# Multi-Scale Modeling and Simulation of Thermoplastic Automated Tape Placement: Effects of Metallic Particles Reinforcement on Part Consolidation

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Surface Description and Its Time Evolution

#### 2.2. Particle Orientation Model

#### Homogenized Thermal Conductivity

## 3. Process Modeling and Simulation

- An Eulerian frame, in which the tape moves while the laying head remains at rest, is considered. This frame choice allows one to reduce the thermal and squeezing flow calculation to the tape cross-section depicted in Figure 2.
- The domain of the study consists of an m-plies laminate. We consider more than 6 plies in order to limit the effect of the boundary condition between the substrate and the tool.
- The metallic particles contained in the prepreg are considered well dispersed and isotropically oriented at the beginning of the forming stage. The orientation evolution and induced properties are computed all along the consolidation process.
- Room temperature was assumed as the initial temperature of the incoming tape.
- Parameters involved in the simulation are reported in Table 2.

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Surface acquisition using a profilometer (

**left**) and measured profile (

**right**) representing the relative height z(m).

**Figure 4.**(

**left**) Heating flux; (

**right**) pressure field applied by the roller associated with a compression force of 600 N (the dimensions being 3 cm (fiber direction) × 1.5 cm (tape width)) − Value of Max Pressure: 5 MPa).

**Figure 5.**Effect of the filler concentration $\varphi $ on viscosity (

**top**) and conductivity (

**bottom**): the uncoupled model.

**Figure 6.**Effect of filler concentration $\varphi $ on the degree of intimate contact: the coupled model.

**Table 1.**Surface roughness parameters according to ISO 4287 (values correspond to the micro- roughness [4]).

Surface | ${\mathit{R}}_{\mathit{a}}(\mathsf{\mu}$m) | ${\mathit{R}}_{\mathit{t}}(\mathsf{\mu}$m) | ${\mathit{R}}_{\mathit{s}}(\mathsf{\mu}$m) |
---|---|---|---|

Surface 1 | $0.8$ | $10.5$ | 103 |

Surface 2 | $2.1$ | $25.3$ | 13 |

**Table 2.**Simulation parameters: specific heat $Cp$; power index n [22]; air and composite conductivities ${K}_{a}$ and ${K}_{m}$, the last associated to the plane perpendicular to the fiber direction; thermal exchange coefficients ${h}_{air}$, ${h}_{mould}$, and ${h}_{roller}$ between the composite and respectively the air, mould, and roller; the applied force $\mathcal{F}$; the laying velocity ${V}_{laser}$; the applied laser power ${P}_{laser}$; the number of plies m; the air and mould temperatures ${T}_{amb}$ and ${T}_{mould}$ respectively; and finally the metallic particles conductivity ${K}_{p}$.

Parameters of Simulation | |||
---|---|---|---|

$\rho \phantom{\rule{0.166667em}{0ex}}Cp$ | 2.2 × 10${}^{6}$ | $\mathcal{F}$ | 600 N |

n | $0.65$ | ${K}_{m}$ | 0.5 W/(m K) |

${K}_{a}$ | 0.024 W/(mK) | ${h}_{c}$ | 4000 K m${}^{2}$/W |

${h}_{air}$ | 10 K m${}^{2}$/W | ${h}_{mould}$ | 2500 K m${}^{2}$/W |

${h}_{roller}$ | 2000 K m${}^{2}$/W | ${V}_{laser}$ | 0.1 m/s |

m | 6 | ${T}_{amb}$ | 25 ${}^{\circ}$C |

${T}_{Mould}$ | 25 ${}^{\circ}$C | ${P}_{laser}$ | 720 W |

${K}_{p}$ | 60 W/(m K) |

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**MDPI and ACS Style**

Leon, A.; Perez, M.; Barasinski, A.; Abisset-Chavanne, E.; Defoort, B.; Chinesta, F. Multi-Scale Modeling and Simulation of Thermoplastic Automated Tape Placement: Effects of Metallic Particles Reinforcement on Part Consolidation. *Nanomaterials* **2019**, *9*, 695.
https://doi.org/10.3390/nano9050695

**AMA Style**

Leon A, Perez M, Barasinski A, Abisset-Chavanne E, Defoort B, Chinesta F. Multi-Scale Modeling and Simulation of Thermoplastic Automated Tape Placement: Effects of Metallic Particles Reinforcement on Part Consolidation. *Nanomaterials*. 2019; 9(5):695.
https://doi.org/10.3390/nano9050695

**Chicago/Turabian Style**

Leon, Angel, Marta Perez, Anaïs Barasinski, Emmanuelle Abisset-Chavanne, Brigitte Defoort, and Francisco Chinesta. 2019. "Multi-Scale Modeling and Simulation of Thermoplastic Automated Tape Placement: Effects of Metallic Particles Reinforcement on Part Consolidation" *Nanomaterials* 9, no. 5: 695.
https://doi.org/10.3390/nano9050695