# Orientation-Dependent Mechanical Behavior of 3D Printed Polylactic Acid Parts: An Experimental–Numerical Study

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^{4}

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## Abstract

**:**

## 1. Introduction

_{1}, E

_{2}, U

_{12}, and G

_{12}, which are critical for understanding the material’s properties. Somireddy et al. [20] introduced a constitutive modeling approach for FFF-printed components using a numerical homogenization technique. Their work revealed that the material behavior within various sections of the structure was not uniform and was influenced by factors like build orientation and part thickness. Domingo-Espin et al. [21] characterized FFF-printed parts as anisotropic solids and derived nine elastic constants for use in simulations. They further designed and produced a basic part in multiple orientations for both physical testing and simulation purposes. Abadi et al. [22] conducted an assessment of the elastic properties of 3D printed fiber-reinforced polymers. Their parametric study findings demonstrated that the quantity of fiber reinforcements and their arrangement significantly affected the structural performance of the 3D printed composite parts made from fiber-reinforced polymers.

## 2. Theoretical Modeling

_{12}, F

_{13}, and F

_{23}represent additional parameters, and various methods exist to determine them. For both criteria, when the right side of the equation reaches 1, failure occurs. As the thickness of the specimens is relatively small compared to other dimensions, the plane stress assumption can be applied. Consequently, the formulas under failure conditions can be expressed as follows:

_{1}= F

_{2}= 0.

_{1}):

_{12}(Tsai–Wu

_{2}):

## 3. Material and Experimental Methodology

#### 3.1. PLA Filament

^{®}, was used for specimen construction. Table 1 displays certain physico-chemical characteristics of this filament.

#### 3.2. D Printer Device

_{L}= 230 °C, T

_{P}= 70 °C, and V

_{L}= 40 mm·s

^{−1}.

#### 3.3. Characterization Methods, Experimental Procedures, and Specimen Preparation

#### 3.3.1. Microscopic Observation

#### 3.3.2. Quasi-Static Tensile Test and Specimen Preparation

## 4. Results and Discussions

#### 4.1. Quasi-Static Tensile Behavior of 3D Printed Specimens

#### 4.1.1. PLA Filaments

#### 4.1.2. Impact of Filament Orientation on the Tensile Behavior (3D Printed Vertical Walls)

- The higher the orientation angle, the higher the strength of the material.
- The higher the orientation angle, the higher the ductility.
- When the orientation angle is increased, Young’s modulus increases by about 40%.
- When the orientation angle is increased, Ductility increases by about 70%.

#### 4.1.3. Quasi-Static Tensile Behavior of 3D Printed Specimens in Various Orientations

#### 4.2. Validation of Tsai–Hill and Tsai–Wu Models

_{1}implements an increase in prediction error. Consequently, we recommend the preferential utilization of either the Tsai–Hill or Tsai–Wu

_{2}criteria for accurate prediction of tensile strength in materials subjected to our experimental conditions. An in-depth evaluation of predictive accuracy suggests that, while a predictive error of less than 20% is generally deemed acceptable for materials of variable nature, the model consistently aligns with its direction of error. This consistency in error direction enhances the reliability of the model’s predictions. Notably, the model tends to adopt a conservative stance in estimating ultimate stress, an outcome that augurs well for the design process as it promotes safety. The outcomes derived from our study effectively capture the nuanced impact of build orientation, with both criteria underscoring the pivotal role of this parameter in determining material performance. It is pertinent to highlight that previous research efforts in this domain often relied on a singular criterion, thereby limiting the precision and applicability of their findings [34,35]. In contrast, our approach utilizes both Tsai–Hill and Tsai–Wu

_{2}criteria, allowing for a more comprehensive integration of multiple phenomena and ensuring a more robust and inclusive understanding of the predictive capabilities of these models.

#### 4.3. Finite Element Analysis

## 5. Perspective: Interaction of Parameters

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Representation of (

**a**) proposed filaments for tensile test, (

**b**) location of specimens on the printed solid blocks, and (

**c**) printed specimens in different orientations.

**Figure 4.**(

**a**–

**e**) Quasi-static tensile behavior and (

**f**) ultimate strength (σ

_{max}) of 3D printed specimens for various orientations.

**Figure 7.**(

**a**–

**e**) Comparison between FEM results and experimental test data of 3D printed specimens for various orientations.

**Figure 8.**Comparison between FEM results and experimental test data of 3D printed specimens during tensile test for (

**a**) θ = 0° and (

**b**) θ = 90°.

Properties | Typical Value |
---|---|

Material density | 1.24 g/cm^{3} |

Diameter (tolerance) | 1.75 mm (±0.01 mm) |

Glass transition temperature | 72 °C |

Crystallization temperature | 103 °C |

Melting temperature | 158 °C |

**Table 2.**Quasi-static tensile behavior of specimens cut from vertical walls printed for various orientations.

Orientation | E (GPa) | Yield Strength (MPa) | ${\mathit{\epsilon}}_{\mathit{f}}$ (mm/mm) |
---|---|---|---|

0° | 0.6 ± 0.052 | 20 ± 1.15 | 0.11 ± 0.019 |

30° | 0.7 ± 0.046 | 25 ± 1.05 | 0.15 ± 0.014 |

45° | 0.9 ± 0.050 | 30 ± 1.09 | 0.17 ± 0.017 |

60° | 1.0 ± 0.054 | 50 ± 1.17 | 0.35 ± 0.022 |

90° | 1.1 ± 0.048 | 65 ± 1.06 | 0.6 ± 0.21 |

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**MDPI and ACS Style**

Vanaei, S.; Rastak, M.; El Magri, A.; Vanaei, H.R.; Raissi, K.; Tcharkhtchi, A.
Orientation-Dependent Mechanical Behavior of 3D Printed Polylactic Acid Parts: An Experimental–Numerical Study. *Machines* **2023**, *11*, 1086.
https://doi.org/10.3390/machines11121086

**AMA Style**

Vanaei S, Rastak M, El Magri A, Vanaei HR, Raissi K, Tcharkhtchi A.
Orientation-Dependent Mechanical Behavior of 3D Printed Polylactic Acid Parts: An Experimental–Numerical Study. *Machines*. 2023; 11(12):1086.
https://doi.org/10.3390/machines11121086

**Chicago/Turabian Style**

Vanaei, Saeedeh, Mohammadali Rastak, Anouar El Magri, Hamid Reza Vanaei, Kaddour Raissi, and Abbas Tcharkhtchi.
2023. "Orientation-Dependent Mechanical Behavior of 3D Printed Polylactic Acid Parts: An Experimental–Numerical Study" *Machines* 11, no. 12: 1086.
https://doi.org/10.3390/machines11121086