# Rotating Bending Fatigue Analysis of Printed Specimens from Assorted Polymer Materials

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Tensile Tests

#### 2.2. Rotating Fatigue Tests

_{a}= 112.5 × t, where R

_{a}is the surface roughness in µm and t the layer height in mm. With the nozzle diameter of the 3D printer used for preparing samples equal to 0.2 mm with a layer height of 0.2 mm, the surface roughness of the used specimens was R

_{a}= 22.5 µm, which is in accordance with the surface roughness that can be found in the literature for similar FFF parameters and polymers [36].

## 3. Fatigue Test Results and Discussion

_{a}represents the constant stress amplitude in the equation where the fatigue life is given in the form of two reversals, 2N

_{f}, while σ

_{m}represents the peak stress in formulation with the given fatigue life, N

_{f}. ${\sigma}_{f}^{\prime}$ and α are the fatigue strength coefficients, while b and β represent the fatigue strength exponent. These last mentioned coefficients belong to the group of model-fitting parameters. The expression given in (3) is widely used in the fatigue analysis based on the stress approach. In order to obtain the mentioned typical S–N curve equation, the least-squares regression model (4) serves as a starting point:

_{i}and y

_{i}are the measured values of stress and the number of cycles for the ith specimen, respectively, from altogether an n number of specimens, and x

_{avg}, y

_{avg}are the average values of the x and y series, given by $\sum {x}_{i}/n$ and $\sum {y}_{i}/n$, respectively. Equation (3) can be written in logarithmic form, taking logarithms with base 10 of both sides of the equation and rearranging it:

^{5}cycles. It is also worth noting, and it can be clearly seen on diagrams, that specimens with the lowest applied stress value reached the failure.

## 4. Conclusions

- Comparison of different infill densities of FFF (3D printed) specimens and infill patterns and their influence on mechanical and fatigue properties;
- Different cycle rate values;
- Numerical modelling, using finite element method, based on proposed analytical models and findings;
- Fracture surface analysis;
- Surface roughness influence on fatigue fracture and cyclic durability;
- Influence of ultraviolet radiation and temperature on FFF polymer specimens.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- ASTM F2792-12a. Standard Terminology for Additive Manufacturing Technologies. Available online: www.astm.org (accessed on 1 March 2021).
- Caulfield, B.; McHugh, P.; Lohfeld, S. Dependence of mechanical properties of polyamide components on build parameters in the SLS process. J. Mater. Process. Technol.
**2007**, 182, 477–488. [Google Scholar] [CrossRef] - Sharma, M.; Ziemian, C. Anisotropic Mechanical Properties of ABS Parts Fabricated by Fused Deposition Modelling. Mech. Eng.
**2012**. [Google Scholar] [CrossRef] [Green Version] - Rendeki, S.; Nagy, B.; Bene, M.; Pentek, A.; Toth, L.; Szanto, Z.; Told, R.; Maroti, P. An Overview on Personal Protective Equipment (PPE) Fabricated with Additive Manufacturing Technologies in the Era of COVID-19 Pandemic. Polymers
**2020**, 12, 2703. [Google Scholar] [CrossRef] [PubMed] - Cantrell, J.T.; Rohde, S.; Damiani, D.; Gurnani, R.; DiSandro, L.; Anton, J.; Young, A.; Jerez, A.; Steinbach, D.; Kroese, C.; et al. Experimental characterization of the mechanical properties of 3D-printed ABS and polycarbonate parts. Rapid Prototyp. J.
**2017**, 23, 811–824. [Google Scholar] [CrossRef] - Barkhad, M.S.; Abu-Jdayil, B.; Mourad, A.H.I.; Iqbal, M.Z. Thermal Insulation and Mechanical Properties of Polylactic Acid (PLA) at Different Processing Conditions. Polymers
**2020**, 12, 2091. [Google Scholar] [CrossRef] [PubMed] - Gong, B.; Cui, S.; Zhao, Y.; Sun, Y.; Ding, Q. Strain-controlled fatigue behaviors of porous PLA-based scaffolds by 3D-printing technology. J. Biomater. Sci. Polym. Ed.
**2017**, 28, 2196–2204. [Google Scholar] [CrossRef] [PubMed] - Tokiwa, Y.; Calabia, B.P. Biodegradability and biodegradation of poly(lactide). Appl. Microbiol. Biotechnol.
**2006**, 72, 244–251. [Google Scholar] [CrossRef] - Senatov, F.; Niaza, K.; Stepashkin, A.; Kaloshkin, S. Low-cycle fatigue behavior of 3d-printed PLA-based porous scaffolds. Compos. Part B Eng.
**2016**, 97, 193–200. [Google Scholar] [CrossRef] - Tanikella, N.G.; Wittbrodt, B.; Pearce, J.M. Tensile strength of commercial polymer materials for fused filament fabrication 3D printing. Addit. Manuf.
**2017**, 15, 40–47. [Google Scholar] [CrossRef] [Green Version] - Johnson, G.A.; French, J.J. Evaluation of Infill Effect on Mechanical Properties of Consumer 3D Printing Materials. Adv. Technol. Innov.
**2018**, 3, 179–184. [Google Scholar] - Ma, Y.-Q.; Pang, Y.-Y. Mechanism study on char formation of zinc acetylacetonate on ABS resin. Chin. J. Polym. Sci.
**2015**, 33, 772–782. [Google Scholar] [CrossRef] - Datta, P.; Guha, C.; Sarkhel, G. Effect of Na-ionomer on dynamic rheological, dynamic mechanical and creep properties of acrylonitrile styrene acrylate (ASA)/Na+1poly (ethylene-co-methacrylic acid) ionomer blend. Polym. Adv. Technol.
**2014**, 25, 1454–1463. [Google Scholar] [CrossRef] - Datta, P.; Guha, C.; Sarkhel, G. Study of Dynamic Rheological, Dynamic Mechanical and Creep Properties of Acrylonitrile Styrene Acrylate (ASA)/Zn+2poly(ethylene-co-methacrylic acid) Ionomer Blend. J. Macromol. Sci. Part A
**2014**, 51, 820–830. [Google Scholar] [CrossRef] - Dickson, A.N.; Abourayana, H.M.; Dowling, D.P. 3D Printing of Fibre-Reinforced Thermoplastic Composites Using Fused Filament Fabrication—A Review. Polymers
**2020**, 12, 2188. [Google Scholar] [CrossRef] [PubMed] - Van Der Klift, F.; Koga, Y.; Todoroki, A.; Ueda, M.; Hirano, Y.; Matsuzaki, R. 3D Printing of Continuous Carbon Fibre Reinforced Thermo-Plastic (CFRTP) Tensile Test Specimens. Open J. Compos. Mater.
**2016**, 6, 18–27. [Google Scholar] [CrossRef] [Green Version] - Khatri, B.; Lappe, K.; Habedank, M.; Mueller, T.; Megnin, C.; Hanemann, T. Fused Deposition Modeling of ABS-Barium Titanate Composites: A Simple Route towards Tailored Dielectric Devices. Polymers
**2018**, 10, 666. [Google Scholar] [CrossRef] [Green Version] - Blanco, I. The Use of Composite Materials in 3D Printing. J. Compos. Sci.
**2020**, 4, 42. [Google Scholar] [CrossRef] [Green Version] - Stoof, D.; Pickering, K.; Zhang, Y. Fused Deposition Modelling of Natural Fibre/Polylactic Acid Composites. J. Compos. Sci.
**2017**, 1, 8. [Google Scholar] [CrossRef] [Green Version] - Liu, X.; Shapiro, V. Homogenization of material properties in additively manufactured structures. Comput. Des.
**2016**, 78, 71–82. [Google Scholar] [CrossRef] [Green Version] - Afrose, M.F.; Masood, S.H.; Nikzad, M.; Iovenitti, P.G. Effects of Build Orientations on Tensile Properties of PLA Material Processed by FDM. Adv. Mater. Res.
**2014**, 1044–1045, 31–34. [Google Scholar] [CrossRef] - Tymrak, B.; Kreiger, M.; Pearce, J. Mechanical properties of components fabricated with open-source 3-D printers under realistic environmental conditions. Mater. Des.
**2014**, 58, 242–246. [Google Scholar] [CrossRef] [Green Version] - Galeja, M.; Hejna, A.; Kosmela, P.; Kulawik, A. Static and Dynamic Mechanical Properties of 3D Printed ABS as a Function of Raster Angle. Materials
**2020**, 13, 297. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Montero, M.; Roundy, S.; Odell, D. Material characterization of fused deposition modeling (FDM) ABS by designed experiments. Proc. Rapid Prototyp. Manuf. Conf.
**2001**, 1–21. [Google Scholar] - Ahn, S.; Montero, M.; Odell, D.; Roundy, S.; Wright, P.K. Anisotropic material properties of fused deposition modeling ABS. Rapid Prototyp. J.
**2002**, 8, 248–257. [Google Scholar] [CrossRef] [Green Version] - Cuan-Urquizo, E.; Barocio, E.; Tejada-Ortigoza, V.; Pipes, R.B.; Rodriguez, C.A.; Roman-Flores, A. Characterization of the Mechanical Properties of FFF Structures and Materials: A Review on the Experimental, Computational and Theoretical Approaches. Materials
**2019**, 12, 895. [Google Scholar] [CrossRef] [Green Version] - Ezeh, O.; Susmel, L. On the fatigue strength of 3D-printed polylactide (PLA). Procedia Struct. Integr.
**2018**, 9, 29–36. [Google Scholar] [CrossRef] - Ziemian, S.; Okwara, M.; Ziemian, C.W. Tensile and fatigue behavior of layered acrylonitrile butadiene styrene. Rapid Prototyp. J.
**2015**, 21, 270–278. [Google Scholar] [CrossRef] - Domingo-Espin, M.; Travieso-Rodriguez, J.A.; Jerez-Mesa, R.; Lluma-Fuentes, J. Fatigue Performance of ABS Specimens Obtained by Fused Filament Fabrication. Materials
**2018**, 11, 2521. [Google Scholar] [CrossRef] [Green Version] - Gomez-Gras, G.; Jerez-Mesa, R.; Travieso-Rodriguez, J.A.; Lluma-Fuentes, J. Fatigue performance of fused filament fabrication PLA specimens. Mater. Des.
**2018**, 140, 278–285. [Google Scholar] [CrossRef] [Green Version] - Raise3D. PLA Filament—Premium Filament. Raise3D. Premium PLA Safety and Technical Data Sheet. 2019. Available online: https://s1.raise3d.com/2020/12/PLA-Data-Sheet.zip (accessed on 1 March 2021).
- Raise3D. ABS Filament—Premium Filament. Raise3D Premium ABS Safety and Technical Data Sheet. 2017. Available online: https://s1.raise3d.com/2020/12/ABS-Data-Sheet.zip (accessed on 1 March 2021).
- Prima Creator. PrimaSelect ASA+ PrimaCreator. PrimaSelect Safety and Technical Data Sheet. 2019. Available online: https://cdn.shopify.com/s/files/1/2424/8853/files/Prima_ASA__webb.pdf?293 (accessed on 1 March 2021).
- Kampker, A.; Triebs, J.B.; Ayvaz, P.; Ilic, D. Investigation of FLM materials for application in high-temperature and high-vibration automotive environments. Procedia CIRP
**2019**, 81, 358–362. [Google Scholar] [CrossRef] - Ibrahim, D.; Ding, S.; Sun, S. Roughness Prediction for FDM Produced Surfaces. In Proceedings of the International Conference Recent treads in Engineering & Technology (ICRET’2014), Batam, Indonesia, 13–14 February 2014; pp. 13–17. [Google Scholar]
- Alsoufi, M.S.; Elsayed, A.E. How Surface Roughness Performance of Printed Parts Manufactured by Desktop FDM 3D Printer with PLA+ is Influenced by Measuring Direction. Am. J. Mech. Eng.
**2017**, 5, 211–222. [Google Scholar] [CrossRef] - Burhan, I.; Kim, H.S. S-N Curve Models for Composite Materials Characterisation: An Evaluative Review. J. Compos. Sci.
**2018**, 2, 38. [Google Scholar] [CrossRef] [Green Version] - Poberezhnyi, L.; Maruschak, P.; Prentkovskis, O.; Danyliuk, I.; Pyrig, T.; Brezinová, J. Fatigue and failure of steel of offshore gas pipeline after the laying operation. Arch. Civ. Mech. Eng.
**2016**, 16, 524–536. [Google Scholar] [CrossRef]

**Figure 1.**Engineering stress–strain diagrams at room temperature for polylactide (PLA), acrylonitrile butadiene styrene (ABS) and acrylonitrile styrene acrylate (ASA+) 3D printed specimens.

Material/Property | PLA | ABS | ASA+ |
---|---|---|---|

Density (g/cm^{3} at 21.5 °C; ISO 1183) | 1.20 | 1.10–1.15 | 1.10 |

Melt Flow Rate (g/10 min) | 210 °C/2.16 kg = 7 ÷ 11 | 220 °C/10 kg = 9 ÷ 14 | 260 °C/5 kg = 45 |

Melting temperature (°C) | 150 | - | 228 |

Glass transition temperature (°C) | 61 | 98.1 | 98 |

Property | This paper | Manufacturer [31] | [Reference] |
---|---|---|---|

Young’s modulus (MPa) | 2923 | 2623 ± 330 | 3340 [22] |

Tensile strength (MPa) | 32.1 | 46.6 ± 0.9 | 48.5 [22] |

Property | This paper | Manufacturer [32] | [Reference] |
---|---|---|---|

Young’s modulus (MPa) | 2182 | 2174 ± 285 | 1960 ± 60 [5]; 1538 [21] |

Tensile strength (MPa) | 22.8 | 33.3 ± 0.8 | 32.8 ± 0.6 [5] 38.65 [21] |

Property | This paper | Manufacturer [33] | [Reference] |
---|---|---|---|

Young’s modulus (MPa) | 1996 | 2020 | 1398.3 [34] |

Tensile strength (MPa) | 29.9 | 48 | 23 [34] |

Coefficient/Cycle Rate | 10 Hz | 20 Hz | 30 Hz |
---|---|---|---|

α | 1488.2 | 349.6 | 474.5 |

β | −0.4219 | −0.227 | −0.284 |

Coefficient/Cycle Rate | 10 Hz | 20 Hz | 30 Hz |
---|---|---|---|

α | 70,213.8 | 1133.9 | 236.8 |

β | −0.926 | −0.487 | −0.250 |

Coefficient/Cycle Rate | 10 Hz | 20 Hz | 30 Hz |
---|---|---|---|

α | 3797.1 | 6574.1 | 753.6 |

β | −0.561 | −0.671 | −0.361 |

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**MDPI and ACS Style**

Brčić, M.; Kršćanski, S.; Brnić, J.
Rotating Bending Fatigue Analysis of Printed Specimens from Assorted Polymer Materials. *Polymers* **2021**, *13*, 1020.
https://doi.org/10.3390/polym13071020

**AMA Style**

Brčić M, Kršćanski S, Brnić J.
Rotating Bending Fatigue Analysis of Printed Specimens from Assorted Polymer Materials. *Polymers*. 2021; 13(7):1020.
https://doi.org/10.3390/polym13071020

**Chicago/Turabian Style**

Brčić, Marino, Sanjin Kršćanski, and Josip Brnić.
2021. "Rotating Bending Fatigue Analysis of Printed Specimens from Assorted Polymer Materials" *Polymers* 13, no. 7: 1020.
https://doi.org/10.3390/polym13071020