# Prediction of Transient Temperature Distributions for Laser Welding of Dissimilar Metals

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}, the model generated a weld width of 6400 µm and a depth of 789 µm. At a lower LED of 297 J/mm

^{2}, the weld width and penetration depth were reduced to 5410 µm and 393 µm [40,41,42,43].

^{2}and 297 J/mm

^{2}). At higher LED (371 J/mm

^{2}), i.e., at lower scanning speed (8 mm/s), the laser remained in contact with the material for a longer time, which further resulted in increased heating time of 0.4 s and higher peak temperature of ~8200 K [40,41,42,43]. As the LED decreased (297 J/mm

^{2}), the heating time reduced to 0.25 s with a much lower peak temperature of ~7800 K. Results also revealed that another phenomenon that governed the weld width and the depth was the Marangoni convection force. Marangoni effect was the mass transfer that occurred due to the gradient in the surface tension in the molten weld pool [40,41,42,43].

## 2. Definition of the Model

- (a)
- Radiation and convection heat loss from the surface are considered for modeling.
- (b)
- The ambient temperature is 298 K and the system is within good thermal isolation from the environment.
- (c)
- The change in phase during the process is also taken into account.
- (d)
- The thermo physical properties of the materials change with the change of temperature.
- (e)
- The position of the laser beam is vertical to the surface.
- (f)
- Latent heat during a phase change is considered for simulation. Latent heat for melting of Ti6Al4V and AISI 316L is 286 kJ/kg and 260 kJ/kg respectively.

_{no}and d0 are constant vectors. The vector v

_{no}is the velocity of the origin of the new frame with respect to the old frame. d is the position vector of the origin of the new frame with respect to the old frame. The velocity of the origin of the new frame is the time derivative of d:

_{no}has three components; Among them, d/dt(d

_{x}) = 0, d/dt(d

_{y}) = 0, and d/dt(d

_{y}) = 2, which means that for any value of t, d

_{x}(t) = d

_{x}0 and d

_{z}(t) = d

_{z}0.

## 3. Numerical Model

_{p}is the specific heat at constant pressure, t is time, T is the temperature, k is the thermal conductivity, Q is volume heat rate and $\overrightarrow{q}$ is the heat flux vector.

_{ext}is the surrounding temperature.

#### Mesh Convergence Analysis

## 4. Results

#### 4.1. Temperature Propagation during the Welding

#### 4.2. Isothermal Contours

#### 4.3. Temperature Probes

#### 4.4. Offsetting the Laser Beam toward Ti-6Al-4V

_{2}layer was formed on the SS side with a width of 24 µm and the tensile strength of the joint could range up to 182 MPa [57].

## 5. Conclusions

- Temperature distribution along the weld line throughout the process at laser spot irradiation shows that the average maximum temperature generated is near 3300 K. Maximum temperatures along the traverse direction (for fixed y value) on z = 0 plane in the middle (x = 5 and x = 15) and edges (x = 0 and x = 20) of the work pieces are approximately 1200 and 1000 K, respectively.
- Temperature distribution along the thickness shows that even the bottom-most surface along the z-axis achieves an average temperature near 2400 K. A significant penetration depth can be achieved. The average temperature of the two domains ranges from 1150 K to 1200 K during the process.
- There are differences in the thermal properties of these two materials. Ti6Al4V has a higher melting temperature. It would take more time than 316L to reach it, as the model was done in zero offsets. The offset of the laser heat source in the same arrangement can create a better-quality welding by adjusting the variations in thermal properties as predicted from the model. Welding interface temperature can be minimized up to 500–1000 K by offsetting the laser beam toward the Ti-6Al-4V side.
- Transient distribution of peak temperature from the weld line along the x-axis is plotted and it decreases as it moves far from the source, for obvious reason. Near the weld line, it decreases sharply and the sharpness decreases as the distance increases from the weld line. The difference of maximum temperature between the edge lines (along x = 0 and x = 20) on the z = 0 plane lies between 20 and 100 K. The maximum temperatures can reach up to 1200 K for both samples along the edges mentioned, which indicates recrystallization for AISI 316 and presence of both α phase and β phase for Ti6Al4V that occur within the sample width range.
- Transient isothermal contours help to understand the heating and cooling phenomena during the process. At higher temperature, AISI316L has a lower thermal conductivity compared to Ti6Al4V; thus, the steel part attains a higher temperature near the weld zone. Temperature history of two nearby points in traverse direction makes it understandable that even within two nearer points; one can be in heating mode and one in cooling mode. This fact demonstrates the complex type of deformation, which is the main source of residual stresses.

## 6. Future Scope

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Temperature propagation contours at (

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

**b**) t = 6 s, (

**c**) t = 10 s, (

**d**) t =13 s, and (

**e**) t =16 s.

**Figure 6.**Isothermal contours at (

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

**b**) t = 6 s, (

**c**) t = 10 s, (

**d**) t = 13 s, and (

**e**) t = 16 s.

**Figure 7.**(

**a**) Maximum and minimum temperature computational plot for domain 1 (AISI 316L side) and (

**b**) comparative average temperature with time for domain 1 (green) and domain 2 (blue).

**Figure 8.**Boundary temperature probe points (

**a**) along weld line (y axis) and (

**b**) along the thickness (z axis).

**Figure 9.**Temperature distribution of three different points (

**a**) along the thickness perpendicular to the weld line and (

**b**) along the weld line.

**Figure 11.**Temperature distribution of temperature probes of two different domains having the same Y = 20 mm.

**Figure 13.**Maximum temperature (computational) on the edge temperature probes along weld line at Z = 0 (green) and Z = −2.5 (blue).

**Figure 16.**Temperature distribution of three different points on interface: (

**a**) 0.3 mm offset and (

**b**) 0.6 mm offset toward Ti6Al4V.

Parameters | Value | Details |
---|---|---|

x0 | 10 [mm] | x coordinate |

y0 | 2 [mm] | y coordinate |

Sigx | 0.200 [mm] | Deviation along x |

Sigy | 0.200 [mm] | Deviation along y |

Rc | 0.001 | Reflection coefficient |

Ac | 5 [1/cm] | Absorption coefficient |

Q0 | 300 [W] | Laser power |

L1 | 10 [mm] | Material size 1 |

L2 | 10 [mm] | Material size 2 |

LZ | 2.5 [mm] | Thickness of the sheet |

Time step | 0.2 | Time step for storing solution |

End time | 17 [s] | End time step |

V | 2.0 [mm/s] | Laser velocity |

L | 40 [mm] | Length of sheet |

Arguments | Upper Limit | Lower Limit |
---|---|---|

a | (L1 + L2) | 0 |

a0 | x0 | x0 |

Siga | Sigx | Sigx |

b | 2(L1 + L2) | 0 |

b0 | y0 | y0 |

sigb | sigy | Sigy |

Name | Value | Unit |
---|---|---|

Density | rho(T) | kg/m³ |

Thermal conductivity | k_iso(T) | W/(m·K) |

Heat capacity at constant pressure | Cp(T) | J/(kg·K) |

Name | Value |
---|---|

Convective heat transfer of air(h) | 10 W/m^{2}K |

Emissivity(ε) | 0.85 |

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**MDPI and ACS Style**

Ghosh, P.S.; Sen, A.; Chattopadhyaya, S.; Sharma, S.; Singh, J.; Dwivedi, S.P.; Saxena, A.; Khan, A.M.; Pimenov, D.Y.; Giasin, K. Prediction of Transient Temperature Distributions for Laser Welding of Dissimilar Metals. *Appl. Sci.* **2021**, *11*, 5829.
https://doi.org/10.3390/app11135829

**AMA Style**

Ghosh PS, Sen A, Chattopadhyaya S, Sharma S, Singh J, Dwivedi SP, Saxena A, Khan AM, Pimenov DY, Giasin K. Prediction of Transient Temperature Distributions for Laser Welding of Dissimilar Metals. *Applied Sciences*. 2021; 11(13):5829.
https://doi.org/10.3390/app11135829

**Chicago/Turabian Style**

Ghosh, Partha Sarathi, Abhishek Sen, Somnath Chattopadhyaya, Shubham Sharma, Jujhar Singh, Shashi Parkash Dwivedi, Ambuj Saxena, Aqib Mashood Khan, Danil Yurievich Pimenov, and Khaled Giasin. 2021. "Prediction of Transient Temperature Distributions for Laser Welding of Dissimilar Metals" *Applied Sciences* 11, no. 13: 5829.
https://doi.org/10.3390/app11135829