# The Effect of a Phase Change on the Temperature Evolution during the Deposition Stage in Fused Filament Fabrication

^{1}

^{2}

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## Abstract

**:**

^{®}code to model cooling in FFF. The deposition and cooling of simple geometries is studied first, in order to assess the differences in cooling of amorphous and semi-crystalline polymers. Acrylonitrile Butadiene Styrene (ABS) was taken as representing an amorphous material. Then, the deposition and cooling of a realistic 3D part is investigated, and the influence of the build orientation is discussed.

## 1. Introduction

## 2. Related Work

## 3. A code for the Prediction of Temperature Evolution during Cooling in FFF

#### 3.1. Current Code

^{®}, which activates/deactivates contacts and thermal conditions arising as the deposition proceeds, depending on the part geometry, deposition sequence and operating conditions. By coupling a bonding criterion to the temperature profile history, it is also possible to predict the degree of bonding between adjacent filaments [28]. The following assumptions are considered in the model:

- The axial heat conduction is neglected. Given the low thermal conductivity of polymers and the small filaments radii, axial heat conduction is much smaller than convection and conduction between adjacent filaments;
- Computations are carried out when the Biot number is lower than 0.1, i.e., when the temperature gradient in each filament cross-section can be neglected;
- The thermal properties of the polymer are assumed to be temperature independent;
- The thermal contact conductance is assumed to be low (high thermal resistance) while bonding is not achieved, and high when bonding occurs.

#### 3.2. Insertion of a Phase Change

- Crystallization development during cooling does not affect the thermal properties, which are taken as temperature independent;
- When the temperature of the ${r}^{th}$ filament segment reaches ${T}_{solid}$, the thermal conditions used to compute ${\tau}_{s}$ are activated at ${\tau}_{l}$;
- If ${\left({\left({T}_{r}\right)}_{i}\right)}_{0}$ is the temperature of the adjacent filament segment for contact $i$ at instant ${\tau}_{l}$, the value of ${\left({T}_{r}\right)}_{i}$ will be assumed as the average between ${\left({\left({T}_{r}\right)}_{i}\right)}_{0}$ and ${T}_{E}$;
- If during a phase change a filament contacts a new hotter filament, its phase change is interrupted and the temperatures are re-computed. When its temperature reaches again ${T}_{solid}$, ${\tau}_{s}$ is computed for the new thermal conditions;

^{®}code is shown in Figure 4. This section was inserted in the computer code previously developed by the authors [35].

## 4. Application of the Code to Simple 3D Printed Structures

^{®}, Edina, MI, USA) and PLA (881N PLA, Filkemp

^{®}, Algueirão–Mem Martins, Portugal). Table 2 identifies the process parameters and computational variables. The heat transfer coefficient h

_{conv}was deduced using the correlation of Churchill and Chu [36], a high conductance between adjacent filaments was assumed, and an intermediate value for the extrusion temperature was considered to be suitable for both ABS and PLA. The version 9.2.0.556344 (R2017a) of MatLab

^{®}was used.

## 5. Applied Case Study

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Evolution of temperature with time for a single PLA filament with and without phase change (at x = 30 mm from the edge).

**Figure 7.**Evolution of temperature with time for filament no. 2 (PLA) with and without phase change (at x = 30 mm from the edge).

**Figure 8.**Evolution of temperature with time for filament no. 2 for ABS and PLA (at x = 30 mm from the edge).

**Figure 10.**Temperature evolution during 3800 s of the cross-section at the middle of the central filament of the 20th layer (counting from the support) for the six build orientations, for ABS and PLA. The curves follow the evolution with time of temperature from the beginning of the deposition of the filament. The actual instants where the deposition began for each build orientation are identified in the respective labels.

**Figure 11.**Temperature evolution of the cross-section at the middle of the central filament of the 20th layer (counting from the support) for the six build orientations (P1 to P6), for ABS and PLA. The curves follow the evolution with time of temperature from the beginning of the deposition of the part. The insets are magnifications of the progress of temperature during short time periods. A, B and C identify the peaks used to prepare Table 4.

Property | ABS | PLA |
---|---|---|

Density $\rho $ (kg/m^{3}) | 1050 | 1300 |

Thermal conductivity $k$ (W/m·$\xb0\mathrm{C}$) | 0.2 | 0.1 |

Specific heat $C$ (J/kg·$\xb0\mathrm{C}$) | 2020 | 2100 |

Latent heat of fusion $\lambda $ (J/kg) | --- | 30 000 |

Solidification temperature ${T}_{solid}$ ($\xb0\mathrm{C}$) | --- | 150 |

Property | Value |
---|---|

Process parameters | |

Extrusion temperature T_{L} ($\xb0\mathrm{C}$) | 230 |

Environment temperature T_{E} ($\xb0\mathrm{C}$) | 25 |

Deposition velocity (m/s) | 0.03 |

Convective heat transfer coefficient h_{conv} (W/m^{2} $\xb0\mathrm{C}$)—natural convection | 30 |

Thermal contact conductance between adjacent filaments h_{i} (W/m^{2}$\xb0\mathrm{C}$) | 200 |

Thermal contact conductance between filaments and support h_{i} (W/m^{2}$\xb0\mathrm{C}$) | 10 |

Fraction of contact area relative to filament area ${\alpha}_{i}$ | 0.2 |

Filament length (mm) | 60 |

Filament cross-section geometry | circle |

Filament cross-section diameter (mm) | 0.25 |

Deposition sequence | Unidirectional and aligned |

Computational parameters | |

Time increment (s) | 0.01 |

Temperature convergence error ($\xb0\mathrm{C}$) | 0.001 |

Build Orientation | Number of Filaments | Contact Area with the Support (mm^{2}) |
---|---|---|

P1 ($XZY$) | 28,800 | 2700 |

P2 ($XYZ$) | 28,800 | 5400 |

P3 ($YXZ$) | 43,200 | 5400 |

P4 ($ZXY$) | 43,200 | 1800 |

P5 ($ZYX$) | 86,400 | 1800 |

P6 ($YZX$) | 86,400 | 2700 |

**Table 4.**The effect of the type of material (ABS vs. PLA) on the temperature of the cross-section at the middle of the central filament of the 20th layer (counting from the support) for six build orientations, P1 to P6 (maximum temperature difference and temperatures of peaks A, B and C in Figure 11).

Build Orientation | Maximum Temperature Difference between ABS and PLA (°C) | Maximum Temperature of Peaks A (°C) | Maximum Temperature of Peaks B (°C) | Maximum Temperature of Peaks C (°C) |
---|---|---|---|---|

P1 | 40.4 | ABS: 56.2 PLA: 64.8 | ABS: 40.7 PLA: 45.2 | ABS: 33.8 PLA: 36.4 |

P2 | 39.4 | ABS: 56.1 PLA: 64.9 | ABS: 40.6 PLA: 45.2 | ABS: 33.7 PLA: 36.4 |

P3 | 41.6 | ABS: 60.3 PLA: 72.6 | ABS: 43.6 PLA: 51.0 | ABS: 35.9 PLA: 39.1 |

P4 | 41.2 | ABS: 61.0 PLA: 70.2 | ABS: 43.8 PLA: 49.8 | ABS: 35.9 PLA: 39.4 |

P5 | 40.4 | ABS: 73.6 PLA: 83.6 | ABS: 52.6 PLA: 59.7 | ABS: 41.4 PLA: 46.1 |

P6 | 40.4 | ABS: 73.6 PLA: 83.5 | ABS: 52.6 PLA: 59.7 | ABS: 41.4 PLA: 46.1 |

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**MDPI and ACS Style**

Costa, S.F.; Duarte, F.M.; Covas, J.A.
The Effect of a Phase Change on the Temperature Evolution during the Deposition Stage in Fused Filament Fabrication. *Computers* **2021**, *10*, 19.
https://doi.org/10.3390/computers10020019

**AMA Style**

Costa SF, Duarte FM, Covas JA.
The Effect of a Phase Change on the Temperature Evolution during the Deposition Stage in Fused Filament Fabrication. *Computers*. 2021; 10(2):19.
https://doi.org/10.3390/computers10020019

**Chicago/Turabian Style**

Costa, Sidonie F., Fernando M. Duarte, and José A. Covas.
2021. "The Effect of a Phase Change on the Temperature Evolution during the Deposition Stage in Fused Filament Fabrication" *Computers* 10, no. 2: 19.
https://doi.org/10.3390/computers10020019