# Modeling of Effect of Infill Density Percentage on Rotating Bending Fatigue Behavior of Additive-Manufactured PLA Polymers

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

^{−2}. This variability in results is due to the PLA supplier and the applied 3D printing parameters. Indeed, the FFF printing process depends on 13 parameters that affect the mechanical performance of the product. These parameters can be categorized into two classes [31]: the layering and device parameters. The first class refers to the topological parameters that can be controlled by the slicing software, such as the raster angle, the print direction (also called build orientation), the infill pattern, the infill density, the layer height, the extrusion width, the air gap, the solid layers, and the perimeters. The second class refers to the parameters associated with the 3D printing device itself, such as the print speed, the nozzle diameter, the nozzle temperature, and the platform temperature. While the influence of FFF printing parameters on quasi-static mechanical characterization has been widely discussed within the literature [31,32,33], there are limited accounts of this effect on fatigue performance. For example, Azadi et al. [34] investigated the impact of the print direction on the bending fatigue properties of PLA: a shorter fatigue lifetime was obtained for vertical specimens than that of horizontal samples. Shanmugam et al. [35] investigated the effect of the nozzle diameter, the extrusion temperature, the bed temperature, the extrusion speed rate, and the layer height on fatigue. They concluded that the printing parameters have a significant impact on fatigue behavior, which need to be optimized. They also concluded that the defects and voids are common problems in FFF, and would be considered factors since they increased the stress concentration.

_{%}) of dog bone samples (25%, 50%, 75%, and 100%) are tested. Wöhler and Basquin models are used to express S–N data. Updated expressions of the cited models are implemented to consider the effect of infill density on fatigue model constants. The new formulations are validated with success according to extra experimental configuration tests.

## 2. Experimental Set-Up and Analysis Methodology

#### 2.1. Fatigue Samples

#### 2.2. Fatigue Testing

#### 2.3. Fatigue Life Modeling

_{f}is the number of cycles to failure, and ${C}_{W1}$ and ${C}_{W2}$ are Wöhler material positive constants.

## 3. Results and Discussion

_{%}) to formulate a unique equation that considers its contribution to the model formulation. The results are validated with additional experiments.

#### 3.1. Fatigue Specimen Sampling

#### 3.2. Fatigue Behavior Modeling

_{f}cycles for a low load (14 MPa). Indeed, the ratio of N

_{f min}to N

_{f max}at 14 MPa is 2.66, 4.84, 6.10 and 6.13 for infill percentages of 25, 50, 75 and 100%, respectively. However, for the other loads, this ratio ranges between 2 and 3.8, between 1.5 and 2.2 and between 1.5 and 2.2 for 35 MPa, 49 MPa and 70 MPa, respectively.

_{f}(Figure 4). The S–N curves show the expected material behavior under a cyclic load: N

_{f}logically goes up with the increase in f

_{%}and decreases with the rise in the load (see Figure 5).

#### 3.2.1. Wöhler Model

^{2}: coefficient of determination).

_{%}. Equations (4) and (5) express the obtained least squares regression with a coefficient of determination of 0.96 for ${C}_{W1}$ and of 0.97 for ${C}_{W2}$.

#### 3.2.2. Basquin Model

_{%}. Equations (6) and (7) express the obtained least squares regression with a coefficient of determination, R

^{2}, of 0.98 for ${C}_{B1}$ and of 0.97 for ${C}_{B2}$.

#### 3.2.3. Validation of Models

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Infill Percentage | ||||
---|---|---|---|---|

Specimen N° | 25% | 50% | 75% | 100% |

1 | 25,300 | 146,050 | 249,250 | 1,020,750 |

2 | 43,200 | 289,800 | 1,454,800 | 424,750 |

3 | 20,000 | 222,400 | 485,300 | 982,700 |

4 | 23,200 | 68,200 | 1,451,940 | 762,700 |

5 | 42,800 | 321,600 | 392,150 | 1,055,780 |

6 | 16,250 | 205,100 | 1,057,400 | 2,284,000 |

7 | 28,500 | 330,300 | 1,520,200 | 2,605,000 |

8 | 31,600 | 188,100 | 872,300 | 2,552,300 |

9 | 38,800 | 290,600 | 558,350 | 435,000 |

10 | 33,100 | 303,700 | 740,150 | 499,150 |

mean | 30,275 | 236,585 | 878,184 | 1,262,213 |

standard deviation | 9349 | 85,866 | 472,994 | 876,096 |

n | 26 | 36 | 79 | 132 |

${\mathit{C}}_{\mathit{W}1}$ | ${\mathit{C}}_{\mathit{W}2}$ | R^{2} | |
---|---|---|---|

25% | 4.719 | 0.0190 | 0.987 |

50% | 5.763 | 0.0329 | 0.950 |

75% | 6.336 | 0.0409 | 0.952 |

100% | 6.460 | 0.0417 | 0.936 |

${\mathit{C}}_{\mathit{B}1}$ | ${\mathit{C}}_{\mathit{B}2}$ | R^{2} | |
---|---|---|---|

25% | 6.206 | 1.4678 | 0.955 |

50% | 8.420 | 2.5953 | 0.956 |

75% | 9.740 | 3.2922 | 0.996 |

100% | 9.974 | 3.3825 | 0.999 |

σ (MPa) | ${\mathbf{f}}_{\mathit{\%}}$ (%) |
---|---|

28 | 35 |

28 | 70 |

28 | 85 |

63 | 40 |

63 | 60 |

63 | 80 |

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**MDPI and ACS Style**

Ftoutou, E.; Allegue, L.; Marouani, H.; Hassine, T.; Fouad, Y.; Mrad, H.
Modeling of Effect of Infill Density Percentage on Rotating Bending Fatigue Behavior of Additive-Manufactured PLA Polymers. *Materials* **2024**, *17*, 471.
https://doi.org/10.3390/ma17020471

**AMA Style**

Ftoutou E, Allegue L, Marouani H, Hassine T, Fouad Y, Mrad H.
Modeling of Effect of Infill Density Percentage on Rotating Bending Fatigue Behavior of Additive-Manufactured PLA Polymers. *Materials*. 2024; 17(2):471.
https://doi.org/10.3390/ma17020471

**Chicago/Turabian Style**

Ftoutou, Ezzeddine, Lamis Allegue, Haykel Marouani, Tarek Hassine, Yasser Fouad, and Hatem Mrad.
2024. "Modeling of Effect of Infill Density Percentage on Rotating Bending Fatigue Behavior of Additive-Manufactured PLA Polymers" *Materials* 17, no. 2: 471.
https://doi.org/10.3390/ma17020471