | 25.1 | 12.7 |

Configurations | Experiment | Simulation | ||
---|---|---|---|---|

1 mm/1 mm | 1 mm | 1 mm | 1 mm | 1 mm |

2.7° | 2.8° | 3° | 3° | |

1.2 mm/1 mm | 1.2 mm | 1 mm | 1.2 mm | 1 mm |

4.9° | 6.1° | 5° | 5.8° |

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. |

© 2024 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**

Aberbache, H.; Mathieu, A.; Haglon, N.; Bolot, R.; Bleurvacq, L.; Corolleur, A.; Laurent, F.
Numerical Study of the Cold Metal Transfer (CMT) Welding of Thin Austenitic Steel Plates with an Equivalent Heat Source Approach. *J. Manuf. Mater. Process.* **2024**, *8*, 20.
https://doi.org/10.3390/jmmp8010020

**AMA Style**

Aberbache H, Mathieu A, Haglon N, Bolot R, Bleurvacq L, Corolleur A, Laurent F.
Numerical Study of the Cold Metal Transfer (CMT) Welding of Thin Austenitic Steel Plates with an Equivalent Heat Source Approach. *Journal of Manufacturing and Materials Processing*. 2024; 8(1):20.
https://doi.org/10.3390/jmmp8010020

**Chicago/Turabian Style**

Aberbache, Hichem, Alexandre Mathieu, Nathan Haglon, Rodolphe Bolot, Laurent Bleurvacq, Axel Corolleur, and Fabrice Laurent.
2024. "Numerical Study of the Cold Metal Transfer (CMT) Welding of Thin Austenitic Steel Plates with an Equivalent Heat Source Approach" *Journal of Manufacturing and Materials Processing* 8, no. 1: 20.
https://doi.org/10.3390/jmmp8010020