# Experimental Study of the Bending Behaviour of the Neovius Porous Structure Made Additively from Aluminium Alloy

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Samples Design

_{R}that expresses in percentages the ratio of the weight of the porous part (structure) in the body in relation to the weight of the same body that would be completely filled with the material, and it is defined by Equation (1) [17].

- Ws is the weight of the porous structure in the body;
- W
_{CFM}is the weight of the body filled completely with the material.

#### 2.2. Samples Production

- Ultimate tensile strength Rm = 410 MPa;
- Yield strength Rp
_{0.2}= 240 MPa; - Young’s modulus E = 70 ± 5 GPa;
- Elongation at break (as built) 5 ± 2%.

#### 2.3. Experimental and Evaluation Methodology

#### 2.3.1. Experimental Procedure

_{max}is reached. This strength parameter is then called (ultimate) flexural strength, bending strength, or modulus of rupture [26,27].

#### 2.3.2. Maximum Bending Stress Calculation

_{max}, given by Equation (3), will occur in the middle of the beam, either at the top or the bottom of the beam section, depending on which distance is larger, and it can be as follows:

- -
- M
_{max}= Fl/2 is the maximal bending moment about the section’s neutral axis (Nmm); - -
- y is the perpendicular distance from the neutral axis to the farthest point on the section (mm);
- -
- Ixx is the second moment of area of the cross-section (moment of inertia) of the beam, about the neutral x-axis (mm
^{4}).

#### 2.3.3. Energy Absorption

#### 2.3.4. Ductility

_{d}and µ

_{E,}were used for the ductility of the beam assessment. The ductility index µ

_{d}is based on the deflection value at the proportionality limit, and it can be described by Formula (4) [29,30]:

- -
- u
_{u}is the deflection at the ultimate load (mm); - -
- u
_{e}is the deflection at the elastic limit (mm).

_{E}is expressed as the quotient of the total and elastic energy and is given by Formula (5) [31,32].

- -
- W
_{e}is the elastic energy (fraction of total), the area under the load-deflection curve up to the elastic limit (J); - -
- W
_{tot}—the total energy, the area under the load-deflection curve up to failure (J).

## 3. Results and Discussions

_{R}= 30% was greater than for structures with W

_{R}= 25%.

^{2}= 0.998). By integrating the obtained polynomial functions, the amount of energy needed up to a failure of the sample was calculated for each sample. The values with standard deviations of the maximum stresses and energy absorptions for the samples characterized by individual relative weights are presented via the diagram in Figure 11.

_{d}(based on the deflection value at the proportionality limit) and by µ

_{E}(expressed as the quotient of the total and elastic energy).

_{d}and µ

_{E}are very similar for the specimens with 15, 20, 25, and 30% relative weights, but for Neovius_50, they are significantly lower. It confirmed the much more brittle behavior of the structure Neovius with 50% relative weight compared to structures with a lower relative weight. The best ductility was shown by the Neovius_15 samples, and based on the evaluation of the experimental data, structures with a relative mass higher than 50% can be expected to behave brittle. The cracks at individual specimens are completed and visualized in Figure 13.

## 4. Conclusions

- -
- Within the presented research, the maximum bending forces of the samples (a sandwich type) with five different volume ratios, 15, 20, 25, 30, and 50%, were measured, as well as the dependences of force on deflection were plotted.
- -
- The maximum stresses and the amount of energy consumption were calculated for individual specimens that differed in relative weight. The results indicated much more brittle behavior of the specimens with 50% relative weight in comparison to others. It was also confirmed by ductility evaluation.
- -
- From the investigated samples, the most suitable choice for an application in aerospace, aviation, automotive, mechanical, or civil engineering practice for components subjected to bending appears to be the structure Neovius, with a relative weight of 30% due to the reported properties concerning the amount of material spent in production (and its weight).
- -
- At the conclusion of the presented research, it can be stated that the achieved results can be considered as a basis for the design of the various components (parts of different machines, equipment, vehicles, and handling means), which are expected to be stressed predominantly (statically and dynamically) by bending. The implementation of such components in the technical equipment will not only reduce the total weight of the system but also save the material needed for the production of such a component, as well as the mechanical properties determined by the designer with regard to product quality, safety, and operational reliability, will be preserved.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Vukelic, G.; Vizentin, G.; Bozic, Z.; Rukavina, L. Failure analysis of a ruptured compressor pressure vessel. Procedia Struct. Integr.
**2021**, 31, 28–32. [Google Scholar] [CrossRef] - Papadopoulous, S.; Pressas, I.; Vazdirvanidis, A.; Pantazopoulos, G. Fatigue failure analysis of roll steel pins from a chain assembly: Fracture mechanism and numerical modelling. Eng. Fail. Anal.
**2019**, 101, 320–328. [Google Scholar] [CrossRef] - Katinic, M.; Kozak, D.; Gelo, I.; Demjanovic, D. Corrosion fatigue failure of steam turbine moving blades: A case study. Eng. Fail. Anal.
**2019**, 106, 104136. [Google Scholar] [CrossRef] - Bacciaglia, A.; Ceruti, A.; Liverani, A. Structural Analysis of Voxel-Based Lattices Using 1D Approach. 3D Print. Addit. Manuf.
**2022**, 9, 365–379. [Google Scholar] [CrossRef] [PubMed] - Vanca, J.; Monkova, K.; Zaludek, M.; Monka, P.P.; Korol, M.; Kozak, D.; Beno, P.; Ferroudji, F. Investigation of the Influence of Orientation on the Tensile Properties of 3D Printed Samples with Gyroid Structure. In Proceedings of the 2022 13th International Conference on Mechanical and Aerospace Engineering (ICMAE), Bratislava, Slovakia, 20–22 July 2022; pp. 526–531. [Google Scholar] [CrossRef]
- Monkova, K.; Zetkova, I.; Kučerová, L.; Zetek, M.; Monka, P.; Daňa, M. Study of 3D printing direction and effects of heat treatment on mechanical properties of MS1 maraging steel. Arch. Appl. Mech.
**2019**, 89, 791–804. [Google Scholar] [CrossRef] - Maskery, I.; Sturm, L.; Aremu, A.; Panesar, A.; Williams, C.; Tuck, C.; Wildman, R.; Ashcroft, I.; Hague, R. Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing. Polymer
**2018**, 152, 62–71. [Google Scholar] [CrossRef] - Dobransky, J.; Kočiško, M.; Baron, P.; Simkulet, V.; Běhálek, L.; Vojnová, E.; Nováková-Marcinčinová, L. Evaluation of the impact energy of the samples produced by the additive manufacturing technology. Metalurgija
**2016**, 55, 477–480. [Google Scholar] - Shirazi, S.F.S.; Gharehkhani, S.; Mehrali, M.; Yarmand, H.; Metselaar, H.S.C.; Kadri, N.A.; Osman, N.A.A. A review on powderbased additive manufacturing for tissue engineering: Selective laser sintering and inkjet 3D printing. Sci. Technol. Adv. Mater.
**2015**, 16, 477–480. [Google Scholar] [CrossRef] - Gullapalli, H.; Masood, S.H. Flexural Behaviour of 2D Cellular Lattice Structures Manufactured by Fused Deposition Modelling. In Advances in Structures, Systems and Materials; Vinyas, M., Loja, A., Reddy, K., Eds.; Springer: Singapore; New York, NY, USA, 2020; pp. 109–117. [Google Scholar]
- Monkova, K.; Monka, P.P.; Tkac, J.; Vanca, J. A Bending Test of the Additively Produced Porous Sample. In Proceedings of the 5th International Conference on the Industry 4.0 Model for Advanced Manufacturing, Belgrade, Serbia, 1–4 June 2020; Lecture Notes in Mechanical Engineering. Springer: Cham, Switzerland, 2020. [Google Scholar] [CrossRef]
- Hung, D.X.; Truong, H.Q.; Tu, T.M. Nonlinear Bending Analysis of FG Porous Beams Reinforced with Graphene Platelets Under Various Boundary Conditions by Ritz Method. In Modern Mechanics and Applications; Khiem, N.T., Van Lien, T., Hung, N.X., Eds.; Lecture Notes in Mechanical Engineering; Springer: Singapore, 2022. [Google Scholar] [CrossRef]
- Choi, H.; Leeghim, H.; Ahn, H.; Choi, D.S.; Lee, C.Y. Fracture Surface of 3D Printed Honeycomb Structures at Low Temperature Environments. J. Nanosci. Nanotechnol.
**2020**, 20, 4235–4238. [Google Scholar] [CrossRef] - Chen, D.; Yang, J.; Kitipornchai, S. Elastic buckling and static bending of shear deformable functionally graded porous beam. Compos. Struct.
**2015**, 133, 54–61. [Google Scholar] [CrossRef] [Green Version] - Şimşek, M.; Yurtcu, H.H. Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Compos. Struct.
**2013**, 97, 378–386. [Google Scholar] [CrossRef] - Phuong, N.T.B.; Tu, T.M.; Phuong, H.T.; Van Long, N. Bending analysis of functionally graded beam with porosities resting on elastic foundation based on neutral surface position. J. Sci. Technol. Civ. Eng. STCE-HUCE
**2019**, 13, 33–45. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gomez, R.; Lugo, K.; Farahat, N.; Mittra, R.; Iyer, L. Techniques for determining the relative weights of spatial harmonics induced in truncated periodic structures such as metamaterials. In Proceedings of the 2008 IEEE Antennas and Propagation Society International Symposium, San Diego, CA, USA, 5–11 July 2008; pp. 1–4. [Google Scholar] [CrossRef]
- Park, S.Y.; Kim, K.S.; AlMangour, B.; Grzesiak, D.; Lee, K.A. Effect of unit cell topology on the tensile loading responses of additive manufactured CoCrMo triply periodic minimal surface sheet lattices. Mater. Des.
**2021**, 206, 109778. [Google Scholar] [CrossRef] - Khan, S.; Masood, S.; Ibrahim, E.; Ahmad, Z. Compressive behaviour of Neovius Triply Periodic Minimal Surface cellular structure manufactured by fused deposition modelling. Virtual Phys. Prototyp.
**2019**, 14, 360–370. [Google Scholar] [CrossRef] - EOS Aluminium AlSi10Mg Material Data Sheet; EOSGmbH: Munich, Germany, 2022.
- Krishnan, M.; Atzeni, E.; Canali, R.; Calignano, F.; Manfredi, D.; Ambrosio, E.P.; Iuliano, L. On the effect of process parameters on properties of AlSi10Mg parts produced by DMLS. Rapid Prototyp. J.
**2014**, 20, 449–458. [Google Scholar] [CrossRef] - Aboulkhair, N.T.; Simonelli, M.; Parry, L.; Ashcroft, I.; Tuck, C.; Hague, R. 3D printing of Aluminium alloys: Additive Manufacturing of Aluminium alloys using selective laser melting. Prog. Mater. Sci.
**2019**, 106, 100578. [Google Scholar] [CrossRef] - Shah, R.K.; Dey, P.P. Process parameter optimization of DMLS process to produce AlSi10Mg components. J. Phys. Conf. Ser.
**2019**, 1240, 012011. [Google Scholar] [CrossRef] - Vazdirvanidis, A.; Pantazopoulos, G.; Louvaris, A. Failure analysis of a hardened and tempered structural steel (42CrMo
_{4}) bar for automotive applications. Eng. Fail. Anal.**2009**, 16, 1033–1038. [Google Scholar] [CrossRef] - Pantazopoulos, G.A. A Short Review on Fracture Mechanisms of Mechanical Components Operated under Industrial Process Conditions: Fractographic Analysis and Selected Prevention Strategies. Metals
**2019**, 9, 148. [Google Scholar] [CrossRef] [Green Version] - Obadimu, S.O.; Kourousis, K.I. Compressive Behaviour of Additively Manufactured Lattice Structures: A Review. Aerospace
**2021**, 8, 207. [Google Scholar] [CrossRef] - Arjunan, A.; Singh, M.; Baroutaji, A.; Wang, C. Additively Manufactured AlSi10Mg Inherently Stable Thin and Thick-Walled Lattice with Negative Poisson’s Ratio. Compos. Struct.
**2020**, 247, 112469. [Google Scholar] [CrossRef] - Bakalarz, M.M.; Tworzewski, P.P. Application of Digital Image Correlation to Evaluate Strain, Stiffness and Ductility of Full-Scale LVL Beams Strengthened by CFRP. Materials
**2023**, 16, 1309. [Google Scholar] [CrossRef] [PubMed] - Subhani, M.; Globa, A.; Al-Ameri, R.; Moloney, J. Flexural strengthening of LVL beam using CFRP. Constr. Build. Mater.
**2017**, 150, 480–489. [Google Scholar] [CrossRef] - Bazios, P.; Tserpes, K.; Pantelakis, S. Modelling and Experimental Validation of the Porosity Effect on the Behaviour of Nano-Crystalline Materials. Metals
**2020**, 10, 821. [Google Scholar] [CrossRef] - Naaman, A.E.; Jeong, S.M. Structural Ductility of Concrete Beams Prestressed with FRP Tendons. In Non-Metallic (FRP) Reinforcement for Concrete Structures, Proceedings of the 2nd International RILEM Symposium (FRPRXS-2), Ghent, Belgium, 23–25 August 1995; RILEM: Bagneus, France, 1995; pp. 379–386. [Google Scholar]
- Stergioudi, F.; Prospathopoulos, A.; Farazas, A.; Tsirogiannis, E.C.; Michailidis, N. Mechanical Properties of AA2024 Aluminum/MWCNTs Nanocomposites Produced Using Different Powder Metallurgy Methods. Metals
**2022**, 12, 1315. [Google Scholar] [CrossRef] - Kalpakjian, S. Manufacturing Processes for Engineering Materials; Addison-Wesley: Reading, MA, USA, 1984; p. 30. ISBN 0-201-11690-1. [Google Scholar]
- Budynas, R.G. Shigley’s Mechanical Engineering Design, 10th ed.; McGraw Hill: New York, NY, USA, 2015; p. 233. ISBN 978-0-07-339820-4. [Google Scholar]
- Mitrovic, N.; Milosevic, M.; Momcilovic, N.; Petrovic, A.; Miskovic, Z.; Sedmak, A.; Popovic, P. Local Strain and Stress Analysis of Globe Valve Housing Subjected to External Axial Loading. In Key Engineering Materials; Trans Tech Publications Ltd.: Zurich, Switzerland, 2014; Volume 586, pp. 214–217. [Google Scholar]
- Nabavi-Kivi, A.; Ayatollahi, M.R.; Schmauder, S.; Khosravani, M.R. Fracture analysis of a 3D-printed ABS specimen: Effects of raster angle and layer orientation. Fiz. Mezomekhanika
**2022**, 25, 26–39. [Google Scholar] [CrossRef]

**Figure 11.**Measured values with standard deviations of (

**a**) the maximum stress and (

**b**) energy absorption for individual relative weights of the Neovius samples.

**Table 1.**Chemical composition of AlSi10Mg alloy [20].

Element | Al | Mg | Si | Ni | Sn | Pb | Cu | Zn | Ti | Mn | Fe |
---|---|---|---|---|---|---|---|---|---|---|---|

wt. (%) | Balance | 0.2 ÷ 0.45 | 9 ÷ 11 | <0.05 | <0.05 | <0.05 | <0.05 | <0.1 | <0.15 | <0.45 | <0.55 |

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**MDPI and ACS Style**

Monkova, K.; Monka, P.P.; Žaludek, M.; Beňo, P.; Hricová, R.; Šmeringaiová, A.
Experimental Study of the Bending Behaviour of the Neovius Porous Structure Made Additively from Aluminium Alloy. *Aerospace* **2023**, *10*, 361.
https://doi.org/10.3390/aerospace10040361

**AMA Style**

Monkova K, Monka PP, Žaludek M, Beňo P, Hricová R, Šmeringaiová A.
Experimental Study of the Bending Behaviour of the Neovius Porous Structure Made Additively from Aluminium Alloy. *Aerospace*. 2023; 10(4):361.
https://doi.org/10.3390/aerospace10040361

**Chicago/Turabian Style**

Monkova, Katarina, Peter Pavol Monka, Milan Žaludek, Pavel Beňo, Romana Hricová, and Anna Šmeringaiová.
2023. "Experimental Study of the Bending Behaviour of the Neovius Porous Structure Made Additively from Aluminium Alloy" *Aerospace* 10, no. 4: 361.
https://doi.org/10.3390/aerospace10040361