# Personalized Artificial Tibia Bone Structure Design and Processing Based on Laser Powder Bed Fusion

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^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{3}and the tap density is 4.8 g/cm

^{3}, which meets the requirements of use. Its specific chemical composition is shown in Table 1. From the scanning electron micrograph in Figure 1, it can be seen that the 316L stainless steel powder used in this experiment has the advantages of high sphericity, less satellite sphere particles, good fluidity, and no segregation of components.

## 3. Laser Powder Bed Fusion Forming Process Principle and Simulation Model

#### 3.1. Heat Source Model

_{h}, b

_{h}, and c

_{h}are the size of the ellipsoid; A is the absorption coefficient of the powder to the laser energy; P is the laser power; and f is the energy distribution coefficient of the molten pool.

#### 3.2. Laser Scattering Model

_{0}is the power density of the laser and δ is the Dirac delta formula.

_{+}and Q

_{−}are the forward and backward power density, respectively, and F is the scattering from the collimated component.

#### 3.3. Heat Transfer Model between Particles

_{ij}is the contact area between particle i and particle j.

_{i}is the incident area of the laser.

_{0}is the intensity of the incident light, a is the absorption coefficient, and z is the penetration depth.

#### 3.4. Heat Transfer in the Molten Pool

_{b}is the equivalent emission coefficient, σ

_{b}is the Stefen–Boltzmann constant, and T

_{a}is the ambient temperature.

_{c}is the natural convection coefficient.

#### 3.5. Flow in the Molten Pool

- Continuity equation is shown in Equation (20):$$\mathit{\Nabla}\xb7\left(\rho \overrightarrow{v}\right)=0,$$
- Law of Conservation of Momentum is shown in Equation (21):$$\frac{\partial}{\partial t}\left(\rho \overrightarrow{v}\right)+\mathit{\Nabla}\left(\rho \overrightarrow{v}\otimes \overrightarrow{v}\right)=\mathit{\Nabla}\xb7\left(\mu \mathit{\Nabla}\overrightarrow{v}\right)-\mathit{\Nabla}P+\rho \overrightarrow{g},$$
- Energy conservation law is shown in Equation (22):$$\frac{\partial h}{\partial t}+\left(\overrightarrow{v}\xb7\mathit{\Nabla}\right)h=-\frac{1}{\rho}\left(\mathit{\Nabla}\xb7k\mathit{\Nabla}T\right)+q,$$

_{g}is the gravity generated on the unit volume of liquid, F

_{b}is the buoyancy generated on the unit volume of liquid, ρ is the material density, T is the surface temperature of the powder bed, and T

_{a}is the ambient temperature.

_{s}is the surface tension coefficient.

_{s0}is the surface tension coefficient at the reference temperature T

_{0}; and σ

^{T}

_{s}is the coefficient of surface tension changing with temperature, which is generally a positive value.

_{0}is the boiling point vapor pressure, T

_{LV}is the boiling point temperature, and ΔH

_{LV}is the effective enthalpy when the metal evaporates.

#### 3.6. Heat Transfer Model of Porous Parts

_{p}is the specific heat capacity at a constant pressure, t is the time, T is the temperature, λ$\mathit{\Nabla}$

^{2}T is the heat diffusion term of the net introduction in the three coordinate directions, and Q is the heat flux density of the internal heat source.

_{s}is the heat flux along the direction of discovery on Γ

_{Q}; and $\overline{T}$ is the given temperature on Γ

_{T}.

- The first is the heat conduction from the solid structural material to the solid structural material;
- The second is the heat conduction from the material inside the hole to the material inside the hole;
- The third type is the heat conduction between the solid structure material and the material inside the hole.

_{D}is the thermal conductivity of the material on the left, λ

_{I}is the thermal conductivity of the composite interface, and λ

_{S}is the thermal conductivity of the material on the right. T

_{D}is the temperature at the green point, T

_{I}is the temperature at the interface, and T

_{S}is the temperature at the yellow point. δ

_{D}is the distance from the green point to the interface in a one-dimensional problem, and δ

_{D}is the relative density at the green point in a three-dimensional problem; in the same way, δ

_{I}is the relative density at the interface of the composite material in a three-dimensional problem, and δ

_{S}is the relative density at the yellow point in a three-dimensional problem.

#### 3.7. Numerical Simulation

^{−6}s, the minimum time step to 10

^{−10}s, the maximum time step to 10

^{−8}s, and the powder layer unit particle mesh size to 4 μm; the final number of meshes is 1.8 million.

## 4. Results and Discussion

#### 4.1. Measurement and Accuracy Improvement of Surface Morphology of Porous Structure

#### 4.2. Personalized 3D Printing and Comprehensive Mechanical Property Test of Tibia

_{1-0.3}, a

_{1-0.35}, a

_{1.2-0.35}, and a

_{1.2-0.4}, respectively. The four groups of porous structures have the same length, width, and height.

_{1.2-0.35}is about 17.99 GPa, which is consistent with the natural mechanical properties of the tibia, and the porosity of a

_{1.2-0.35}is also the largest, which meets the medical standards for personalized implantation. Therefore, after comprehensively considering the pore size, porosity, equivalent elastic modulus, laser powder bed fusion molding constraint and tensile strength, the regular octahedron structure with square cell body unit side length a = 1.2 mm and pillar diameter d = 0.35 mm is selected as the best parameter for the design of porous structure of tibial implant.

- Using the scanning command of SolidWorks software, first scan a square scanning body with diameter D through the center of the upper surface, the lower surface, and the two side planes. Similarly, scan another scanning body with diameter D in the plane perpendicular to the scanning body. Finally, the regular octahedron structure model is obtained by cutting off the vertices of six faces through a cube with side length.
- The regular octahedral cell body unit is used to generate the regular octahedral structure porous model through plane and spatial array, and then the tibial implant solid model and spatial regular octahedral porous structure are transformed into STL format.
- The Boolean intersection operation is carried out in magics software to obtain the porous tibial implant model with the external characteristics of tibial implant and the porous characteristics of regular octahedron, which is used for the pretreatment of laser powder bed fusion manufacturing.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**Single-layer single-channel scanning: (

**a**) 1 × 10

^{−4}s. (

**b**) 2 × 10

^{−4}s. (

**c**) 3 × 10

^{−4}s. (

**d**) 4 × 10

^{−4}s. (

**e**) 5 × 10

^{−4}s. (

**f**) 6 × 10

^{−4}s. (

**g**) 7 × 10

^{−4}s. (

**h**) 8 × 10

^{−4}s. (

**i**) 9 × 10

^{−4}s (

**j**) 10 × 10

^{−4}s.

**Figure 10.**The change of the cross-sectional shape of the molten pool: (

**a**) 1 × 10

^{−4}s. (

**b**) 2 × 10

^{−4}s. (

**c**) 3 × 10

^{−4}s. (

**d**) 4 × 10

^{−4}s. (

**e**) 5 × 10

^{−4}s. (

**f**) 6 × 10

^{−4}s. (

**g**) 7 × 10

^{−4}s. (

**h**) 8 × 10

^{−4}s. (

**i**) 9 × 10

^{−4}s (

**j**) 10 × 10

^{−4}s.

**Figure 11.**(

**a**) Unoptimized sheet stainless steel part and SEM. (

**b**) Unoptimized cubic stainless-steel part and SEM. (

**c**) Unoptimized porous stainless-steel part and SEM. (

**d**) Optimized porous stainless-steel part and SEM.

**Figure 13.**SEM of porous stainless-steel part after substrate and material preheating: (

**a**) ×200. (

**b**) ×500.

**Figure 15.**Tensile property test of samples ((

**a**) structure of test sample; (

**b**) printed tensile samples; (

**c**) tensile test results of standard structural samples; (

**d**) tensile test results of porous structure samples).

C | Si | Mn | P | S | Ni | Cr | Mo | Fe |
---|---|---|---|---|---|---|---|---|

≤0.03 | ≤0.75 | ≤2.00 | ≤0.035 | ≤0.03 | 12.5–13.0 | 17.5–18.0 | 2.25–2.5 | margin |

Sample | Side Length of Cube (a/mm) | Pillar Diameter (d/um) | Aperture Size (D _{p}/um) | Design Porosity (Φ _{p}/%) |
---|---|---|---|---|

1 | 1 | 300 | 407.11 | 71.07 |

2 | 1 | 350 | 357.11 | 62.99 |

3 | 1.2 | 350 | 498.53 | 72.38 |

4 | 1.2 | 400 | 448.53 | 65.72 |

Sample | Elastic Modulus |
---|---|

a_{1-0.3} | 18.45 |

a_{1-0.35} | 29.75 |

a_{1.2-0.35} | 17.99 |

a_{1.2-0.4} | 37.40 |

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## Share and Cite

**MDPI and ACS Style**

Yang, N.; Gong, Y.; Chen, H.; Li, W.; Zhou, C.; Zhou, R.; Shao, H.
Personalized Artificial Tibia Bone Structure Design and Processing Based on Laser Powder Bed Fusion. *Machines* **2022**, *10*, 205.
https://doi.org/10.3390/machines10030205

**AMA Style**

Yang N, Gong Y, Chen H, Li W, Zhou C, Zhou R, Shao H.
Personalized Artificial Tibia Bone Structure Design and Processing Based on Laser Powder Bed Fusion. *Machines*. 2022; 10(3):205.
https://doi.org/10.3390/machines10030205

**Chicago/Turabian Style**

Yang, Nan, Youping Gong, Honghao Chen, Wenxin Li, Chuanping Zhou, Rougang Zhou, and Huifeng Shao.
2022. "Personalized Artificial Tibia Bone Structure Design and Processing Based on Laser Powder Bed Fusion" *Machines* 10, no. 3: 205.
https://doi.org/10.3390/machines10030205