# Influence of Material Property Variation on Computationally Calculated Melt Pool Temperature during Laser Melting Process

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Finite Element Modeling

#### 2.1. Governing Equations

- (x,y,z) = coordinate system attached to the heat source
- Q = power generation per unit volume in the domain D (W m
^{−3}) - k
_{x}, k_{y}, k_{z}= thermal conductivity in the x, y and z directions (W m^{−1}K^{−1}) - c = specific heat capacity (J kg
^{−1}K^{−1}) - ρ = density (kg m
^{−3}) - t = time (s)
- v = velocity of laser (m s
^{−1})

_{o}for (x,y,z) ∈ D

- k
_{n}= thermal conductivity normal to S (W/m-K) - h = heat transfer coefficient for convection (W/m
^{2}-K) - σ = Stefan–Boltzmann constant for radiation (5.67 × 10
^{−8}W/m^{2}-K^{4}) - ε = emissivity
- T
_{o}= ambient temperature (K) - q = heat flux normal to S (W/m
^{2})

#### 2.2. Description of the Model

_{0}= radius of laser spot = 50 μm. The moving heat source was modeled by reassigning the location of the distributed heat flux calculated using Equation (4) at different time steps. For example, several element sets, each having laser spot dimension, are chosen on the powder surface. The distributed heat flux was applied on the element set 1 in load step 1 and nodal temperatures are numerically calculated utilizing Equation (1). Heat flux was then applied on the element set 2 in the second load step, and so on. Thus, a nodal temperature history was obtained as a function of time. The time was calculated based on the scanning velocity and heat source location. The transient heat transfer model was then run and nodal temperature was documented as a function of time for use in the subsequent steps.

#### 2.3. Material Properties

#### 2.4. Experimental Data to Verify Reference FEA Model

## 3. Variation in Material Properties

^{3}/K (also presented by Equation (5)). The slope is varied from −0.15 to −0.3 kg/m

^{3}/K to generate five sets of density data. Similarly, the slope of the base specific heat plot is 0.2 J/kg-K/K and is varied between 0.1 J/kg-K/K and 0.3 J/kg-K/K to generate five sets of specific heat data (Figure 9). The temperature dependent thermal conductivity used for the analysis is shown in Figure 10, where the base slope is 0.0139 W/m-K/K and was varied from 0.005 W/m-K/K to 0.03 W/m-K/K to create seven sets of data. In addition, thermal conductivity was varied before and after melting point to identify which one has more significant effect on melt pool temperature. These variations are shown in Figure 11 and Figure 12, where slopes are varied only before and after melting temperature, respectively.

## 4. Results and Discussion

#### 4.1. Sensitivity to Density

#### 4.2. Sensitivity to Specific Heat

#### 4.3. Sensitivity to Thermal Conductivity

## 5. Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Single layer of Ti-64 on top of a substrate. In this particular case, the substrate material is also Ti-64. Element sizes in layer and substrate are shown by zooming associated elements.

**Figure 5.**Comparison of maximum FEA temperature that is averaged over a camera pixel and IR data of Ti-64 sample at 400 W and 200 to 1100 mm/s.

**Figure 6.**(

**a**) Two-dimensional and (

**b**) three-dimensional confocal microscopy images of single beads Ti-64 samples produced at laser power of 400 W at scanning speed of 200 mm/s.

**Figure 10.**Seven sets of thermal conductivity data generated by varying the base slope (shown in Equation (7)) between 0.005 and 0.03 W/m-K/K.

**Figure 13.**Sensitivity of peak temperature to density. Percentage change of peak temperature with respect to that calculated with base density at different process parameters.

**Figure 14.**Sensitivity of peak temperature to specific heat. Percentage change of peak temperature with respect to that calculated with base specific heat at different process parameters.

**Figure 15.**Sensitivity of peak temperature to thermal conductivity. Percentage change of peak temperature with respect to that calculated with base thermal conductivity at different process parameters.

**Figure 16.**Sensitivity of peak temperature to thermal conductivity. Change of peak temperature with respect to that calculated with base thermal conductivity at varying process parameters. Slope of thermal conductivity–temperature plot before the melting point is varied only.

**Figure 17.**Sensitivity of peak temperature to thermal conductivity. Change of peak temperature with respect to that calculated with base thermal conductivity at varying process parameters. Slope of thermal conductivity–temperature plot after the melting point is varied only.

Initial Temperature | 298 K |
---|---|

Convection | - |

Convective heat transfer coefficient | 20 W/m^{2}-K |

Ambient temperature | 298 K |

Radiation | - |

Emissivity | 0.35 |

Element | C | O | N | H | Fe | Al | V | Cu | Sn | Y | Ti |
---|---|---|---|---|---|---|---|---|---|---|---|

% wt | 0.02 | 0.14–0.17 | 0.02 | 0.013 | 0.05–0.25 | 5.50–6.75 | 3.5–4.5 | <0.10 | <0.10 | <0.005 | Balance |

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**MDPI and ACS Style**

Ahmed, S.H.; Mian, A.
Influence of Material Property Variation on Computationally Calculated Melt Pool Temperature during Laser Melting Process. *Metals* **2019**, *9*, 456.
https://doi.org/10.3390/met9040456

**AMA Style**

Ahmed SH, Mian A.
Influence of Material Property Variation on Computationally Calculated Melt Pool Temperature during Laser Melting Process. *Metals*. 2019; 9(4):456.
https://doi.org/10.3390/met9040456

**Chicago/Turabian Style**

Ahmed, Sazzad H., and Ahsan Mian.
2019. "Influence of Material Property Variation on Computationally Calculated Melt Pool Temperature during Laser Melting Process" *Metals* 9, no. 4: 456.
https://doi.org/10.3390/met9040456