# Experimental, Computational, and Dimensional Analysis of the Mechanical Performance of Fused Filament Fabrication Parts

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material Characterization

## 3. Experimental Procedure

#### 3.1. Uniaxial Tensile Tests

- Young’s modulus in the printing direction ${E}_{\perp}$ was obtained from the V-Cover specimen;
- Young’s modulus in the plane of isotropy ${E}_{iso}$ was obtained from the H-Cover specimen;
- The shear modulus in the printing direction G was obtained from the 45-Cover specimen with:$$G=\frac{{E}_{1}}{2(1+{\nu}_{12})}$$
- The shear modulus in the plane of isotropy ${G}_{iso}$ was obtained with:$${G}_{iso}=\frac{{E}_{iso}}{2(1+{\nu}_{iso})}$$

- Young’s modulus in the direction parallel to the filament ${E}_{\Vert}$ was obtained from the H-Contour specimen;
- Young’s modulus in the plane of isotropy ${E}_{iso}$ was obtained from the V-Contour specimen;
- The shear modulus in the direction parallel to the filament G was obtained from the 45-Contour specimen with Equation (2);
- The shear modulus in the plane of isotropy ${G}_{iso}$ was obtained from Equation (3).

#### 3.2. Bending Tests

^{2}. All samples for the bending tests were printed with contours and covers with a thickness equal to 1 mm, and the in-fill structure was conformed by a ±45° linear pattern.

## 4. Computational Characterization

#### 4.1. Representative Volume Element

#### 4.2. Multiscale Computational Homogenization

Algorithm 1: First-order computational homogenization. |

## 5. Experimental and Computational Results

#### 5.1. Tensile Tests

#### 5.2. Homogenization

#### 5.3. Experimental Validation

## 6. Dimensional Analysis on the Three-Zone Model

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AM | Additive Manufacturing |

MJF | Multi-Jet Fusion |

SLM | Selective Laser Melting |

EBM | Electron Beam Melting |

FFF | Fused Filament Fabrication |

FDM | Fused Deposition Modeling |

PLA | Polylactic Acid |

ABS/GP | General Purpose Acrylonitrile Butadiene Styrene |

ABS/PC | Polycarbonate Acrylonitrile Butadiene Styrene |

RVE | Representative Volume Element |

FOCH | First-Order Computational Homogenization |

BC | Boundary Condition |

ML | Machine Learning |

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**Figure 10.**Non-dimensional relationships for PLA, ABS/GP, and ABS/PC referred to raw material properties. (

**a**) Cover zone. (

**b**) Contour zone.

**Figure 11.**Non-dimensional relationships for PLA, ABS/GP, and ABS/PC referred to ${E}_{\Vert}$. (

**a**) Cover zone. (

**b**) Contour zone.

**Figure 12.**Non-dimensional relationships for the inner zone from all tested materials: Young’s modulus in direction X (

**a**), Young’s modulus in direction Z (

**b**), shear modulus in the XY plane (

**c**), shear modulus in the YZ plane (

**d**).

${\mathit{E}}_{\mathit{x}}$ | ${\mathit{E}}_{\mathit{y}}$ | ${\mathit{E}}_{\mathit{z}}$ | ${\mathit{\nu}}_{\mathbf{xy}}$ | ${\mathit{\nu}}_{\mathbf{yz}}$ | ${\mathit{\nu}}_{\mathbf{zx}}$ | ${\mathit{G}}_{\mathbf{xy}}$ | ${\mathit{G}}_{\mathbf{yz}}$ | ${\mathit{G}}_{\mathbf{zx}}$ | |
---|---|---|---|---|---|---|---|---|---|

Cover | ${E}_{iso}$ | ${E}_{iso}$ | ${E}_{\perp}$ | ${\nu}_{iso}$ | $\nu $ | $\nu $ | ${G}_{iso}$ | G | G |

Contour | ${E}_{\Vert}$ | ${E}_{iso}$ | ${E}_{iso}$ | $\nu $ | ${\nu}_{iso}$ | $\nu $ | G | ${G}_{iso}$ | G |

Printing Parameter | Value |
---|---|

Extrusion temperature (°C) | 250 |

Base temperature (°C) | 95 |

Layer thickness (mm) | 0.15 |

First layer printing speed (mm/s) | 15 |

Contour printing speed (mm/s) | 18 |

Cover printing speed (mm/s) | 20 |

Inner printing speed (mm/s) | 25 |

Material Properties | Cover | Contour |
---|---|---|

${E}_{\Vert}$ (GPa) ${E}_{\perp}$ (GPa) | 1.53 ± 0.09 | 1.86 ± 0.04 |

${E}_{iso}$ (GPa) | 1.51 ± 0.5 | 1.51 ± 0.03 |

${\nu}_{iso}$ | 0.36 ± 0.01 | 0.36 ± 0.01 |

$\nu $ | 0.36 ± 0.01 | 0.36 ± 0.01 |

G (GPa) | 0.232 ± 0.02 | 0.559 ± 0.02 |

${G}_{iso}$ (GPa) | 0.555 ± 0.2 | 0.555 ± 0.01 |

In-Fill (%) | 10 | 20 | 50 |
---|---|---|---|

${E}_{x}$ (MPa) | 0.61 | 5.47 | 129.99 |

${E}_{y}$ (MPa) | 0.61 | 5.47 | 130.02 |

${E}_{z}$ (MPa) | 186.00 | 372.00 | 930.00 |

${\nu}_{xy}$ | 0.99 | 0.9739 | 0.8022 |

${\nu}_{yz}$ | 0.3528 | 0.3530 | 0.3530 |

${\nu}_{xz}$ | 0.3532 | 0.3530 | 0.3530 |

${G}_{xy}$ (MPa) | 53.33 | 106.98 | 274.11 |

${G}_{yz}$ (MPa) | 35.84 | 74.83 | 219.43 |

${G}_{xz}$ (MPa) | 35.84 | 74.83 | 219.43 |

**Table 5.**Comparison between experimental and simulation results for the square cross-section bending test (ABS/PC material).

In-Fill Density (%) | Printing Orientation | ${\mathit{K}}_{\mathbf{experimental}}$ $(\mathit{N}/\mathbf{mm})$ | ${\mathit{K}}_{\mathbf{simulation}}$ $(\mathit{N}/\mathbf{mm})$ | Relative Difference (%) |
---|---|---|---|---|

10 | H | 174.33 | 161.18 | 7.54 |

V | 139.10 | 135.77 | 2.39 | |

20 | H | 179.26 | 177.13 | 1.19 |

V | 139.61 | 150.49 | 7.79 | |

50 | H | 223.25 | 220.67 | 1.16 |

V | 186.38 | 182.46 | 2.10 |

ASTM | Orientation | Pattern | Nomenclature | Characterized Property |
---|---|---|---|---|

ASTM D638 | Horizontal | Crossed (cover) | H-Cover | ${E}_{iso}^{cover}$, ${G}_{iso}^{cover}$ |

Aligned (contour) | H-Contour | ${E}_{\Vert}$ | ||

Vertical | Crossed (cover) | V-Cover | ${E}_{\perp}$ | |

Aligned (contour) | V-Contour | ${E}_{iso}^{contour}$, ${G}_{iso}^{contour}$ | ||

45° | Crossed (cover) | 45-Cover | ${G}^{cover}$ | |

Aligned (contour) | 45-Contour | ${G}^{contour}$ | ||

ASTM D790 | Horizontal | In-fill 10% | H-10 | |

In-fill 20% | H-20 | |||

In-fill 50% | H-50 | |||

Vertical | In-fill 10% | V-10 | ||

In-fill 20% | V-20 | |||

In-fill 50% | V-50 |

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

${E}_{iso}^{cover}/{E}_{\Vert}$ | 0.80 |

${G}_{iso}^{cover}/{E}_{\Vert}$ | 0.30 |

${E}_{\Vert}/{E}_{raw}$ | 0.87 |

${E}_{iso}^{contour}/{E}_{\Vert}$ | 0.82 |

${G}^{contour}/{E}_{\Vert}$ | 0.31 |

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**MDPI and ACS Style**

Rivet, I.; Dialami, N.; Cervera, M.; Chiumenti, M.; Reyes, G.; Pérez, M.A.
Experimental, Computational, and Dimensional Analysis of the Mechanical Performance of Fused Filament Fabrication Parts. *Polymers* **2021**, *13*, 1766.
https://doi.org/10.3390/polym13111766

**AMA Style**

Rivet I, Dialami N, Cervera M, Chiumenti M, Reyes G, Pérez MA.
Experimental, Computational, and Dimensional Analysis of the Mechanical Performance of Fused Filament Fabrication Parts. *Polymers*. 2021; 13(11):1766.
https://doi.org/10.3390/polym13111766

**Chicago/Turabian Style**

Rivet, Iván, Narges Dialami, Miguel Cervera, Michele Chiumenti, Guillermo Reyes, and Marco A. Pérez.
2021. "Experimental, Computational, and Dimensional Analysis of the Mechanical Performance of Fused Filament Fabrication Parts" *Polymers* 13, no. 11: 1766.
https://doi.org/10.3390/polym13111766