# Multi-Scale Mechanical Property Prediction for Laser Metal Deposition

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## Abstract

**:**

## 1. Introduction

## 2. A Cladding Stacking Model

#### 2.1. Model Introduction

#### 2.2. Experimental Verification

## 3. A Process–Structure–Property Multi-Scale Simulation Framework

#### 3.1. Simulation Method of Meso-Scale Powder Evolution Processes

#### 3.1.1. Geometry Modeling

#### 3.1.2. Heat Source Model

_{c}and y

_{c}are the laser center point locations, and the heat flux distribution shape can be selected by changing the order n.

#### 3.1.3. Heat Transfer Model

**q**is the heat flux in the

**r**direction, which is perpendicular to the isothermal plane, and the negative sign indicates that the heat transfer direction is opposite to the temperature gradient direction, $\lambda $ is the thermal conductivity and T is the temperature.

_{0}is the ambient temperature.

#### 3.1.4. Phase Transition Model

_{m}is the melting temperature, σ is the transition interval standard deviation. For example, for pure solids α (T) = 0, and for pure liquids α(T) = 1.

#### 3.1.5. Material Model

#### 3.2. Simulation Method of Microstructure Formations

#### 3.2.1. Nucleation Model

#### 3.2.2. Growth Model

#### 3.3. Prediction Method of Mechanical Properties of Macro-Scale Components

## 4. Simulation Cases, Results and Discussion

#### 4.1. Simulation of Meso-Scale Processes

#### 4.2. Simulation of Microstructures

#### 4.3. Prediction of Macro-Scale Mechanical Properties

## 5. Conclusions

- The range of the heat-affected zone in LMD can be determined by a heat-affected zone coefficient R. If the R is N, the subsequent cladding layer will have an influence on the N-layer structures beneath it;
- Based on the structural evolution history in the heat-affected zone, the cladding stacking model can quickly predict the overall structure of the fabricated component;
- The process–structure–property multi-scale simulation framework based on the cladding stacking model can predict the macro-scale mechanical properties of the final fabricated component according to the process parameters;
- Under multi-layer printings, the structure in the cladding layers gradually grows continuously from the substrate, showing a columnar crystal morphology on the whole, and finally forming three typical microstructure regions of the top, middle and bottom due to the influence of the heat-affected zone and heat dissipation conditions;
- The height of the fabricated material shows a linear increasing trend with the number of layers; the width is less affected by the number of layers; and
- The length of the cross-section grain of the fabricated material shows a linear growth trend with the number of layers; the width increases rapidly within the heat-affected zone and then reaches stability.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic showing the structural evolution process of the LMD multilayer printing: (

**a**–

**d**) represent the solidified structure of the cladding layers by 1,2,3,4 printing, respectively; (

**e**) represents the overall solidified structure of the cladding layers by n + 2 printing.

**Figure 3.**Prediction of the overall structure of fabricated components based on the structural evolution history of the heat-affected zone: (

**a**) represents the prediction of a regular part; (

**b**) represents the prediction of an irregular part.

**Figure 6.**Metallographic observations on the cross-section of each specimen: (

**a**–

**h**) represent the solidified structure of each specimen.

**Figure 14.**The simulated cladding layers by HOTM: (

**a**–

**d**) represent the solidified material by 1,2,3,4 printing, respectively.

Laser Power (W) | Scan Speed (mm/min) | Powder Feed Rate (g/min) | Hatch Spacing (mm) | Powder Diameter (μm) |
---|---|---|---|---|

3000 | 600 | 10 | 0.5 | 53–180 |

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

Specific heat capacity of solid (J/(kg·K)) | 611 | Latent heat melting (kJ/kg) | 286 |

Specific heat capacity of liquid (J/(kg·K)) | 900 | Latent heat vaporization (kJ/kg) | 9700 |

Thermal conductivity of solid (W/(m·K)) | 6.8 | Coefficient of compressibility, b | 2 × 10^{10} |

Thermal conductivity of liquid (W/(m·K)) | 32.5 | Coefficient of compressibility, c | 47.65 |

Coefficient of thermal expansion of solid (/℃) | 9.1 × 10^{−6} | Coefficient of compressibility, α1 | −1 |

Coefficient of thermal expansion of liquid (/℃) | 1.6 × 10^{−5} | Coefficient of compressibility, α2 | −0.354 |

Melting temperature (℃) | 1650 | Bulk modulus (GPa) | See Figure 12 |

Boiling temperature (℃) | 3260 | Shear modulus (GPa) | See Figure 12 |

Convective heat conduction coefficient (W/(m^{2}·K)) | 50 | Viscosity (Pa·s) | See Figure 12 |

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

Liquidus temperature (℃) | 1650 |

Solidus temperature (℃) | 1554 |

Maximum nucleation density, ${n}_{\mathrm{max}}$ (m^{−3}) | 1 × 10^{9} |

Average of supercooling, $\mathrm{\Delta}{T}_{n}$ (k) | 32 |

Standard deviation of supercooling, $\mathrm{\Delta}{T}_{\sigma}$ (k) | 8 |

Coefficient of growth, α | 0 |

Coefficient of growth, β | 3.19 × 10^{−5} |

Cell size (μm) | 20 |

Experiment | CA | Relative Error (%) | |
---|---|---|---|

Average length (mm) | 1.97 | 2.01 | 2.03 |

Average width (mm) | 0.85 | 0.81 | 4.71 |

**Table 5.**α transverse isotropic elastic tensor parameter of the phase [40].

C_{ij} | Value (GPa) |
---|---|

C_{11} = C_{22} | 170 |

C_{33} | 204 |

C_{12} = C_{21} | 98 |

C_{13} = C_{31} = C_{23} = C_{32} | 86 |

C_{44} | 72 |

C_{55} = C_{66} | 102 |

Other C_{ij} | 0 |

Tensile Specimen No. | Experiment (GPa) | Experimental Average (GPa) | Simulation (GPa) | Relative Error (%) |
---|---|---|---|---|

1 | 69.22 | 69.31 | 65.72 | |

2 | 69.45 | 5.18 | ||

3 | 69.25 |

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**MDPI and ACS Style**

Fan, J.; Yuan, Q.; Chen, G.; Liao, H.; Li, B.; Bai, G.
Multi-Scale Mechanical Property Prediction for Laser Metal Deposition. *Aerospace* **2022**, *9*, 656.
https://doi.org/10.3390/aerospace9110656

**AMA Style**

Fan J, Yuan Q, Chen G, Liao H, Li B, Bai G.
Multi-Scale Mechanical Property Prediction for Laser Metal Deposition. *Aerospace*. 2022; 9(11):656.
https://doi.org/10.3390/aerospace9110656

**Chicago/Turabian Style**

Fan, Jiang, Qinghao Yuan, Gaoxiang Chen, Huming Liao, Bo Li, and Guangchen Bai.
2022. "Multi-Scale Mechanical Property Prediction for Laser Metal Deposition" *Aerospace* 9, no. 11: 656.
https://doi.org/10.3390/aerospace9110656