# Thermo-Mechanical Coupling Numerical Simulation for Extreme High-Speed Laser Cladding of Chrome-Iron Alloy

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{3}square specimen was cut out of the surface of a 45 steel shaft part using the wire-cutting method, and the surface was cleaned of stains using alcohol, inlaid, ground, and polished. The width and height of the molten layer were observed and measured using an optical display, and when measuring the height and width of the coating, each value was measured three times and then averaged. A schematic diagram of the coating width and height measurement is shown in Figure 1. W is the coating width, and H is the coating height. When the coating’s surface has the phenomenon of sticky powder, the powder particles were then excluded when measuring the coating’s width and height dimensions. When conducting the observation of the coating’s microstructure, a corrosion treatment was carried out using a 10% FeCl

_{3}hydrochloric acid solution and a 4% HNO

_{3}alcohol solution for 10 s each. After the corrosion treatment was completed, the microstructure was observed using either scanning electron microscopy or optical microscopy.

## 3. Finite Element Simulation

#### 3.1. The Control Equation and Boundary Conditions

_{0}is the initial ambient temperature; h is the convection heat transfer coefficient; T

_{s}is the material surface temperature; σ is the Stefan–Boltzmann constant; ε is the material surface radiation coefficient; and A is the material surface absorption coefficient for laser energy.

#### 3.2. Heat Source Model

_{1}is the proportion of energy allocated to the high-order Gaussian heat source, which is 0.8; r is the distance from the center of the laser beam; R is the radius of the laser beam; and n is the order of the heat source.

_{2}is the energy ratio allocated to the variable-density heat source, taken as 0.2; R is the distance from the center of the laser beam; r is the radius of the laser beam; a

_{1}is an empirical parameter, taken as 1.6; and h

_{0}is the depth of laser heating on the substrate.

#### 3.3. Finite Element Model

#### 3.4. Material Parameter Model

## 4. Results and Discussion

#### 4.1. The Influence of the Process Parameters on the Macro-Shape of the Coating Layer

#### 4.2. Temperature Field Numerical Simulation and Verification

#### 4.3. The Influence of the Cooling Rate and Temperature Gradient on the Coating Structure

^{6}°C/s, respectively; the maximum temperature occurs between the point C at the interface between the substrate and the molten layer, where the temperature is approximately 1753 °C and the cooling rate is approximately 8 × 10

^{5}°C/s, respectively. The melt pool temperature tends to decrease from top to bottom, and the cooling rate was found to be higher at the top of the melt pool and lower at the bottom of the melt pool, due to the obvious convective heat exchange arising on the surface of the melt pool and the obvious heat conduction occurring at the bottom [28].

#### 4.4. Stress Field Simulation Analysis and Prediction

## 5. Conclusions

- (1)
- Abaqus finite element software was used to create a numerical model for extreme high-speed laser cladding based on a composite heat source and the live-dead cell approach. An analysis of the effects of the laser power and the cladding speed on the cladding section size and surface morphology was performed after a 431 stainless steel coating was clad onto a 45 steel shaft. A laser power of 2400 W, a cladding speed of 20 m/min, and a powder feeding rate of 20.32 g/min were chosen as the ideal process parameters for numerical simulation computation. The maximum temperature of the melt pool was calculated to be 2780 °C using this parameter and was found by a temperature field calculation. The numerical model was shown to be accurate, as the predicted size and heat effect zone of the melt pool were in good agreement with the experimental data.
- (2)
- The influence of different process parameters on the melt pool size was also analyzed. The laser power and the powder feed rate were found to be positively correlated to the melt pool’s width and height, while the laser cladding rate was found to be negatively correlated to the melt pool’s width and height.
- (3)
- To examine the cladding section’s microstructure, a numerical simulation of the temperature gradient and the cooling rate was performed. The microstructure of the clad layer varied depending on its location: at the top, the cooling rate was highest, the temperature gradient was largest, and the clad layer’s dendrite crystals were chaotic and fine; in the middle, the cooling rate was highest, the temperature gradient was smaller, and the clad layer’s dendrite crystals were coarse and long.
- (4)
- Cladding layer residual stress curve analysis was also performed. There was a lot of tension at the coating–substrate interface, more tension on the clad layer’s surface than in its interior, and a lot of tension in the coating itself. The clad layer’s residual stress was found to have mostly originated in the laser’s scanning direction.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 8.**Numerical simulation of the melt pool cross-section compared with experimental coating morphology.

**Figure 9.**Temperature law curve of the selected node. (

**a**) Thermal cycle curve in the depth direction of the melt pool; and (

**b**) heat-up-cooling rate curve of nodes.

**Figure 10.**Temperature gradient profile of the selected path. (

**a**) Temperature gradient in the depth direction MN of the melt pool; and (

**b**) temperature gradient in the direction KL of the melt pool width.

**Figure 11.**Microstructures of different locations of the cladding layer. (

**a**) Top; (

**b**) middle; and (

**c**) bottom.

**Figure 13.**Residual stress on different paths of the coating. (

**a**) Path KL; (

**b**) path MN; and (

**c**) path GH.

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

431 | 0.19 | 17.19 | 0.81 | 1.36 | 0.92 | 0.04 | Bal |

45 | 0.42 | 0.25 | 0.72 | 0.35 | 0.03 | 0.03 | Bal |

Experiment No. | Laser Power/W | Cladding Speed/(m/min) | Powder Feeding Rate/(g/min) |
---|---|---|---|

1 | 1800 | 20 | 20.32 |

2 | 2000 | 20 | 20.32 |

3 | 2200 | 20 | 20.32 |

4 | 2400 | 20 | 20.32 |

5 | 2400 | 15 | 20.32 |

6 | 2400 | 25 | 20.32 |

7 | 2400 | 30 | 20.32 |

8 | 2400 | 20 | 16.54 |

9 | 2400 | 20 | 30.36 |

10 | 2400 | 20 | 35.79 |

Temperature /°C | Specific Heat Capacity /(J·kg/°C) | Thermal Conductivity /(W·m/°C) | Density /(g/cm ^{3}) | Elastic Modulus /GPa | Expansion Coefficient /10 ^{−6}/°C | Poisson’s Ratio |
---|---|---|---|---|---|---|

25 | 457.62 | 17.29 | 7.74 | 196.35 | 17.56 | 0.29 |

300 | 539.35 | 20.35 | 7.62 | 177.32 | 18.28 | 0.31 |

600 | 667.48 | 23.69 | 7.49 | 151.56 | 19.12 | 0.34 |

900 | 681.76 | 26.97 | 7.35 | 121.48 | 20.92 | 0.34 |

1200 | 754.57 | 30.35 | 7.19 | 87.97 | 21.51 | 0.37 |

1300 | 855.98 | 31.48 | 7.14 | 72.34 | 21.92 | 0.39 |

1400 | 1054.31 | 32.36 | 7.07 | 35.35 | 23.02 | 0.39 |

1450 | 1948.47 | 32.39 | 7.02 | 15.67 | 24.10 | 0.42 |

Temperature /°C | Specific Heat Capacity /(J·kg/°C) | Thermal Conductivity /(W·m/°C) | Density /(g/cm ^{3}) | Elastic Modulus /GPa | Expansion Coefficient /10 ^{−6}/°C | Poisson’s Ratio |
---|---|---|---|---|---|---|

25 | 453.63 | 16.94 | 8.04 | 210.32 | 8.26 | 0.29 |

200 | 498.52 | 19.03 | 7.93 | 199.68 | 9.35 | 0.33 |

400 | 535.98 | 21.41 | 7.82 | 165.42 | 10.51 | 0.33 |

600 | 567.76 | 23.8 | 7.71 | 147.65 | 11.87 | 0.35 |

800 | 598.13 | 26.18 | 7.60 | 128.53 | 14.85 | 0.37 |

1000 | 629.98 | 28.56 | 7.49 | 108.98 | 14.96 | 0.42 |

1200 | 661.31 | 30.94 | 7.39 | 88.62 | 14.95 | 0.42 |

1400 | 698.64 | 33.33 | 7.29 | 67.75 | 15.04 | 0.42 |

Point | A | B | C |

Temperature gradient G/(°C/mm) | 1.63 × 10^{3} | 5.36 × 10^{3} | 8.72 × 10^{3} |

Cooling rate V/(°C/s) | 2.12 × 10^{4} | 2.67 × 10^{4} | 3.68 × 10^{4} |

Shape control factor K/(°C/(mm ^{2}·s)) | 125.33 | 1076.01 | 2066.26 |

Growth rate R/(mm/s) | 1.30 | 4.98 | 1.42 |

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**MDPI and ACS Style**

Nian, L.; Wang, M.; Ge, X.; Wang, X.; Xu, Y.
Thermo-Mechanical Coupling Numerical Simulation for Extreme High-Speed Laser Cladding of Chrome-Iron Alloy. *Coatings* **2023**, *13*, 879.
https://doi.org/10.3390/coatings13050879

**AMA Style**

Nian L, Wang M, Ge X, Wang X, Xu Y.
Thermo-Mechanical Coupling Numerical Simulation for Extreme High-Speed Laser Cladding of Chrome-Iron Alloy. *Coatings*. 2023; 13(5):879.
https://doi.org/10.3390/coatings13050879

**Chicago/Turabian Style**

Nian, Liangxiao, Miaohui Wang, Xueyuan Ge, Xin Wang, and Yifei Xu.
2023. "Thermo-Mechanical Coupling Numerical Simulation for Extreme High-Speed Laser Cladding of Chrome-Iron Alloy" *Coatings* 13, no. 5: 879.
https://doi.org/10.3390/coatings13050879