# Thermal Insulation and Compressive Performances of 3D Printing Flexible Load-Bearing and Thermal Insulation Integrated Lattice

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. BWR Lattice Structures

#### 2.2. Materials

#### 2.3. Additive Manufacturing Process

#### 2.4. Characterizations

## 3. Results

#### 3.1. Relative Density

_{0}could be calculated by the equation below:

_{Ti}/g·mm

^{−3}was the density of TC4, ρ

_{L}/g·mm

^{−3}was the real density of lattice. According to the two calculation methods for lattice mass m

_{L}/g, ρ

_{L}could be calculated by Equation (3):

_{T}/mm

^{3}was the volume of the single core, and V

_{L}/mm

^{3}was the real volume of the lattice.

_{0}of the BWR lattices were calculated by Equations (1) and (3), and it was obvious that the lightweight level of S-2 was higher. There was less impact for ρ

_{0}on the mechanical and thermal insulation performances for both the two lattices because of the low values. Hence, the influence taken from the difference of ρ

_{0}was ignored in this work.

#### 3.2. Thermal Insulation Performance

_{2}/°C) with heating time was shown in Figure 4a. T

_{2}would reach and stabilize around the aimed temperature in 30 s, which was 700 °C. To simplify the calculations, T

_{2}was taken as 700 °C in the subsequent discussions.

_{1}/°C) with heating time was shown in Figure 4b. There were four stages, which were preheated, high speed rising, low speed rising, and stability, in the curve of T

_{1}for S-1 (T

_{1}

^{S−1}). T

_{1}

^{S−1}reached the maximum (230 °C) at the time of 6 min and then stayed constant. Different from S-1, there were only three stages, which were preheated, low speed rising, and stability, in the curve of T

_{1}for S-2 (T

_{1}

^{S−2}). This might be due to the difference in thermal conductivity between S-1 and S-2. This is a topic for further research, as the balance temperature was in the focus of this paper. Generally, the thermal insulation performance could be evaluated by thermal insulation efficiency. It was calculated by dividing the temperature difference between T

_{1}and T

_{2}by T

_{2}. At 700 °C, the thermal insulation efficiency of S-2 reached 83% and that of S-1 was 67%. S-2 showed favorable thermal insulation performance.

_{1}in the BWR lattice. This will be discussed in Section 4.1 in detail.

#### 3.3. Compressive Performance

#### 3.4. Cycle Resilient Performance

_{r}/mm and the broken thickness H

_{b}/mm and could be calculated by Equation (4). The deformation and recovery ability of the lattice were both taken into account. Compared with the recovery rate, it provided a more intuitive representation of the lattice flexibility.

_{r}did not decay. The BWR lattice exhibited favorable resilient properties after compressive failure and cyclic deformation, which played a key role in maintaining thermal insulation performance. It would be discussed in Section 4.2 in detail.

## 4. Discussions

#### 4.1. Thermal Transfer Process of the BWR Lattice

#### 4.1.1. Calculations of Thermal Flow and Equivalent Coefficient of Thermal Conductivity

_{0}/W was calculated. Since the thermal transfer process achieved a steady state after the temperature reached equilibrium, according to Fourier’s law [23] (Equation (5)), Φ

_{0}was calculated.

_{0}/mm

^{2}was the area of thermal conduction, λ

_{0}/W·m

^{−1}·°C

^{−1}was the coefficient of thermal conductivity (CTC), and S/mm was the distance of thermal conduction. Based on the geometry of the lattice, A

_{0}and S could be calculated.

_{1}/W was calculated.

_{1}/mm

^{2}was the cross-section of the equivalent panel, λ

_{r}/W·m

^{−1}·°C

^{−1}was the equivalent coefficient of thermal conductivity (ECTC) of the lattice. Since Φ

_{2}and Φ

_{1}were equal, the formula for λ

_{r}could be obtained by associating Equation (5) with Equation (8).

_{0}, and T

_{1}were brought into Equations (8) and (9) to calculate λ

_{r}and Φ

_{1}for S-1 and S-2, and the results were shown in Figure 7.

_{r}was closely related to the L, H, and k, and was independent of m and n. Hence, the ECTC of the lattice was equal to that of the core. To improve the thermal insulation performance of the lattice, it was necessary to increase the width-thickness ratio as much as possible.

_{2}/W was calculated, assuming that the radiation occurred only through the panel along the thickness direction and was not generated by the rods. To the thermal radiative transfer model between infinitely large flat panels [23], Equation (10) could be obtained.

^{−8}W/(m

^{2}·°C

^{4}), ε

_{1}was the IR emissivity of the heated surface, ε

_{2}was the IR emissivity of the insulated surface, A

_{f}/mm

^{2}was the radiation area of the lattice. The degree of oxidation had a great influence on the IR emissivity of the metal surface. According to the references, ε

_{1}and ε

_{2}were taken as 0.8 and 0.2, respectively [26,27]. The formula for A

_{f}was obtained by the geometric relationship of the lattice, as shown in Figure 7b.

_{2}of S-1 and S-2 could be calculated by Equations (10) and (11), and the results were shown in Figure 7c. It was noted the influence of lattice on Φ

_{2}was taken by the blocking for IR. It was consistent with the experimental phenomenon in Section 3.2.

_{1}and Φ

_{2}. As shown in Figure 7d, Φ

_{1}was a relatively low percentage of Φ, and thermal radiation was the main way of the thermal transfer for the BWR lattice. It differed from the experience that the main thermal transfer way of the conventional lattice at 700 °C was thermal conduction. The reason was that the thermal conduction of the lattice was suppressed by the big width-thickness ratio structure. It explained why the BWR lattice obtained favorable thermal insulation performance.

#### 4.1.2. Analysis of Thermal Insulation Performance

_{2}was, the higher the thermal insulation efficiency. T

_{2}at a steady state was related to the thermal flux Φ′/W·m

^{−2}of the insulated surface, hence the thermal insulation performance of the lattice could be improved by decreasing Φ′.

_{1′}/W and thermal radiation flux Φ

_{2′}/W, and the calculations were performed by the equations below:

#### 4.2. Resilient Performance of the BWR Lattice

#### 4.2.1. Resilient Mechanism

#### 4.2.2. Influence of Compressive Failure on Thermal Insulation

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Design and 3D printing of the BWR lattice. (

**a**) Core of the BWR lattice; (

**b**) Vertical placement for specimen.

**Figure 2.**Measurement of thermal insulation performance for the BWR lattice: (

**a**) Image of thermal insulation performance test platform; (

**b**) Positions of thermocouples.

**Figure 4.**Thermal insulation performance of the BWR lattices: (

**a**) Curve of T

_{2}with heating time; (

**b**) Curve of T

_{1}with heating time; (

**c**) Image of S-1 after heating; (

**d**) Image of S-2 after heating.

**Figure 5.**Compressive performance of the BWR lattice: (

**a**) Force-Displacement curve of the BWR lattice; (

**b**) Compressive process of S-2.

**Figure 6.**Resilient and cycle resilient performance of the BWR lattices: (

**a**) Resilient performance; (

**b**) Cycle resilient performance of S-2; (

**c**) Image of the recovered S-1; (

**d**) Image of the recovered S-2.

**Figure 7.**Calculation of lattice thermal conduction performance: (

**a**) Equivalent coefficient of thermal conductivity; (

**b**) Schematic diagram of thermal radiation; (

**c**) Thermal flow of the lattices; (

**d**) Ratio of Φ1 in thermal flow.

**Figure 10.**Morphology of lattice after compressive failure: (

**a**) Morphology of rods in S-1; (

**b**) Morphology of rods in S-2; (

**c**) Morphology of rod connection positions in S-2; (

**d**) Morphology of rod deformation in S-2.

k | Designed Structure | Printed Structure | Truss Diameter /mm | Cell Size /mm | Lattice Size /mm | |
---|---|---|---|---|---|---|

S-1 | 6 | 0.75 | 15 × 15 × 2.5 | 45 × 45 × 10 | ||

S-2 | 8 | 0.75 | 20 × 20 × 2.5 | 40 × 40 × 20 |

Element | Al | V | Fe | O | N | Ti |
---|---|---|---|---|---|---|

Component (wt.%) | 6.16 | 4.3 | 0.163 | 0.0924 | 0.0104 | Bal. |

Scan Strategy | Scan Speed /mm·s ^{−1} | Laser Power /W | Hatch Spacing /μm | Layer Thickness /μm | |
---|---|---|---|---|---|

Parameters | S type | 900 | 95 | 60 | 30 |

λ_{0}/W·m ^{−1}·°C^{−1} | H /mm | L /mm | D /mm | n | m | |
---|---|---|---|---|---|---|

S-1 | 7.96 | 2.5 | 15 | 0.75 | 9 | 4 |

S-2 | 7.96 | 2.5 | 20 | 0.75 | 4 | 8 |

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**MDPI and ACS Style**

Wang, X.; Li, A.; Liu, X.; Wan, X.
Thermal Insulation and Compressive Performances of 3D Printing Flexible Load-Bearing and Thermal Insulation Integrated Lattice. *Materials* **2022**, *15*, 8625.
https://doi.org/10.3390/ma15238625

**AMA Style**

Wang X, Li A, Liu X, Wan X.
Thermal Insulation and Compressive Performances of 3D Printing Flexible Load-Bearing and Thermal Insulation Integrated Lattice. *Materials*. 2022; 15(23):8625.
https://doi.org/10.3390/ma15238625

**Chicago/Turabian Style**

Wang, Xin, Ang Li, Xuefeng Liu, and Xiangrui Wan.
2022. "Thermal Insulation and Compressive Performances of 3D Printing Flexible Load-Bearing and Thermal Insulation Integrated Lattice" *Materials* 15, no. 23: 8625.
https://doi.org/10.3390/ma15238625