# Numerical Investigation of the Cycling Loading Behavior of 3D-Printed Poly-Lactic Acid (PLA) Cylindrical Lightweight Samples during Compression Testing

^{*}

## Abstract

**:**

## 1. Introduction

^{3}. Afterward, compression tests were performed on dense cylinders by using a Shimadzu AGS-X materials tester to investigate the mechanical characteristics of both materials. Six to ten specimens for each type of material were used for the compression test and the stiffness (Young’s modulus) and yield point were reported. Torres et al. [18] presented the effect of major processing parameters on the properties of materials obtained from poly-lactic acid components modeled by MEX tested in torsion. The findings showed that the result improved with heat treatment, and the infill effect on ductility. The thickness of the layer and density of infill [32] have significant impacts on optimizing the strength of the part. Recently, for environmental reasons, biodegradable polymers such as PLA have been used instead of conventional polymers. PLA was used in biomedical applications, containers, packages, auto parts, and so on. PLA is a crystalline polymer and its Young’s modulus and tensile strength are 2 to 3 GPa and 50 to 70 MPa, respectively. PLA is very brittle, and its low toughness limits the use of PLA. To improve this fragility, PLA is combined with other flexible polymers. The biocompatibility of PLA was approved for food and medicine applications because of its good mechanical properties and processing performance [21,33]. PLA is a thermoplastic aliphatic polyester polymer derived from renewable sources. It has been considered as a potential environmentally friendly alternative to its oil counterparts. It is used for food contact, packaging, and scaffolding applications and is among the most widely used polymers, especially because of its ability to crystallize stress, heat crystallize, impact-modified, fill, copolymerize and process in most excellent polymer processing.

## 2. Materials and Methods

#### 2.1. Equivalent Strain Approach

#### 2.2. Numerical Simulation

## 3. Results and Discussion

#### 3.1. Comparison of Numerical Simulation and Experimental Results

#### 3.2. Model Shape Influence on Simulation Results

#### 3.3. Simulation Results along a Specific Path

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Åkerlund, E. Development of polymer based composite filaments for 3d printing. In Teknisk Naturvetenskaplig Fakultet UTH-Enheten; Uppsala Universitet: Uppsala, Sweden, 2019; ISSN 1650-8297. [Google Scholar]
- Tappa, K.; Jammalamadaka, U. Novel biomaterials used in medical 3D printing techniques. J. Funct. Biomater
**2018**, 9, 17. [Google Scholar] [CrossRef] [PubMed][Green Version] - Gebisa, A.W.; Lemu, H.G. Investigating effects of Fused-deposition modeling (FDM) processing parameters on flexural properties of ULTEM 9085 using designed experiment. Materials
**2018**, 11, 500. [Google Scholar] [CrossRef] [PubMed][Green Version] - Dezaki, M.L.; Ariffin, M.K.A.M.; Serjouei, A.; Zolfagharian, A.; Hatami, S.; Bodaghi, M. Influence of infill patterns generated by cad and fdm 3d printer on surface roughness and tensile strength properties. Appl. Sci
**2021**, 11, 7272. [Google Scholar] [CrossRef] - Mercado-Colmenero, J.M.; Rubio-Paramio, M.A.; la Rubia, M.D.; Lozano-Arjona, D.; Martin-Doñate, C. A numerical and experimental study of the compression uniaxial properties of PLA manufactured with FDM technology based on product specifications. Int. J. Adv. Manuf. Technol.
**2019**, 103, 1893–1909. [Google Scholar] [CrossRef] - Primo, T.; Calabrese, M.; del Prete, A.; Anglani, A. Additive manufacturing integration with topology optimization methodology for innovative product design. Int. J. Adv. Manuf. Technol.
**2017**, 93, 467–479. [Google Scholar] [CrossRef] - Mercado-Colmenero, J.M.; Muriana, J.A.M.; Rubio-Paramio, M.A.; Martín-Doñate, C. An automated manufacturing analysis of plastic parts using faceted surfaces. In Lecture Notes in Mechanical Engineering, Proceedings of the International Joint Conference on Mechanics, Design Engineering & Advanced Manufacturing (JCM 2016), Catania, Italy, 14–16 September 2016; Springer: Cham, Switzerland, 2017; pp. 119–128. [Google Scholar] [CrossRef]
- Leary, M.; Merli, L.; Torti, F.; Mazur, M.; Brandt, M. Optimal topology for additive manufacture: A method for enabling additive manufacture of support-free optimal structures. Mater. Des.
**2014**, 63, 678–690. [Google Scholar] [CrossRef] - Thompson, M.K.; Moroni, G.; Vaneker, T.; Fadel, G.; Campbell, R.I.; Gibson, I.; Bernard, A.; Schulz, J.; Graf, P.; Ahuja, B.; et al. Design for Additive Manufacturing: Trends, opportunities, considerations, and constraints. CIRP Ann. Manuf. Technol.
**2016**, 65, 737–760. [Google Scholar] [CrossRef][Green Version] - Martini, M.; Scaccia, M.; Marchello, G.; Abidi, H.; D’Imperio, M.; Cannella, F. An Outline of Fused Deposition Modeling: System Models and Control Strategies. Appl. Sci.
**2022**, 12, 5400. [Google Scholar] [CrossRef] - Mohseni, M.; Hutmacher, D.W.; Castro, N.J. Independent evaluation of medical-grade bioresorbable filaments for fused deposition modelling/fused filament fabrication of tissue engineered constructs. Polymers
**2018**, 10, 40. [Google Scholar] [CrossRef][Green Version] - Wang, X.; Jiang, M.; Zhou, Z.; Gou, J.; Hui, D. 3D printing of polymer matrix composites: A review and prospective. Compos. Part B Eng.
**2017**, 110, 442–458. [Google Scholar] [CrossRef] - Mercado-Colmenero, J.M.; Rubio-Paramio, M.A.; Guerrero-Villar, F.; Martin-Doñate, C. A numerical and experimental study of a new Savonius wind rotor adaptation based on product design requirements. Energy Convers. Manag.
**2018**, 158, 210–234. [Google Scholar] [CrossRef] - Zhai, Y.; Lados, D.A.; Lagoy, J.L. Additive Manufacturing: Making imagination the major Limitation. JOM
**2014**, 66, 808–816. [Google Scholar] [CrossRef][Green Version] - Mansour, S.; Hague, R. Impact of rapid manufacturing on design for manufacture for injection moulding. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf.
**2003**, 217, 453–461. [Google Scholar] [CrossRef][Green Version] - Kanani, A.Y.; Rennie, A.E.W. Additively manufactured foamed polylactic acid for lightweight structures. Rapid Prototyp. J. 2022; ahead-of-print. [Google Scholar] [CrossRef]
- Perween, S.; Fahad, M.; Khan, M.A. Systematic experimental evaluation of function based cellular lattice structure manufactured by 3d printing. Appl. Sci.
**2021**, 11, 10489. [Google Scholar] [CrossRef] - Torres, J.; Cotelo, J.; Karl, J.; Gordon, A.P. Mechanical property optimization of FDM PLA in shear with multiple objectives. JOM
**2015**, 67, 1183–1193. [Google Scholar] [CrossRef] - Camargo, J.C.; Machado, Á.R.; Almeida, E.C.; Silva, E.F.M.S. Mechanical properties of PLA-graphene filament for FDM 3D printing. Int. J. Adv. Manuf. Technol.
**2019**, 103, 2423–2443. [Google Scholar] [CrossRef] - Equbal, A.; Equbal, M.I.; Badruddin, I.A.; Algahtani, A. A critical insight into the use of FDM for production of EDM electrode. Alexandria Eng. J.
**2022**, 61, 4057–4066. [Google Scholar] [CrossRef] - Sood, A.K.; Ohdar, R.K.; Mahapatra, S.S. Experimental investigation and empirical modelling of FDM process for compressive strength improvement. J. Adv. Res.
**2012**, 3, 81–90. [Google Scholar] [CrossRef][Green Version] - Engineering, M.; Ament, N. Technology Estimation of Electrical Conductivity of ABS and PLA Based EDM Electrode Fabricated By Using FDM 3D. Int. J. Mod. Eng. Res.
**2018**, 5, 332–338. [Google Scholar] - Kim, H.-J.; Lim, S.-W.; Lee, M.-K.; Ju, S.W.; Park, S.-H.; Ahn, J.-S.; Hwang, K.-G. Which three-dimensional printing technology can replace conventional manual method of manufacturing oral appliance? A preliminary comparative study of physical and mechanical properties. Appl. Sci.
**2022**, 12, 130. [Google Scholar] [CrossRef] - Wichniarek, R.; Hamrol, A.; Kuczko, W.; Górski, F.; Rogalewicz, M. ABS filament moisture compensation possibilities in the FDM process. CIRP J. Manuf. Sci. Technol.
**2021**, 35, 550–559. [Google Scholar] [CrossRef] - Anitha, R.; Arunachalam, S.; Radhakrishnan, P. Critical parameters influencing the quality of prototypes in fused deposition modelling. J. Mater. Process. Technol.
**2001**, 118, 385–388. [Google Scholar] [CrossRef] - Lee, B.H.; Abdullah, J.; Khan, Z.A. Optimization of rapid prototyping parameters for production of flexible ABS object. J. Mater. Process. Technol.
**2005**, 169, 54–61. [Google Scholar] [CrossRef] - Croccolo, D.; de Agostinis, M.; Olmi, G. Experimental characterization and analytical modelling of the mechanical behaviour of fused deposition processed parts made of ABS-M30. Comput. Mater. Sci.
**2013**, 79, 506–518. [Google Scholar] [CrossRef] - Hikmat, M.; Rostam, S.; Ahmed, Y.M. Investigation of tensile property-based Taguchi method of PLA parts fabricated by FDM 3D printing technology. Results Eng.
**2021**, 11, 100264. [Google Scholar] [CrossRef] - Kumar, M.; Mohol, S.S.; Sharma, V. A computational approach from design to degradation of additively manufactured scaffold for bone tissue engineering application. Rapid Prototyp. J. 2022; ahead-of-print. [Google Scholar] [CrossRef]
- Haq, R.H.A.; Rahman, M.N.A.; Ariffin, A.M.T.; Hassan, M.F.; Yunos, M.Z.; Adzila, S. Characterization and Mechanical Analysis of PCL/PLA composites for FDM feedstock filament. IOP Conf. Ser. Mater. Sci. Eng.
**2017**, 226, 012038. [Google Scholar] [CrossRef] - Ostafinska, A.; Fortelný, I.; Hodan, J.; Krejčíková, S.; Nevoralová, M.; Kredatusová, J.; Kruliš, Z.; Kotek, J.; Šlouf, M. Strong synergistic effects in PLA/PCL blends: Impact of PLA matrix viscosity. J. Mech. Behav. Biomed. Mater.
**2017**, 69, 229–241. [Google Scholar] [CrossRef] - Rashed, K.; Kafi, A.; Simons, R.; Bateman, S. Fused filament fabrication of nylon 6/66 copolymer: Parametric study comparing full factorial and Taguchi design of experiments. Rapid Prototyp. J.
**2022**, 28, 1111–1128. [Google Scholar] [CrossRef] - Upadhyay, K.; Dwivedi, R.; Kumar Singh, A. Determination and Comparison of the Anisotropic Strengths of Fused Deposition Modeling P400 ABS. In Advances in 3D Printing & Additive manufacturing Technologies; Wimpenny, D.I., Pandey, P.M., Kumar, L.J., Eds.; Springer: Singapore, 2017; pp. 9–28. [Google Scholar] [CrossRef]
- Domingo-Espin, M.; Puigoriol-Forcada, J.M.; Garcia-Granada, A.A.; Llumà, J.; Borros, S.; Reyes, G. Mechanical property characterization and simulation of fused deposition modeling Polycarbonate parts. Mater. Des.
**2015**, 83, 670–677. [Google Scholar] [CrossRef] - Pepelnjak, T.; Karimi, A.; Maček, A.; Mole, N. Altering the elastic properties of 3D printed poly-lactic acid (PLA) parts by compressive cyclic loading. Materials
**2020**, 13, 4456. [Google Scholar] [CrossRef] - Wang, X.; Zhang, J.; Wang, Z.; Liang, W.; Zhou, L. Finite element simulation of the failure process of single fiber composites considering interface properties. Compos. Part B Eng.
**2013**, 45, 573–580. [Google Scholar] [CrossRef] - Zhou, S.; Wang, Z.; Zhou, J.; Wu, X. Experimental and numerical investigation on bolted composite joint made by vacuum assisted resin injection. Compos. Part B Eng.
**2013**, 45, 1620–1628. [Google Scholar] [CrossRef] - Bles, G.; Nowacki, W.K.; Tourabi, A. Experimental study of the cyclic visco-elasto-plastic behaviour of a polyamide fibre strap. Int. J. Solids Struct.
**2009**, 46, 2693–2705. [Google Scholar] [CrossRef][Green Version] - Barkey, M.E.; Lee, Y.L. Strain-Based Multiaxial Fatigue Analysis; Elsevier Inc.: Amsterdam, The Netherlands, 2012. [Google Scholar]
- Yu, G.-H.; Ma, G.-W.; Qiang, H.-F.; Xhang, Y.-Q. Generalized Plasticity; Springer: Berlin/Heidelberg, Germany, 2006. [Google Scholar]
- Rodrigues, D.E.S.; Belinha, J.; Jorge, R.M.N.; Dinis, L. Numerical simulation of compression and tensile tests on thermoplastics: A meshless approach. J. Mater. Des. Appl.
**2019**, 233, 286–306. [Google Scholar] [CrossRef] - Colby, R.B. Equivalent Plastic Strain for the Hill’s Yield Criterion under General Three-Dimensionalloading. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 2013; pp. 1–45. [Google Scholar]
- Shamsaei, N.; Fatemi, A. Effect of microstructure and hardness on non-proportional cyclic hardening coefficient and predictions. Mater. Sci. Eng. A
**2010**, 527, 3015–3024. [Google Scholar] [CrossRef] - Oztan, C.; Karkkainen, R.; Fittipaldi, M.; Nygren, G.; Roberson, L.; Lane, M.; Celik, E. Microstructure and mechanical properties of three dimensional-printed continuous fiber composites. J. Compos. Mater
**2019**, 53, 271–280. [Google Scholar] [CrossRef]

**Figure 1.**Schematic diagram of the universal testing machine (UTM) (

**left**) and the located sample between the compression plates (

**right**) [35].

**Figure 2.**A summary of the research in the experimental part [35] and the validation of the experimental results using numerical simulations.

**Figure 3.**The chart for altered ES as a function of PEEQ (

**left**) and the dependency of the elastic stiffness of the sample on the constitutive cycles and the loading path for 2.4 mm ILD considering at an initial tool displacement of 0.2 mm [35] (

**right**).

**Figure 4.**(

**A**) Microscopic cross-section image of MEX-produced specimen with 100% infill. (

**B**) The microscopic image from the top view of the MEX-produced specimen sample with 100% infill.

**Figure 5.**(

**A**) Dividing the cross-section of the sample into twelve equal symmetrical parts; (

**B**) halving the height of one of the symmetrical parts.

**Figure 7.**Three-dimensional model of the MEX-produced specimen with boundary conditions assigned to the middle cross-section of the model, the amount of layers of the model, and tool (orange points represent the boundary conditions that applied to the model).

**Figure 8.**Compressive plastic stress–strain diagram [1].

**Figure 10.**ES changes diagram in terms of the number of cycles (experiment and numerical simulation).

**Figure 11.**Compression force–displacement diagram and comparison between numerical simulation results (layer-by-layer) and experimental results (Exp. No. 1–4).

**Figure 12.**Compression force–displacement diagram and comparison between numerical simulation results of the layered and simplified geometrical models.

**Figure 14.**Mises stress (MPa)–distance diagram in specific paths at the end of each cycle. (

**a**) Path 1 and (

**b**) Path 2.

**Figure 15.**Elastic strain (maximum principle)–distance diagram in specific paths at the end of each cycle. (

**a**) Path 1 and (

**b**) Path 2.

**Figure 16.**Equivalent plastic strain diagram in Path 1 in (

**a**) Cycle 1, (

**b**) Cycle 2, (

**c**) Cycle 3, (

**d**) Cycle 4, and (

**e**) Cycle 5.

**Figure 17.**Equivalent plastic strain diagram in Path 2 in (

**a**) Cycle 1, (

**b**) Cycle 2, (

**c**) Cycle 3, (

**d**) Cycle 4, and (

**e**) Cycle 5.

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

Density (ρ) | kg/m^{3} | 1240 [5] |

Initial Young’s modulus (E) (altered with PEEQ during the simulation) | MPa | 2800 [35] |

Poisson’s ratio (υ) | - | 0.36 |

Yield strength (σ_{y}) | MPa | 59 |

**Table 2.**Results of the ES of the sample in experiments and model in the numerical simulation, induced by cyclic compressive loading.

Number of Cycles | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Elastic stiffness in the experiment [35] (MPa) | 2800 | 2970 | 2998 | 3005 | 3015 |

Elastic stiffness in the numerical simulation (MPa) | 2732.8 | 2936.8 | 3005.0 | 3036.5 | 3057.5 |

**Table 3.**Summary of the ES percentage changes in the experiments and numerical simulation, induced by cyclic compressive loading.

Cycles Comparison | 2 → 1 | 3 → 1 | 4 → 1 | 5 → 1 |
---|---|---|---|---|

Percentage of elastic stiffness changes in experiment compared to the first cycle (%) | 6.1 | 7.1 | 7.3 | 7.7 |

Percentage of elastic stiffness changes in numerical simulation compared to the first cycle (%) | 7.5 | 10 | 11.1 | 11.9 |

Percentage difference between the experiment and numerical simulation results (%) | 1.4 | 2.9 | 3.8 | 4.2 |

**Table 4.**Summary of the ES of the geometrical simplified model changes and the layer model changes in the numerical simulation, induced by cyclic compressive loading.

Number of Cycles | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Elastic stiffness in the geometrical simplified model (MPa) | 2818.2 | 2943.9 | 2989.1 | 3018.2 | 3039.8 |

Elastic stiffness in the layer-by-layer model (MPa) | 2732.8 | 2936.8 | 3005.0 | 3036.5 | 3057.5 |

Elastic stiffness in the experiment [35] (MPa) | 2800 | 2970 | 2998 | 3005 | 3015 |

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**MDPI and ACS Style**

Karimi, A.; Mole, N.; Pepelnjak, T.
Numerical Investigation of the Cycling Loading Behavior of 3D-Printed Poly-Lactic Acid (PLA) Cylindrical Lightweight Samples during Compression Testing. *Appl. Sci.* **2022**, *12*, 8018.
https://doi.org/10.3390/app12168018

**AMA Style**

Karimi A, Mole N, Pepelnjak T.
Numerical Investigation of the Cycling Loading Behavior of 3D-Printed Poly-Lactic Acid (PLA) Cylindrical Lightweight Samples during Compression Testing. *Applied Sciences*. 2022; 12(16):8018.
https://doi.org/10.3390/app12168018

**Chicago/Turabian Style**

Karimi, Ako, Nikolaj Mole, and Tomaž Pepelnjak.
2022. "Numerical Investigation of the Cycling Loading Behavior of 3D-Printed Poly-Lactic Acid (PLA) Cylindrical Lightweight Samples during Compression Testing" *Applied Sciences* 12, no. 16: 8018.
https://doi.org/10.3390/app12168018