Sandwich Panel Design Suitable for Selective Laser Sintering Additive Manufacturing

UNIVERSITY OF LJUBLJANA

Faculty of Mechanical Engineering

Sandwich panel design suitable for selective laser sintering additive manufacturing

A Master’s thesis of the second-cycle master’s study programme in MECHANICAL ENGINEERING – a research and development programme.

Pau Vidal Bravo

Ljubljana, February 2021

UNIVERSITY OF LJUBLJANA

Faculty of Mechanical Engineering

Sandwich panel design suitable for selective laser sintering additive manufacturing

A Master’s thesis of the second-cycle master’s study programme in MECHANICAL ENGINEERING – a research and development programme.

Pau Vidal Bravo

Advisor: prof. dr. Jernej Klemenc, univ. dipl. inž.

Ljubljana, February 2021

Candidate Pau VIDAL BRAVO

MAGISTRSKI STUDIJSKI PROGRAM Il. STOPNJE: MAG ID914 E

NASLOV TEME: Konstruiranje sendvic panelov primernih za izdelavo z dodajno tehnologijo selektivnega laserskega sintranja

Uporaba dodajnih tehnologij predstavlja revolucijo v izdelavi prototipov in koncnih izdelkov, ker omogoca izdelavo oblik in struktur, ki jih ni mogoce izdelati s tradicionalnimi izdelovalnimi postopki. Dodajne tehnologije so se pojavile na trgu s ciljem zadovoljitve potreb po izdelavi personaliziranih izdelkov ter maloserijskih kompleksnih izdelkov z visoko dodano vrednostjo. Fokus tega magistrskega dela bo usmerjen v dodajno tehnologijo selektivnega laserskega sintranja. Cilj magistrskega dela je razviti konstrukcijo sendvic panela, ki bo lahko uporabljen v nosilnih strukturah, obremenjenih z upogibnirni obremenitvami. Kandidat naj se naprej seznani s tehnologijo selektivnega laserskega sintranja (SLS) na osnovi relevantne literature. Nato naj pregleda zadnje stanje razvoja na podrocju konstruiranja sendvic panelov. Na osnovi pridobljenih znanj naj skonstruira taksne oblike panelov z notranjirni podpomimi strukturami, ki bodo primerni za uporabo v upogibno obremenjenih planamih nosilnih strukturah. Za vsak tip panela naj izvede tri staticne preskuse: nateznega, striznega in tritockovno upogibnega. Eksperimentalne rezultate naj primerja s simulacijami. Za najboljsi(e) panel(e) naj izvede se utripne dinamicne preskuse s ciljem ocene dinamicne zdrzljivosti.

Magistrsko delo je treba oddati v jezikovno in terrninoloskopravilnem angleskem jeziku. Rok za oddajo tega dela je sest mesecev od dneva prevzema.

MASTER THESIS- MASTER'S DEGREE STUDY No. MAG 11/914 E

TITLE Sandwich panel design suitable forselective laser sintering additive manufacturing

The use of the additive manufacturing revolutionizes the way to develop prototypes and final parts, because it allows shapes and structures not possible in traditional manufacturing processes. These technologies have been introduced to the market to satisfy the demand of personalized parts with high geometry complexity and small series, high valued products. In this thesis the focused will be put on the Selective Laser Sintering (SLS) additive manufacturingtechnology. The objective of this M.Sc. thesis is to develop a core of a sandwich panel that is useful for application in different structures, which are exposed to bending loads. The candidate should first acquire knowledge on the Selective Laser Sintering (SLS) by studying the relevant literature. Then the state-of the-art theoretical and practical topics related to the design of sandwich panels should be reviewed. This should be followed by a design of the most suitable panels that can be used for supporting the bending loads of planar structures. For each case of the panel three kind of static tests should be made, i.e. a compression, a shear and a three-point bending test. The experimental results should be compared to the numerical simulations. For the most promising design(s) the pulsating fatigue tests should finally be carried out to assess the fatigue resistance of such structures.

The submitted master thesis must be written in standard English. The master thesis must be submitted six months after it was accepted.

Mentor Digitally signed by J ER N EJ JERNEJ KLEMENC 1a�= 2021-01-14 Prof. PhD. Jemei� Klemenc KLEMENC l ' 08:30:48 +01 '00' I hereby confirmthe receipt of the master thesis

Date ......

Student Signature ......

I, the undersigned Pau Vidal Bravo, student of the Faculty Of Mechanical Engineering at the University of Ljubljana, with registration number 70085228, author of the written final work of studies, entitled: Sandwich panel design suitable for selective laser sintering additive manufacturing

DECLARE that

1.a) The written final work of studies is a result of my independent work; 2. The printed form of the written final work of studies is identical to the electronic form of the written final work of studies;

3. I acquired all the necessary permissions for the use of data and copyrighted works in the written final work of studies and clearly marked them in the written final work of studies;

4. During the preparation of the written final work of studies I acted in accordance with ethical principles and obtained, where necessary, agreement of the ethics commission;

5. I give my consent to the use of the electronic form of the written final work of studies for the detection of content similarity with other works, using similarity detection software that is connected with the study information system of the university member;

6. I transfer to the UL – free of charge, non•exclusively, geographically and time•wise unlimited – the right of saving the work in the electronic form, the right of reproduction, as well as the right of making the written final work of studies available to the public on the World Wide Web via the Repository of the UL;

7. I give my consent to the publication of my personal data included in the written final work of studies and in this declaration, together with the publication of the written final work of studies;

8. I give my consent to the use of my birth date in COBISS record.

In Ljubljana, 12 February 2021 Student's signature: ______

Acknowledgements

I would like to thank my tutor Jernej Klemenc, who has been always very helpful and has always find time for me, even though the great amount of work that he had. From the very begging, he has been very attentive to me.

Also, I would like to thank the Ph.D. student Jure Kajbič who has help me a lot during all the master thesis, from the printing to the simulations with Abaqus.

Last but not least, I would like to thank my family for all the support that they have given me during all the years of my studies, from the bachelor's degree to now the master thesis. Without their moral and economical support, I could not reach this goal.

Declaration

1. I, the undersigned Pau Vidal Bravo, born 26 December 1996 in Girona, a student at the Faculty of Mechanical Engineering at the University of Ljubljana, hereby declare that this master’s thesis titled Sandwich panel design suitable for Selective Laser Sintering additive manufacturing is my own original work created under the supervision of my advisor prof. Dr. Jernej Klemenc.

2. I hereby declare that the submitted electronic copy of this master’s thesis is identical to the printed copy.

3. Pursuant to the provisions of the Copyright and Related Rights Act (Official Gazette of the Republic of Slovenia, No. 21/1995 as amended), I hereby expressly give my permission for this master’s thesis to be published on the websites of the Faculty of Mechanical Engineering and the University of Ljubljana.

4. By signing this Declaration, I grant my permission for this master’s thesis to be made publicly accessible online via the Repository of the University of Ljubljana.

By signing this document, I certify that: ‐ the presented text is the product of my own original research in its entirety. ‐ the presented text adheres to linguistic and stylistic conventions and the technical requirements of the Guidelines for Composing Final Theses, meaning that: ‐ the works and opinions of other authors used in this master’s thesis are appropriately cited or acknowledged pursuant to the Guidelines for Composing Final Theses, and ‐ I have obtained the permission for the use of any data and original work reproduced in the text in full (either as text or as a graphic) from their respective authors and duly noted that in the text itself. ‐ I am aware that plagiarism, i.e., the misrepresentation of someone else’s work (be it text or graphics) as my own, is a crime under the Criminal Code of the Republic of Slovenia (Official Gazette of the Republic of Slovenia, No. 55/2008 as amended); ‐ I am aware of the potential repercussions concerning my status at the Faculty of Mechanical Engineering at the University of Ljubljana as per the applicable Rules should plagiarism be proven in connection to the submitted master’s thesis.

Ljubljana, 12 February 2021 Signature of the author: ______

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Abstract (in English)

UDC 621.9.048.7:621.762.5:678.6(043.2) Serial No.: MAG II/914 E

Sandwich panel design suitable for selective laser sintering additive manufacturing

Pau Vidal Bravo

Keywords: Selective laser sintering Polyamide 12 Sandwich panel Design Honeycomb structure Lattice structure

The use of additive manufacturing revolutionizes the way to develop prototypes and final parts because it allows shapes and structures not possible in traditional manufacturing processes. These technologies have been introduced to the market to satisfy the demand for personalized parts with high geometry complexity and small series, high valued products. In this thesis, the focus has been on the Selective Laser Sintering (SLS) additive manufacturing technology.

The objective of this M.Sc. thesis has been to develop a core of a sandwich panel that is useful for application in different structures, which were exposed to compression, shear, bending and fatigue loads. It has been mandatory to first acquire knowledge on the Selective Laser Sintering (SLS) by studying the relevant literature. Then the state-of-the- art theoretical and practical topics related to the design of sandwich panels had been reviewed. This was followed by a design of the most suitable panels that can be used for supporting the bending loads of planar structures, these designs have been made with Solidworks software. For each case of the panel, three kinds of static tests had been made, i.e., a compression, a shear, and a three-point bending test. The experimental results have been compared to the numerical simulations made with the finite element software Abaqus. At the end, the most promising designs were studied under the pulsating fatigue tests to assess the fatigue resistance of such structures.

Povzetek (in Slovene)

UDC 621.9.048.7:621.762.5:678.6(043.2) Serial No.: MAG II/914 E

Konstruiranje sendvič panelov primernih za izdelavo z dodajno tehnologijo selektivnega laserskega sintranja

Pau Vidal Bravo

Ključne besede: selektivno lasersko sintranje Poliamid 12 sendvič plošča konstruiranje strukturno satovje mrežasta struktura

Cilj magistrskega dela je bil razviti konstrukcijo sendvič plošče, ki bo lahko uporabljen v nosilnih strukturah, obremenjenih z upogibnirni obremenitvami. Zato smo se naprej seznanili s tehnologijo selektivnega laserskega sintranja (SLS) na osnovi relevantne literature. Nato smo pregledali zadnje stanje razvoja na podrocju konstruiranja sendvic panelov. Skonstruirali smo takšne oblike panelov z notranjimi podpornimi strukturami, ki so primerni za uporabo v upogibno obremenjenih planamih nosilnih strukturah. Za vsak tip panela smo izvedli tri statične preskuse: nateznega, strižnega in tritočkovno upogibnega. Eksperimentalne rezultate smo primerjali s simulacijami. Za najboljše plošče smo izvedli še utripne dinamične preskuse s ciljem ocene njihove dinamične zdržljivosti.

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Table of contents

Acknowledgements ...... v Declaration ...... vii Abstract (in English) ...... ix Povzetek (in Slovene) ...... xi Table of contents ...... xiii List of figures ...... xvii List of tables ...... xx List of symbols used ...... xxii List of acronyms used ...... xxv

1. Introduction ...... 1

1.1 Background ...... 1 1.2 Objectives ...... 1

2. State of the art ...... 4

2.1. Additive Manufacturing ...... 4 2.1.1. Description ...... 4 2.1.1. Advantages and disadvantages of AM ...... 4 2.2. Selective Laser Sintering ...... 6 2.2.1. Description ...... 6 2.2.2. Materials and main uses/applications ...... 6 2.2.3. Advantages and disadvantages ...... 7 2.2.4. Sinterit LISA printer ...... 7 2.3. Sandwich panels ...... 9 2.3.1. Definition ...... 9 2.3.2. Types and materials of general sandwich structures ...... 10 2.3.3. Applications ...... 11

3. Methodology ...... 13

3.1. Designs ...... 13 3.1.1. Composite materials ...... 13 3.1.1.1. Description ...... 13 3.1.1.2. Matrix type classification...... 14

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3.1.2. Polyamide 12 ...... 17 3.1.3. Printing process ...... 20 3.1.3.1. Print ...... 20 3.1.3.2. Post-process ...... 22 3.1.4. Limitations and assumptions ...... 23 3.1.4.1. Material ...... 23 3.1.4.2. SLS Printing ...... 23 3.1.5. Core designs ...... 26 3.1.5.1. Honeycomb ...... 26 3.1.5.2. Re-entrant honeycomb ...... 32 3.1.5.3. Lattice structure ...... 35 3.1.5.4. Iso Grid ...... 37 3.2. Experimental work ...... 39 3.2.1. Compression test ...... 39 3.2.1.1. Introduction ...... 39 3.2.1.2. Methodology ...... 40 3.2.1.3. Specimens ...... 41 3.2.1.4. Results ...... 43 3.2.2. Shear test ...... 45 3.2.2.1. Introduction ...... 45 3.2.2.2. Methodology ...... 46 3.2.2.3. Specimens ...... 46 3.2.2.4. Results ...... 47 3.2.3. Bending test ...... 49 3.2.3.1. Introduction ...... 49 3.2.3.2. Methodology ...... 50 3.2.3.3. Specimens ...... 52 3.2.3.4. Results ...... 54 3.2.4. Fatigue test...... 55 3.2.4.1. Introduction ...... 55 3.2.4.2. Methodology ...... 55 3.2.4.3. Specimens ...... 56 3.2.4.4. Results ...... 56 3.3. Finite element simulations ...... 58 3.3.1. Abaqus ...... 59 3.3.1.1. Part ...... 59 3.3.1.2. Property ...... 60 3.3.1.3. Assembly ...... 61 3.3.1.4. Step ...... 61 3.3.1.5. Load ...... 62 3.3.1.6. Mesh...... 63 3.3.1.7. Job ...... 64 3.3.1.8. Visualization ...... 65 3.3.2. Results ...... 65 3.3.2.1. Shear ...... 65 3.3.2.2. Bending ...... 66

xiv

4. Results and discussion ...... 69

4.1. Experimental tests ...... 69 4.1.1. Compression ...... 69 4.1.2. Shear ...... 70 4.1.3. Bending ...... 71 4.1.4. Fatigue ...... 73 4.2. Tests contrasted with Abaqus ...... 74 4.2.1. Shear ...... 74 4.2.1.1. J1 ...... 74 4.2.1.2. J3S...... 75 4.2.1.3. TS ...... 76 4.2.1.4. OHCS ...... 77 4.2.2. Bending ...... 78 4.2.2.1. J3B ...... 78 4.2.2.2. TB ...... 79

5. Conclusions ...... 82

6. Bibliography ...... 84

7. Annex ...... 87

xvi

List of figures

Figure 2.1: Scheme of an SLS 3D printer basing on the construction of Sinterit Lisa [3] ...... 6 Figure 2.2: Sinterit Lisa 3D printer [3] ...... 8 Figure 2.3: Sandwich panel, honeycomb type ...... 9 Figure 2.4: Airplane Vultee BT-15 [7] ...... 11 Figure 3.1: Porsche 911 S turbo ...... 14 Figure 3.2: Disposals of the reinforcements in metal matrix composites[9] ...... 15 Figure 3.3: NASA-space vehicle X-38 during a test flight[11]...... 16 Figure 3.4: Total material used in the Boeing 787 Dreamliner [13] ...... 17 Figure 3.5: First compression test specimens ...... 18 Figure 3.6: Hygroscopicity of the different polyamides [14] ...... 19 Figure 3.7: Ultimate tensile strength is given by the manufacturer [15] ...... 19 Figure 3.8: “Preset” Sinterit Studio section...... 20 Figure 3.9: "Models" Sinterit Studio section ...... 21 Figure 3.10: Print process...... 22 Figure 3.11: Sinterit sandblaster ...... 22 Figure 3.12: Cleaning tools ...... 22 Figure 3.13: Specimens 0°, 45°, 90° print orientations to the Z-axis print direction. [17] ...... 23 Figure 3.14: Comparative Chart of different printing directions[17] ...... 24 Figure 3.15: Remaining powder inside the specimen ...... 25 Figure 3.16: TGM inducing residual stress [18] ...... 26 Figure 3.17: Regular hexagonal honeycomb ...... 27 Figure 3.18: Honeycomb directions [23] ...... 27 Figure 3.19: Honeycomb in-plane design, compression specimen ...... 28 Figure 3.20: Honeycomb out-of-plane design, compression specimen ...... 29 Figure 3.21: Stress concentrations due to a circle ...... 30 Figure 3.22: Top and bottom part of the open honeycomb ...... 31 Figure 3.23: Unit cell of the open honeycomb ...... 31 Figure 3.24: Open honeycomb core, top view ...... 32 Figure 3.25: Open honeycomb, front view...... 32 Figure 3.26: Deformation under axial load: a) Conventional honeycombs and b) Re-entrant (auxetic) honeycombs [26] ...... 33 Figure 3.27: Re-entrant honeycomb unit cell ...... 33 Figure 3.28: Re-entrant honeycomb in-plane, compression specimen ...... 34 Figure 3.29: Unity cell reference axes [24] ...... 34 Figure 3.30: Re-entrant honeycomb out-of-plane, compression specimen ...... 35 Figure 3.31: Unit cell tetrahedral design [27] ...... 36 Figure 3.32: Tetrahedron distribution, without top face sheet ...... 37 Figure 3.33: J1 core ...... 38

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Figure 3.34: Detailed J1 hollow for powder extraction ...... 38 Figure 3.35: J2 middle cross-section, top view ...... 38 Figure 3.36: Detailed J2 hollow for powder extraction ...... 38 Figure 3.37: J3 middle cross-section, top view ...... 39 Figure 3.38: Detailed J3 hollow for powder extraction ...... 39 Figure 3.39: Parts of the compression test...... 40 Figure 3.40: Top utensil for bigger areas ...... 41 Figure 3.41: Compression test dimension’s specimens ...... 41 Figure 3.42: Parts of the shear test ...... 46 Figure 3.43: Shear test dimension’s specimens ...... 47 Figure 3.44: Shear diagram ...... 47 Figure 3.45: Shear strain ...... 48 Figure 3.46: Moment's diagram. a) Three-point test. b) Four-point test ...... 50 Figure 3.47: Parts of the bending test, first methodology ...... 51 Figure 3.48: Parts of bending test, the second methodology ...... 51 Figure 3.49: Bending test dimension’s specimens ...... 52 Figure 3.50: Curve deformation, specimen before the cut ...... 53 Figure 3.51: Straight edges, specimen after the cut ...... 53 Figure 3.52: Printed support profile ...... 54 Figure 3.53: Printed support front ...... 54 Figure 3.54: Maximum moment at application area ...... 57 Figure 3.55: Symmetry planes ...... 59 Figure 3.56: Reduced specimen ...... 59 Figure 3.57: Symmetry planes bending ...... 60 Figure 3.58: Reduced bending specimen...... 60 Figure 3.59: Assembled part ...... 61 Figure 3.60: Model steps ...... 62 Figure 3.61: Boundary conditions ...... 63 Figure 3.62: BC in the model ...... 63 Figure 3.63: Design's mesh ...... 64 Figure 3.64: Shear specimen displacement ...... 65 Figure 3.65: Abaqus shear results, force-displacement plot ...... 66 Figure 3.66: Abaqus bending results, force-displacement plot ...... 67 Figure 4.1: Shear test stress-strain diagram ...... 71 Figure 4.2: Bending test force-displacement diagram ...... 72 Figure 4.3: Force-cycles plot ...... 73 Figure 4.4: Force-displacement J1S charts comparison ...... 75 Figure 4.5: Force-displacement J3S charts comparison ...... 76 Figure 4.6: Force-displacement TS charts comparison ...... 77 Figure 4.7: Force-displacement OHCS charts comparison ...... 78 Figure 4.8: Force-displacement J3B charts comparison ...... 79

xviii

Figure 4.9: Force-displacement TB charts comparison ...... 80

xix

List of tables

Table 2.1: Additive manufacture classification according to the type [1] ...... 5 Table 2.2: Principal types and materials used for sandwich panels ...... 10 Table 3.1: Values used ...... 27 Table 3.2: Values used ...... 33 Table 3.3: Dimension's values ...... 42 Table 3.4: Number and section of the first compression test ...... 42 Table 3.5: Number and section of the second compression test ...... 42 Table 3.6: Number and section of the third compression test ...... 43 Table 3.7: Results of the compression test...... 45 Table 3.8: Shear specimens ...... 45 Table 3.9: Dimension's values ...... 47 Table 3.10: Shear test results ...... 49 Table 3.11: Diameter supports and longitude between them ...... 51 Table 3.12: Constants’ values ...... 52 Table 3.13: b values...... 53 Table 3.14: Bending test results ...... 55 Table 3.15: Fatigue test specimens ...... 55 Table 3.16: First fatigue test inputs ...... 56 Table 3.17: Second fatigue test inputs ...... 57 Table 3.18: Third fatigue test results ...... 58 Table 4.1: Criteria of compression test...... 70 Table 4.2: Shear test results ...... 70 Table 4.3: Bending test results ...... 72 Table 4.4: Fatigue test results ...... 73 Table 4.5: J1S Test vs Abaqus ...... 74 Table 4.6: J3S Test vs Abaqus ...... 75 Table 4.7: TS Test vs Abaqus ...... 76 Table 4.8: OHCS Test vs Abaqus ...... 77 Table 4.9: J3B Test vs Abaqus ...... 78 Table 4.10: Test vs Abaqus ...... 79

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List of symbols used

Symbol Unit Meaning

A m2 Surface area a mm Designs width b mm Length of the designs f Hz Test frequencies 퐹 N Bending load 푤 grams Compression weight designs h mm Wall height ℎ푐 mm Core height Kt - Stress concentration factor l mm Wall length 퐿 mm Distance between supports 퐿0 mm Initial displacement 푀푚푎푥 N mm Maximum bending moment 푃 N Load p mm Middle shear specimen layer t mm Wall thickness T degrees Temperature 푡푠 mm Sheet layers thickness ∗ 퐸1 MPa Elastic modulus in the X direction ∗ 퐸2 MPa Elastic modulus in the Y direction ∗ 퐺12 MPa Shear modulus in XY direction ∗ 휈12 - Poisson ratio in XY direction ∗ 휈21 - Poisson ratio in YX direction 𝜎1 MPa Stress in the X direction 𝜎2 MPa Stress in the Y direction 휀1 - Strain in the X direction 휀2 - Strain in the Y direction 퐸푠 MPa Elastic modulus of the solid 𝜌∗ kg/m3 The density of the design 3 𝜌푠 kg/m The density of the full solid design 휈푠 - The Poisson ratio of the solid 𝜎푐 MPa Compression stress 휀푐 % Compression strain ∆퐿 mm Displacement increment 퐸퐶 MPa Compression Elastic modulus 𝜎퐼퐼 MPa Stress at point II 𝜎퐼 MPa Stress at the point I 휀퐼퐼 - Strain at point II 휀퐼 - Strain at the point I 휏푠 MPa Shear stress 훾 rads Shear strain 휀휏 - Shear real strain

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∅ mm Supports diameters

Indices

휔 Importance parameter

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xxiv

List of acronyms used

Acronym Meaning

3D Three dimensions AM Additive Manufacturing BC Boundary Conditions CAD Computer Aided Design CAM Computer Aided Manufacturing CMC Ceramic Matrix Composite DLP Digital light processing DMLS Direct Metal Laser Sintering EBM Electron Beam Melting FDM Fuel Deposition Modelling HCI Honeycomb in-plane HCO Honeycomb out-of-plane HCO-2 Honeycomb out-of-plane second version J1 Iso grid 1 J1-2 Iso grid 1 second version J1S Iso grid 1 Shear J2 Iso grid 2 J3 Iso grid 3 J3-2 Iso grid 3 version 2 J3B Iso grid 3 Bending J3F Iso grid 3 Fatigue J3S Iso grid 3 Shear LAVEK Laboratorij za vrednotenje konstrukcij LDM Liquid Deposition Modelling LED Light-Emitting Diode MIM Material Increase Manufacturing MMC Metal Matrix Composite OHC Open Honeycomb OHC-2 Open Honeycomb second version OHCS Open Honeycomb Shear PA12 Polyamide 12 PEEK Polyether-Ether-Ketone PMC Polymer Matric Composite RHCI Re-entrant Honeycomb in-plane RHCO Re-entrant Honeycomb out-of-plane SHS Selective Heat Sintering SLA Stereolithography SLM Selective Laser Melting SLS Selective Laser Sintering SP Square Pyramid STL Stereolithography TB Tetrahedron Bending

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Acronym Meaning

TF Tetrahedron Fatigue TGM Temperature Gradient Mechanism TPS Thermal Protection System TPU Thermoplastic Polyurethane Powders TS Tetrahedron Shear XSYMM Symmetry on X direction YSYMM Symmetry on Y direction ZSYMM Symmetry on Z direction

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1. Introduction

1.1 Background

The use of additive manufacturing revolutionizes the way to develop prototypes and final parts because it allows shapes and structures not possible in traditional manufacturing processes. They have been introduced to the market to satisfy the demand for personalized parts with high geometry complexity and small series, in other words, high valued products that due to the manufacturing process, has a high cost or a big production time.

There are a lot of different types of additive manufacturing, but this master’s thesis will be focused on Selective Laser Sintering (SLS) 3D printing because it is the best method used in the laboratory for structure evaluation (LAVEK). It was also possible to use Fuel Deposition Modelling (FDM), but the surface accuracy was not as good as in the SLS technology, so this thesis needs to use a technology that does not make lose strength to the specimens, the SLS technology was selected.

This technology is going to be used to print sandwich-panel specimens, which are strong and lightweight composite structures made by different components of modern composites. It plays an important role across industries, such as aircraft or automation. There are several types of materials and different shapes used in creating these sandwich panels. This master’s thesis will study different designs, by comparing them and choosing the candidates with better results, the material used will be polyamide 12 (PA12) powder, which “Sinterit Lisa” uses as a building material.

The results obtained in this thesis will be used for evaluating if it is possible to develop products like the car seat that would be designed by these structures. In the automotive industry every step matter so this type of structures could allow reducing the weight of the speed cars, that could mean reducing prices.

1.2 Objectives

The main purpose of this master’s thesis is to develop a sandwich panel core useful for application in different load-carrying structures. It is expected that the studied designs will be strong and stiff enough to pass the different tests proposed.

1 1.2. Objectives

The first objective of this master’s thesis is to acquire knowledge on Selective Laser Sintering (SLS), which is an additive manufacturing technology that uses a laser to sinter powdered plastic material into a solid structure base on a 3D model. This is done by the study of literature based on that kind of additive manufacturing.

Another objective is to acquire knowledge on the geometry of the sandwich panels, for this, it is mandatory to learn from papers and studies that are already made. This will allow developing some designs on the software Solidworks and then test them on the finite element software Abaqus. For this reason, it will be necessary to learn how to use this software.

Combining those technologies, it is expected to develop a light-weight design of a sandwich panel made by polyamide-12, which is the main objective of the master’s thesis.

The scope is divided into 4 chapters, without taking into account the introduction.

Chapter 2 gives a general vision of what it is additive manufacturing technology. The different types of technology are named, and the advantages and disadvantages are explained. Selective Laser sintering technology is simplified to give a vision of how it works. The materials and applications are described, as well as the advantages and disadvantages. It also contains the specifications for the SLS Sinterit Lisa printer used. An introduction to the sandwich panels is made. In it, the general types and materials used with this structure are presented, together with some applications that they have in the industry.

Chapter 3 gives a context that allows understanding what the composites materials are, and which applications they have, even though the PA12 powder for its own is not a composite material, this chapter explains the different properties of this material. A general knowledge of how the printing process and post-process is given. The limitations and assumptions of the thesis are explained and last but not least, the different developed designs are explained in detail. Also, the different test made compression, shear, bending, and fatigue are explained. For each one there is an introduction, the methodology is explained, the specimens are described, and the obtained results are presented. The results from each test are a criterion to select designs to move on to the next test, in other words, the bests specimens results of the compression test will be selected to do the shear, the bests shear results will be selected to do the bending and fatigue. Moreover, the experimental results from the tests developed are used to contrast them to the results from the finite elements software Abaqus. Also, a guide to performing the test with the software is explained.

Chapter 4 describes and discuss the final results of the thesis while in Chapter 5 the conclusions are presented.

2. State of the art

2.1. Additive Manufacturing

2.1.1.Description

Additive manufacturing is a technique for fabricating parts in precise geometry using computer-aided design (CAD) and computer-aided manufacturing (CAM). Today it is being presented as an industrial revolution in more and more industrial sectors (biomedicine, aerospace, automotive, architecture, etc.) for the manufacture of prototypes or functional parts with high added value.

Different technologies have been developed for the manufacture of parts by material input, but all of them are very similar. The processes of material or additive supply are those that solidify a material, originally in a solid, liquid, or powder state, by successive layers within a predetermined space and with electronic procedures. These methods are also known by the acronym MIM (Material Increase Manufacturing) and their classification can be made according to different factors such as the "starting material" or the "process of obtaining the model”[1]. The classification of the AM technologies is given in Table 2.1

2.1.1.Advantages and disadvantages of AM

According to Gonzales and Alvarez [2], the manufacturing processes of conventional parts are conditioned by a series of limitations related to the obtaining of certain shapes, such as holes with curved trajectory, moulding angles, control of tool collisions with parts of complex geometry, without forgetting that some manufacturing processes do not comply with a commitment to sustainability in manufacturing and have associated waste related to the use of coolants.

Additive Manufacturing techniques are mainly distinguished from conventional techniques by two characteristics that also give them great competitive advantages as they do not make the manufacturing process more expensive: the geometric complexity of the part to be manufactured and the personalized design of the part to be manufactured.

4 2.State of the art

Table 2.1: Additive manufacture classification according to the type [1]

Type Technology Material Extrusion or injection Fused deposition Modelling Thermoplastics, Eutectic (FDM) metal alloys, edible Print by injection (Inkjet Rapid products Prototyping o Polijet) Granular Liquid Deposition Modelling Almost any metal alloy (LDM) Electron Beam Melting (EBM) Titanium alloys Selective Heat Sintering (SHS) Thermoplastics in powder Selective Laser Sintering (SLS- Thermoplastics, metal DMLS) powder, ceramic powder 3D printing with injection head of Plaster ink on powder bed Photo-polymerization Stereolithography (SLA) Photopolymer Digital light processing (DLP) Liquid resin

From the point of view of the production of industrial components, it is necessary to emphasize as clear advantages:

‐ Reduction of the 'time to market' of new designs. ‐ Short production series. ‐ Reduction of assembly errors and their associated costs. ‐ Reduction of tooling investment costs. ‐ Hybrid processes: it is always possible to combine different manufacturing processes. ‐ Optimization of material use. ‐ It causes more sustainable manufacturing.

However, additive manufacturing technologies have some drawbacks that must be considered when choosing the most suitable technology for the needs and requirements of the product to be manufactured.

‐ Manufacturing in layers produces what is known as the staircase effect, causing the layout of curved twins to be complicated and the surface finishes to have a high level of roughness. ‐ The manufacturing operation, as such, in some technologies can be slow; therefore, it is typically suitable for small production series. ‐ The materials used in some of the technologies may not be suitable for the product to be manufactured. ‐ Layering produces anisotropic materials. The stress behaviour of the components in service may be inadequate. ‐ The tolerances obtained are even higher than in other manufacturing methods.

5 2.2. Selective Laser Sintering

2.2. Selective Laser Sintering

2.2.1.Description

Most of the materials for three-dimensional printing are in powder form, using it as a base for additive manufacturing methods that are becoming attractive and practical for the sector industries.

In this context, the SLS is an additive manufacturing technology that uses a laser to sinters powder of the top layer of a container bed to print the 3D design pattern. The bed then descends, and a roller spreads a thin new layer of powdered material on top of the previous one. The powder supply is stored in another chamber which slightly ascends, layer by layer, enabling the roller to drag the particles to form the new layer. The process continues the same way until the part is completed. It is possible to see the procedure in Figure 2.1.

Once finished, the object can cool, the bed is raised, and the parts are broken out. Finally, the product is bead blasted to remove any remaining material. A high percentage of unused powder can be reused, and this technology conserves a lot of waste material compared to traditional ones [2].

Figure 2.1: Scheme of an SLS 3D printer basing on the construction of Sinterit Lisa [3]

2.2.2.Materials and main uses/applications

The SLS technique can use several materials, mainly plastics such as polyamides (nylon), polystyrenes, and thermoplastic elastomers. Using nylon, a strong and slightly flexible object may be manufactured. Additionally, the non-melted powder can act as a scaffold, supporting the structure and allowing complex shapes to be created. However, hollow

6 2.State of the art cavities may require the addition of escape holes to allow unsintered powder to be eliminated.

There are many existing uses for this AM technology, principally rapid design model prototypes, functional prototypes or wind-tunnel test models, series of small functional components with low volume production, customized products, etc. Another popular use is in the manufacture of customized products; this is especially relevant in the medical field for the manufacture of objects such as hearing aids, dental retainers, and prosthetics. Additionally, lightweight objects using complex lattice structures can be designed for specific uses [4].

2.2.3.Advantages and disadvantages

Just as with any other 3D printing technology, SLS also has its pros and cons. The biggest advantage of SLS is that there is no need for additional support material, regardless of the part’s geometry.

As parts are built inside the powder bin, the non-sintered powder acts as a support material to the printed part. After the part has been printed, it is left with no markings of the support material on its surface. The powder need only be brushed away.

Apart from this unique advantage, there are a few more. Because parts are built by a laser, which solidifies a cross-sectional area of each part, multiple parts can easily be printed at once. This makes SLS ideal for small manufacturing runs. The goal with SLS printers is to fill the build area with as many prints as possible to reduce the non-sintered waste powder [5].

Unlike FDM, parts printed with an SLS printer cannot be used right after the print process is complete. That is because parts must cool down, which can take a long time.

The most significant disadvantage of SLS is that it requires high-end technology and a lot of power. As such, the post-process might take a long time to do it, depending on the geometry. And closed geometries cannot be printed because the powder will get stuck in the middle of the printed object.

2.2.4.Sinterit LISA printer

The SLS printing is already explained in the previous chapter, thus this chapter does not claim to repeat this information but to clarify what the printer can do for the following master thesis.

The Sinterit Lisa printer is the model that will be used to make the sandwich panels that will be studied. So, it is important to explain their specifications and limits to consider.

7 2.2. Selective Laser Sintering

The Sinterit Lisa offers a minimum layer thickness of up to 0.075 mm, XY accuracy of .05 mm, and a 150 x 200 x 150 mm build volume. The dimension of the build volume determines the maximum number of specimens able to print at the same time and the schedule spent to print all of them, see the printer in Figure 2.2.

The following list considers all the specifications for the Sinterit Lisa 3D Printer according to the manufacturer [3]:

‐ Powder Diameter: 20 – 100 microns ‐ Recommended min. wall thickness: 0.8 mm ‐ Build Volume: 150 x 200 x 150 mm ‐ Printing Temperature: 190°C Max. ‐ Printing Technology: SLS ‐ Light Source: Class iv infrared laser, 5w, 808nm ‐ Material type: PA12 powder, TPU powder ‐ Layer Thickness: 75 – 175 microns ‐ Platform Leveling: Automatic powder spreading ‐ Dimensions: 650 x 550 x 400 mm ‐ Print Speed Guideline: 10 mm/hr in Z-direction, depending on model and material ‐ File Format: STL

Figure 2.2: Sinterit Lisa 3D printer [3]

8 2.State of the art

2.3. Sandwich panels

2.3.1. Definition

The flexural rigidity of a plate or beam type structural element is directly proportional to the modulus of elasticity and the moment of inertia; therefore, it is possible to increase it if it is divided into two, separated from each other by a low-density material. This structure is called a sandwich. A schematic draw is shown in Figure 2.3.

Structural sandwich panels with cellular core are used in aircraft and automotive construction, in load-bearing structures, and in wherever weight-saving is required. This type of structure allows the engineer a bunch of new options regarding low weight elements, high stiffness, and excellent dynamic properties.

A sandwich panel is made by two thin layers named face sheets or skins from a high- stiffness material. Between them, there is a low-density material. The skins absorb the normal stress. The core’s material works like the beam’s web absorbing the shear stress. Moreover, the core distributes the compression forces through all the panels resulting in a uniformly resistant surface without weak points or concentrations of overloads and stabilizes the surface coatings of bending or flexing sides [6].

On the other hand, there is also an adhesive, normally it is a film of epoxy. They can be classified by their thickness, like ultralight, lights, and medium.

Figure 2.3: Sandwich panel, honeycomb type

9 2.3. Sandwich panels

2.3.2.Types and materials of general sandwich structures

Table 2.2 presents the materials that are more used for skins and cores, as well as the most typical distributions for sandwich panels:

Table 2.2: Principal types and materials used for sandwich panels

Type Cores Skins layers - Metallic - Polyurethane foam - Laminates

- Polystyrene - Thermoplastics foam FOAM - Metallic - Metallic - Laminates

- Asbestos / - Composite materials concrete NERVED PLATE - Aluminium - Plywood Wood - - Laminates - Nomex® - Aluminium HONEYCOMB - Kevlar

Regarding the materials used for the core, it is possible to classify them into two main groups: metallic and non-metallic. Among the metallics, we can find both steel and light alloys, especially aluminium.

Nevertheless, among the non-metallic materials core, it is possible to found; Nomex®, which is a fibre of aramid/phenolic resin, which presents great properties of resistance and tenacity. Also, there are carbon fibre, resin epoxy, Kevlar, and glass fibre impregnated with resin. Those materials are used mostly for creating honeycomb structures, but to create new cores some foams unify parts of the core when, for example, there are different densities in the same panel, or it is also used as an adhesive of the layers.

This type of structure has huge importance in the composite materials because it allows to increase the rigidity and resistance of a structure under compression or under a flexural load, with an increase of the inertia moment and a very lightweight.

10 2.State of the art

2.3.3. Applications

The composite-material sandwich types, due to the high durability to flexural forces and mostly due to the lightweight, are one of the principal configurations used nowadays, especially in the aircraft industry, civil or military.

It was during the Second World War, when all the involved countries were in a race for developing the best war technology, that the US Army Air Force designed the Vultee BT- 15 -see Figure 2.4. It was a training aircraft, which fuselage consisted of a polyester resin reinforced fibreglass sandwich and honeycomb core made of balsa wood [6].

Figure 2.4: Airplane Vultee BT-15 [7]

3. Methodology

3.1. Designs

In this chapter a general introduction to composite mateirals is made in order to have a wider vision of this material. Then the material used to print the specimens is explained, polyamide 12. The printing proces is described as well as the limitations and assumptions taken into account. Finally, the diferent designs elaborated are described.

3.1.1.Composite materials

3.1.1.1. Description

In general, any material formed by more than one element can be considered as a composite material, fitting into this group metals, alloys, concrete, and natural compounds such as bones and wood among many others. Even though this master’s thesis uses specimens of polyamide 12 without reinforcements, it is mandatory to make an introduction of the composite materials and their classification by the matrix type, to give a better context of the material used.

From the engineering point of view, composite materials are defined as any system combination of materials built from a union (not chemical) of two or more components, which give rise to a new one with specific properties and characteristics, these new properties being none of the previous ones.

From the mechanical point of view, it is said that we are in the presence of a composite when the material functions not only depend on the spatial position (heterogeneous medium) but they are also discontinuous functions.

For a material to be considered, strictly speaking, a composite material must fulfill a series of considerations among which we can highlight that this artificially manufactured, apart from the composite material must be formed by two or more different phases, either chemically and/or physically, and they must also be separated by a well-defined interface, being out of this group, therefore, the ceramic materials.

13 3.1. Designs

The mentioned interface zone is a region of variable chemical composition, where the connection between the matrix and the reinforcement takes place, which ensures the transfer of the loads applied between the two and conditions the final mechanical properties of these materials [8].

The matrix has as fundamental objectives the protection of the reinforcements against external agents such as abrasion or corrosion, as well as transferring and distributing the loads that they support. Therefore, the cohesion between matrix and fibres must be sufficiently large so that no discontinuities arise on the surfaces between them so that mutual attacks that could weaken the fibre or alter the interface are avoided.

With the reinforcements, the aim is therefore to achieve an increase in the normal values of some physical properties, but above all those inherent in the mechanical (resistance, elastic limit, hardness) or thermal (conductivity, melting point) characteristics. All these properties are included in the common denomination of thermoplastic properties. The anisotropy or change of the mentioned properties, according to the chosen direction, is a unique property of composite materials. This leads to greater complexity in design, as it gives rise to unexpected failures or non-intuitive behaviour. But on the other hand, it allows the design of the material, together with the structure, optimally adapted to its function.

3.1.1.2. Matrix type classification

Metal matrix composites

The MMCs are characterized by their greater resistance to the composite material, as well as their good rigidity and toughness to fracture. The metallic matrix has a low anisotropy and good behaviour at high temperatures. However, this type of matrix is limited by its high density, in addition to offering certain difficulty for its processing and machining. This type of matrix has been specially designed for structural applications in the automotive, aerospace, military, electrical, and electronics industries, which usually require high rigidity, strength, and low weight.

Toyota has since used metal matrix composites in the Yamaha-designed 2ZZ-GE engine which is used in the later Lotus Elise S2 versions as well as Toyota car models, including the eponymous Toyota Matrix. Porsche also uses MMCs to reinforce the engine's cylinder sleeves in the Boxster and 911, see Figure 3.1.

Figure 3.1: Porsche 911 S turbo

14 3. Methodology

These compounds are made up of two different materials; a metal as a matrix and a reinforcement that can be present in fibres, either short or long, or ceramic or metal particles. Both components differ from each other in form or composition at the macroscopic level, presenting an interface in the contact zone.

There are three types of metal dies: aluminium alloys, titanium, and copper. Finally, the choice of reinforcement will depend on the melting temperature of the metal matrix material.

In the metal matrix, the reinforcement could be presented in different positions, those are fibres or sheets, whiskers or short fibres and particles. See them in Figure 3.2.

Figure 3.2: Disposals of the reinforcements in metal matrix composites[9]

The most used reinforcement in the compounds with the metallic matrix are the particles, since they are more economic and allow to obtain greater isotropy of properties in the product [8].

Ceramic matrix

Ceramic matrix composite materials, or CMCs, have different characteristics and behaviour than metal matrix composite materials and, as will be seen later, polymer matrix composite materials. In the polymer, the fibres provide most of the mechanical resistance, while the matrix provides sufficient tenacity to the whole. On the other hand, the ceramic matrix is very resistant and rigid, but fragile and not very tenacious. To remedy this lack of toughness, fibres are used, which, as with the metal matrices, can be short or long, so that they block the propagation of any cracks that the matrix may contain.

The main reinforcement used for this type of matrix is short fibres or whiskers, obtaining mechanical characteristics that are much higher than those of unreinforced ceramics, achieving a material that is more resistant to instantaneous failure, and reducing the

15 3.1. Designs probability of failure over time, due to the much slower growth of the cracks when the material is subjected to service stress.

The properties at high temperatures and high resistance to thermal shocks, maintaining its tenacity, resistance to breakage and creep, make these compounds ideal for use in cutting tools, for production by machining, components of thermal engines, and any other industrial components that are subject to abrasion, corrosive environments, or high temperatures.

Space transportation systems are exposed to temperatures of up to 1700°C during the re- entry phase into the earth’s atmosphere. Besides the nose area of the fuselage and of the wings, the surfaces of the steering control units and the shingles of the Thermal Protection System (TPS) are thermomechanical high-loaded structures, which are preferably made of CMC materials [10]. See an example of space vehicle with ceramic matrix composite materials in Figure 3.3.

Figure 3.3: NASA-space vehicle X-38 during a test flight[11]

Polymeric matrix

Polymer matrix composite (PMC) is the material that consists of a polymer (resin) matrix combined with a fibrous reinforcing dispersed phase. Polymer matrix composites are very popular due to their low cost and simple fabrication method. Both types of polymer, thermoplastic and thermosetting polymers are being used as matrices with natural fibres to prepare the natural reinforced polymer matrix composite [12].

Thermoset resins include polyesters, vinyl esters, epoxies, bismaleimides, and polyamides. Thermoset polyesters are commonly used in fibre-reinforced plastics, and epoxies are the most trending matrix in advanced composites resins. Epoxies (polymers) have very good electrical insulating properties and are free from volatile material [13]. It is possible to find this material in the aircraft industry, ships manufacturing, trains, and wind blades. The reinforcement is made with glass or carbon fibres.

16 3. Methodology

Thermoplastic resins include some polyesters, polyetherimide, polyamide imides, polyphenylene sulfide, polyether-ether-ketone (PEEK), and liquid crystal polymers. They are used frequently in the automotive, construction, and aircraft industry.

Polymer matrix composites (PMC’s) are made by a variety of short or continuous fibres bonded together by an organic polymer matrix. The continuous reinforcement of PMCs is responsible for their high strength and stiffness. The most important reinforcements used are glass, graphite, and aramid.

The PMC is designed so that the mechanical loads to which the structure is subjected in service are supported by the reinforcement and the matrix is used to bond the fibres together and to transfer loads between them. Combination of strong and stiff reinforcement like carbon fibre and glass fibre, along with advances in polymer research to produce high- performance resins as matrix material has helped to meet the challenges for complex designs of modern aircraft, in Figure 3.4 is possible to see the importance of composite materials in this industry due to approximate 50% of the total weight of the material is composite.

The large-scale use of advanced polymer composites in current programs of development of military fighter aircraft, civil transport aircraft, helicopters, satellites, launch vehicles, and missiles is the most glowing example of the utilization of the potential of PMC’s.

Figure 3.4: Total material used in the Boeing 787 Dreamliner [13]

3.1.2.Polyamide 12

To develop the sandwich panel designs is necessary to use a powder material in the additive manufacturing process. The SLS Lisa printer allows for usage of PA12 and TPU powders, but the one used in this master's thesis is the PA12, also known as Nylon 12. In Figure 3.5 it is possible to see some specimens made by this material.

17 3.1. Designs

Figure 3.5: First compression test specimens

Although polyamides are one of the oldest thermoplastic material groups, they have outgrown many other more modern thermoplastic polymers in almost all industrial sectors, from textiles to aeronautics. They are used to make the matrix of composite materials, which are supported by reinforcements, typically made of glass fibre or carbonium. PA12 for itself cannot be considered a composite material thus it has no reinforcements.

Within the group of aliphatic polyamides, perhaps the most widely used materials are polyamide 6 or polyamide 6-6, due to their good mechanical, chemical, and thermal properties. Although PA12 has slightly lower mechanical properties than PA6 or PA6-6, it has become the most common material in 3D SLS printing mainly for two reasons: its lower melting point and its low hygroscopicity [14].

The last property is of great importance. One of the main general characteristics of polyamides is their great capacity to absorb water, except in the case of PA12 and PA11 where the range is considerably lower, as can be seen in Figure 3.6.

During the 3D printing process, the powder is heated to high temperatures, eliminating the water from hydration during the process. A material with a high hygroscopicity will release high amounts of water during the printing process, reducing its volume and may interfere with the sintering process.

18 3. Methodology

Figure 3.6: Hygroscopicity of the different polyamides [14]

It has an ultimate tensile strength of 41 MPa with an elongation of 13%, see Figure 3.7, as well as an impact resistance of 15-20 KJ/m2, which makes it a highly versatile material. Besides, its low hygroscopicity makes its dimensional stability very good, especially in environments with high variations in temperature and humidity. It also stands out for its high reusability, requiring only 30% of the material to be used for cooling [15].

Figure 3.7: Ultimate tensile strength is given by the manufacturer [15]

19 3.1. Designs

3.1.3.Printing process

3.1.3.1. Print

It has been used the “Sinterit Studio” software to prepare the G-code for printing the specimens. It is a very user-friendly and basic software that guides the user step by step into the printing process. The software’s disadvantage is that is not possible to customize a lot of the parameters of the printing process. So, in this software, the first step to produce the specimen is the “Preset”, where a few parameters can be selected, see Figure 3.8 [16].

‐ The “Sinterit” Printer Model.

‐ The used “Sinterit” Powder type, which is Polyamide 12.

The desired Layer Height [mm]: The Layer Height can be increased or decreased to a default suggested value set automatically by the software after the Powder Type has been selected. Increasing the Layer Height, it is possible to achieve greater print speed but with loss inaccuracy. On the other hand, by decreasing the Layer height, it is possible to achieve greater accuracy but with losing in print speed.

‐ The desired Laser Power Ratio: The laser power can be increased or decreased to a default value set automatically by the software after the Powder Type has been selected. The default Laser Power Ratio is 1.0, by increasing it is possible to achieve greater durability of the printed objects but there is the possibility of losing in precision and print speed. On the other hand, decreasing the Laser Power Ratio is possible to achieve greater precision of the printed objects and higher print speed but there is the possibility of losing durability.

‐ The desired Print Surface Temperature Offset [°C]: The print surface temperature can be slightly increased or decreased to a default value set automatically by the software after the Powder Type has been selected.

‐ The Shrink Ratio in X, Y, and Z axes: It is possible to slightly expand or contract the objects in the desired direction to make them have the right dimensions after the print has finished and the objects cooled down. The allowed Shrink Ratio range is from 0.9 to 1.1.

Figure 3.8: “Preset” Sinterit Studio section

20 3. Methodology

The second software step is the “Models” section, where is possible to see the 3D CAD specimen, see Figure 3.9. It is important to consider that the maximum volume allowed is 90 130 x 130 mm. The designs are printed in 0º and 90º to optimizes the space in the powder bed.

Figure 3.9: "Models" Sinterit Studio section

The third section is “Slice” where is possible to slice into layers the previous imported 3D objects and saving the file to print. The fourth section is “Preview” where is possible to view the layers of the previous sliced 3D objects. The last section is “Printers” where is possible to see the state of the printers connected by Wi-Fi. At the top of the machine, there is a small window from which is possible to see the inside process, it is illuminated with some LEDs, see Figure 3.10. The temperature near the glass is warmer due to the laser uses high temperature to melts the powder.

21 3.1. Designs

Figure 3.10: Print process

3.1.3.2. Post-process

After the specimens have been printed in the powder bed, the print chamber needs to be cooled down, then the specimens are allowed to be removed to clean them. So, in this post- process has been used a “Sinterit” sandblaster machine, see Figure 3.11, that sandblast all the specimens for removing the unfused powder weakly attached to the specimen’s surface. Apart from the sandblaster machine, it has been also necessary to clean the specimens with thin tools and brushes to helping remove the inside powder, see Figure 3.12.

This step is very important because the specimens have small hollows to remove the powder and can be very difficult to extract it all, the procedure should be done carefully to not break some parts.

Figure 3.11: Sinterit sandblaster Figure 3.12: Cleaning tools

22 3. Methodology

3.1.4.Limitations and assumptions

When printing the corresponding specimens, it is necessary to consider a series of limitations and assumptions that have been considered to carry out this master's thesis. These can be given for two different reasons: due to the use of PA12 as a material, and due to the use of SLS additive manufacturing technology.

3.1.4.1. Material

PA 12 is a powder material that has several usages as it is said in chapter 3.1.2, however, the powder used for making these specimens has no reinforcements, which is typical among composite materials. For this reason, the models do not increase in the normal values of some physical properties. This can be traduced to obtain specimens with fewer resistances than specimens made by composite materials, which are used for made sandwich panels in high technology industries.

3.1.4.2. SLS Printing

Direction

This type of additive manufacturing uses the print layer by layer, so theoretically, it produces a part where the resistance and rigidity properties depend on that printing direction. The fact of printing layer by layer makes the printed part anisotropic, in other words, the properties changes depending on the study direction. There are three main different angles along which it is possible to print the specimens in the SLS additive manufacturing, those are 0º, 45º, and 90º, see Figure 3.13 attached.

Figure 3.13: Specimens 0°, 45°, 90° print orientations to the Z-axis print direction. [17]

23 3.1. Designs

However, it has been experimentally demonstrated that Young’s modulus for the PA12 dog-bone specimens printed in those directions are not so different, whereas the ultimate stress is more irregular [17].

In Figure 3.14, is possible to see the stress-strain diagram for three different printing directions: 0TPA12_6 is a dog-bone specimen printed in angle 0, while 45TPA12_4 is for 45º and 90TPA12_1 if for 90º. The curves have a similar slope (Young’s modulus), but the first one to break is the 0º, followed by the 45º and ending with 90º.

For this reason, in this master’s thesis is assumed that the used material is not anisotropic but is isotropic, this simplifies calculus. Although the printing direction is not so important as it was thought in the beginning, all the specimens are being printed in 90º and 0º, but only for printing optimization.

Figure 3.14: Comparative Chart of different printing directions[17]

Powder bed dimensions

The dimensions of the machine are limited to a certain volume of powder. Moreover, the powder beds cannot print an unlimited number of specimens at the same time, it is necessary to make a planning every time that some specimens are printed, to optimize the resources. The usable dimensions of the powder bed are 90x130x130, in Figure 3.13 is possible to see it.

Indirectly, as it is not possible to print all the specimens at the same time, it also takes more days to print them all. So, time is another limitation to consider. For example, printing the fatigue specimens requires about 98 hours and it is only possible to print 4 in one load. So, to print the bending and fatigue specimens, which are 12 specimens, it has been necessary 294 hours.

24 3. Methodology

Geometry

As it is explained in chapter 2.3, these structures are made by two thin layers named face sheets or skins from a high-stiffness material, where between them there is a low-density material (core).

In this master’s thesis, the objective is to develop a sandwich panel type that is made by the same material and printed all together, in other words, the skins and the core are from the same material and are printed at the same time. This means that no glue is needed thus the impression allows to keep together the part. On the other hand, the SLS technology uses powder as a support of the part and as a material to sinter. Therefore, closed geometries are not useful in this type of additive manufacturing because the powder gets stuck inside (see Figure 3.15) and it is impossible to remove and reuse it.

Figure 3.15: Remaining powder inside the specimen

For this reason, closed geometries are being developed with some orifices to extract all the powder. However, these orifices are also points of stress concentrations. Even though, open geometries are also considered and developed.

Residual stresses

The utilization of SLS technology gives a lot of advantages but also some disadvantages. A limitation to consider is the residual stresses that the printed parts obtain.

However, in most cases, residual stresses are unwanted since they result in deformations from the intended shape. Moreover, tensile pre-stress adds to the stresses caused by external loading, thus reducing the strength of the parts and favouring the propagation of cracks from the surface.

Laser-based processes (laser welding, SLM, etc.) are known to introduce large amounts of residual stress, due to the large thermal gradients which are inherently present in the processes.

25 3.1. Designs

In SLS there is a mechanism, which introduces residual stress, and it is called the temperature gradient mechanism (TGM, Figure 3.16). Owing to the rapid heating of the upper surface by the laser beam and the rather slow heat conduction, a steep temperature gradient develops. The material strength simultaneously reduces due to the temperature rise. Since the expansion of the heated top layer is restricted by the underlying material, elastic compressive strains are induced. When the material’s yield strength is reached, the top layer will be plastically compressed. During cooling, the plastically compressed upper layers start shrinking and a bending angle towards the laser beam develops [18].

Figure 3.16: TGM inducing residual stress [18]

3.1.5.Core designs

In every design the core thickness used is 15 mm, giving to the top and bottom face sheet a thickness of 2,5 mm, in total the specimens are 20 mm high. The reason is to try to optimize at maximum every print, so with less thickness of the sandwich panels, it is possible to print more specimens. All the designs have been made with the Solidworks software.

3.1.5.1. Honeycomb

As the SLS technology uses powder as a material to print, plus all the specimens are printed with the top and bottom layer of the sandwich panels, printing closed areas do not permit cleaning all the powder from inside as is explained in chapter 3.1.4 For this reason, it is necessary to study two different disposals for the honeycomb design: out-of-plane with holes and in-plane type.

It is very common to use sandwich panels with honeycomb cores of composite material for applications where low weight and high rigidity material is required. [19]. The most common honeycomb structure is composed of hexagonal cells [20]: the six sides of the cell have the l and h dimensions, but in this thesis, they are evaluated as equal, in other words, h and l have the same value. The angle θ is 30º and the wall thickness is t. Furthermore, the size of the cell (distance between two opposite sides) is 푙 · √3 [21]

26 3. Methodology

Due to the mathematical simplicity, analytical modelling with unit cell structures has been adopted by many researchers to establish comprehensive and in-depth design knowledge with several regular 3D cellular structures [22]. In this context the unit cell to study in in- plane design and in out-of-plane design is presented in Figure 3.17, and the values are in Table 3.1

Figure 3.17: Regular hexagonal honeycomb

Table 3.1: Values used

푡 1,34 푚푚 휃 30° 푙 = ℎ 5 푚푚

The values of Table 3.1 are used for both designs, out-of-plane, and in-plane Therefore, in each design, the shapes have isotropic properties because they do not depend on direction. The reference axes X1, X2, X3 are in Figure 3.18

Figure 3.18: Honeycomb directions [23]

The in-plane stiffnesses and strengths (X1 and X2 plane) are the lowest, thus stresses make the cell walls bend. On the other hand, the out-of-plane stiffnesses and strengths (X3 plane)

27 3.1. Designs are much larger because they require the axial extension or compression of the cell walls, but the specimens to study will need to have some holes in the walls to extract the powder, which reduces the Young modulus of this design [23].

Honeycomb in-plane

When this structure is loaded in X1 or X2 direction, it deforms in a linear-elastic way, the cell walls bend. The response can be described by five parameters: two elastic moduli ∗ ∗ ∗ ∗ ∗ 퐸1and 퐸2, a shear modulus 퐺12, and two Poisson’s ratios 휈12, 휈21 [23]. See the disposal in Figure 3.19.

Figure 3.19: Honeycomb in-plane design, compression specimen

The goal of this thesis is to find the ideal design for SLS technology. It is not a question of studying each design in-depth, but of finding the one that fits best. Therefore, not all the moduli will be studied, but the focus will be on Young’s modulus. All the equations are explained in Annex A, that is possible to find the formula demonstration made by J. Gibson and F. Ashby in 1999 [21] in the Cellular Solids Structure and Properties book.

According to J. Gibson and F. Ashby, 1999 [23] the young’s modulus parallel to X1 is just ∗ 퐸1 = 𝜎1/휀1, giving equation (3.1)

∗ 3 퐸1 푡 cos 휃 = ( ) (3.1) 퐸 푙 ℎ 2 푠 ( ⁄푙 + sin 휃) sin 휃

∗ On the other hand, the young’s modulus parallel to X2 is just 퐸2 = 𝜎2/휀2, giving equation (3.2)

퐸∗ 푡 3 (ℎ⁄ + sin 휃) 2 푙 (3.2) = ( ) 3 퐸푠 푙 푐표푠 휃

Nevertheless, for regular hexagons with walls of uniform thickness as in this case of study, ∗ ∗ both Young’s moduli 퐸1and 퐸2can be reduced to the same value, see equation (3.3)

28 3. Methodology

퐸∗ 퐸∗ 푡 3 1 = 2 = 2,3 ( ) (3.3) 퐸푠 퐸푠 푙

Where 퐸푠 is the solid-material Young’s modulus.

Honeycomb out-of-plane

The honeycomb out-of-plane disposal is the most used design due to mechanical properties are stronger than in the honeycomb in-plane design because the cell wall tends to contract or expand instead of bending that gives stiffer and stronger properties in X3 direction than in-plane disposal [23].

Five additional parameters are needed to describe out-of-plane deformation. Again, all of them are out of the scope of this thesis, so it will only be focussing on the Young modulus. Is possible to see the designed core for this honeycomb type in Figure 3.20, where the top and bottom face sheets are hidden to allow for the inside view.

Figure 3.20: Honeycomb out-of-plane design, compression specimen

The holes are made to allow for the powder extraction. The manufacturer says that is required diameter’s holes from 3 to 5 mm. As the side of the hexagon is 5 mm, the diameter chosen for the holes is 3,5 mm.

If the honeycomb core is loaded in the X3 direction the cell walls just actually contract and the stiffness depends on how many cell walls there are. So, the modulus in the X3 direction is equal to the area fraction times the modulus of the solid. That is just the same as the volume fraction or the relative density. This is described in equation (3.4), which has been taken from (J. Gibson and F. Ashby, 1999)

29 3.1. Designs

ℎ 𝜌∗ ( ⁄푙 + 2) 퐸∗ = 퐸 ( ⁄ ) = 퐸 · (푡⁄ ) · (3.4) 3 푠 𝜌푠 푠 푙 ℎ 2 · ( ⁄푙 + sin 휃) · cos 휃

For regular hexagons, equation (3.4) can be reduced as equation (3.5) :

∗ 퐸3 푡 = 1,15 · ( ⁄푙) (3.5) 퐸푠

The modulus goes linearly with t over l, whereas in the in-plane direction it goes with t over l cubic. Therefore, out-of-plane honeycombs are stiffer and stronger than in-plane honeycombs, so it can be considered that there is a huge anisotropy in honeycomb structures.

Nevertheless, the design made has holes in the cell walls, which reduces de rigidity of the structure. Because of that, there are stress concentrations on the sides of the notches. In Figure 3.21 the stress concentrations made by a circle can be seen, for a specimen under axial load.

Figure 3.21: Stress concentrations due to a circle

These concentrations produce an increase in stress. This is considered in the stress concentration factor (Kt) which is a parameter that does not depend on the material, just on the geometry, equation (3.6)

𝜎 = 퐾푡 · 𝜎 푟푒푎푙 푡ℎ푒표푟𝑖푐 (3.6)

It is expected that this design will be stronger than the in-plane one, even though those holes produce stress concentrations, which however would not be enough to have less stiffness. The young modulus is studied as a function of the factor t/l (Equation (3.5)) and in the in-plane design, the formula is cubic (Equation (3.3)), which makes young modulus smaller than in out-of-plane because the cell unity thickness t is always smaller than the side length l even considering the effect of the holes.

30 3. Methodology

‘Open’ honeycomb

The fact that the core is printed among the top and bottom face sheet limit the designs to open structures that might be not so rigid as a closed one. For this reason, an ‘open’ honeycomb has been developed. It is made to try to copy as much as it is possible the rigidity of the honeycomb out-of-plane.

The unity cell consists of an empty hexagonal prism, which reduces its area through a 5mm high from the bottom to the top. The top part is an inverted copy of the bottom. These parts also have a transversal cut to let extract the powder, see Figure 3.22. The three prisms are 5 mm high, so all together are 15 mm high.

Figure 3.22: Top and bottom part of the open honeycomb

The centre consists of a simple empty hexagonal prism with some supports to the other unit cells to improve the rigidity of the design, see Figure 3.23

Figure 3.23: Unit cell of the open honeycomb

The result is a hexagonal structure with some gaps to enable extract the powder. From the top view, it reminds of a honeycomb out-of-plane design, see in Figure 3.24. On the front view is possible to see the spaces made to make easier the powder cleaning, see Figure 3.25.

31 3.1. Designs

Figure 3.24: Open honeycomb core, top view

Figure 3.25: Open honeycomb, front view

3.1.5.2. Re-entrant honeycomb

The re-entrant honeycomb has been chosen for being a similar design to the conventional honeycomb but presents other properties. These designs are considered auxetic cellular structures because they exhibit negative Poisson’s ratios so that, unlike regular cellular structures, they show lateral shrinkage upon axial loads. See Figure 3.26: a) schematic diagram of a conventional hexagonal structure and how it deforms when stretched, producing a conventional positive Poisson’s ratio. b) A re-entrant honeycomb producing a negative Poisson’s ratio.

The auxetic honeycombs present some advantages over the conventional honeycomb positive Poisson’s ratio, those are improvements of many physical properties such as energy absorption capability, in-plane fracture toughness, and the ability to form dome shape curvatures under out-of-plane bending [24]. In the second place, it is been demonstrated that the re-entrant honeycomb presents better fatigue strength than the honeycomb [25], so for all these reasons it is considered this type of structure to be studied.

32 3. Methodology

a) Conventional honeycomb b) Auxetic honeycomb

Figure 3.26: Deformation under axial load: a) Conventional honeycombs and b) Re-entrant (auxetic) honeycombs [26]

The same issue as in conventional honeycomb design is presented in the re-entrant one. They are printed in the same SLS technology, so the extracting powder problem also takes place with this design. For this reason, it is necessary to study two disposals: the in-plane and the out-of-plane with holes.

As in honeycomb designs, these are modelled with unit cell structures. In this context, the unit cell to study in in-plane design and out-of-plane design is presented in Figure 3.27

Figure 3.27: Re-entrant honeycomb unit cell

Nowadays, auxetic honeycombs have attracted many researchers to develop new designs that can be implemented in many industrial applications for their properties over the regular honeycomb. While the honeycomb designs have the dimensions of Table 3.2, these have the following:

Table 3.2: Values used

푡 1,34 푚푚 휃 −30° ℎ 5 푚푚 푙 2,5 푚푚

33 3.1. Designs

Re-entrant honeycomb in-plane

In the first place, the re-entrant honeycomb in-plane disposal is explained, see Figure 3.28. The idea was to try to keep at maximum the similarities with the conventional honeycomb as possible. For this reason, the thickness is the same, and the has well. What is not possible is to have the same dimensions for h and l longitudes.

Figure 3.28: Re-entrant honeycomb in-plane, compression specimen

To study this design, it is compared to the conventional honeycomb in-plane with the unity cell’s elastic modulus. This is evaluated with the following expressions derived and presented by J. Gibson and FF. Ashby [23], K. Zied, M. Osman, and T. Elmahdy [24], see equations (3.7) and (3.8), and in Figure 3.29 see the reference axes

Figure 3.29: Unity cell reference axes [24]

1 퐸 = [ ] (3.7) 푥 푏 cos 휃 cos2휃 cos2휃 2ℎ/푙 + 푠𝑖푛2휃 ( ) ( + + ) ℎ/푙 + sin 휃 퐾푓 퐾ℎ 퐾푠

1 퐸 = [ ] (3.8) 푦 ℎ sin2휃 sin2휃 cos 휃 푏 + sin 휃 ( + + ) 푙 퐾푓 cos 휃 퐾ℎ cos 휃 퐾푠

34 3. Methodology

Where b is the deepness of the specimen for the in-plane design (thickness in z plane) and 3 퐾푓 = 퐸푠푏(푡/푙) , 퐾ℎ = [퐸푠푏/2(1 + 휈푠)](푡/푙), 퐾푓 = 퐸푠푏(푡/푙). 퐸푠 is equal to the solid- material elastic’s modulus and 휈푠 to the Poisson ratio of the solid. The angle  must be negative for the above-listed equations to be valid.

Re-entrant honeycomb out-of-plane

This design has a similar cross-section to the conventional honeycomb out-of-plane but with the advantages of the auxetic structures. For this reason, it is expected to be as stiff and stronger as the normal honeycomb or even stronger. Moreover, the holes made to extract the powder are the same diameter as the first design, so the stresses concentration are very similar too, see Figure 3.30.

Figure 3.30: Re-entrant honeycomb out-of-plane, compression specimen

3.1.5.3. Lattice structure

The past designs have good stiffness and strength properties, but they have the disadvantage that needs a lot of powder to be finished. More powder means more time and weight, but the purpose of using sandwich panels is to have a strong structure and at the same time lightweight. Nevertheless, using less powder allows reducing costs, a very important point in all companies.

35 3.1. Designs

For sure that a structure with more crossed section will be stronger and stiffer but it is also important to recycle the powder, with open-cell structures is very easy to do it. So, two lattice light-weight structures will be studied: Square Pyramid and Tetrahedron.

Square Pyramid

In this context, this pentahedron core design has been developed. According to T. Liu, Z. C. Deng, and T. J. Lu [27]. The unit cell for this structure is the following, see Figure 3.31

Figure 3.31: Unit cell tetrahedral design [27]

Where ℎ푐 is 15 mm equal for all specimens, as well as 푡푓 is 2,5 mm. The diameter of the bars is 3 mm, and the distance D is 14,85 mm. The directions of the unit cells are one next to another.

This specimen is very light but is not expected to be very strong. As it will be explained in Chapter 3.2, some specimens will be chosen from the compression test to carry on with the thesis, the method used will be a ratio that involves strength and weight. So, with that ratio, it will be possible to obtain a conclusion of this specimen.

Tetrahedron

Tetrahedron design is like the square pyramid, but with some differences. The unit cell is not composed of four-bar but from three. The diameter of the bars has been increased to 5 mm to obtain a stronger specimen. Also, the directions of the unit cells are not one next to another, they are put to compose a hexagon between them, see Figure 3.32. The purpose is to recreate the conventional honeycomb out-of-plane distribution to try to obtain similar properties. This design has been made with the help of the Ph.D. student, Jure Kajbič.

36 3. Methodology

Figure 3.32: Tetrahedron distribution, without top face sheet

3.1.5.4. Iso Grid

The idea is to recreate the honeycomb out-of-plane distribution with other shapes. Moreover, the holes to extract the powder have been improved to make it easier to clean the inside. These designs are a completely new creation and are inspired as a hierarchical configuration that can make lattice structures more efficient in bearing load according to M. Li, C. Lai, Q. Zheng, B. Han, H. Wu, and H. Fan, [28]. Three different designs have been developed: J1, J2, and J3. These designs have been made with the help of the Ph.D. student, Jure Kajbič.

This is the first design that uses triangles and hexagons in a position that allows having hexagons everywhere through the cross-section, in other words, each unit cell next to each other compose a bigger hexagon. The triangles act like “empty columns” to hold the structure, see Figure 3.33. The holes used in the past honeycomb designs have been transformed to a bigger parallelogram, that are located on the faces of the hexagons, see in Figure 3.34. The idea is to have a lighter weight design as possible but at the same time the stronger as it can be.

37 3.1. Designs

Figure 3.34: Detailed J1 hollow for Figure 3.33: J1 core powder extraction

The second design it is been inspired on J1 but uses triangles as the main part of the unity cell [28], and the unions between them are “empty hexagons”. It has inverted the J1 design where the main unity cell were the hexagons, and the triangles were the columns. In Figure 3.35 is possible to see the middle cross-section of the pattern, where the hexagonal form can be seen. The notch is wider than in the J1 and it is located on the columns of the pattern, see Figure 3.36. This design is heavier than J1, so it is expected to be stiffer and stronger.

Figure 3.36: Detailed J2 hollow for powder Figure 3.35: J2 middle cross-section, top view extraction

38 3. Methodology

The third design is the opposite of the J2 pattern or a combination of J1 and J2. Now the empty hollows are not the hexagons, they are the columns of the design, their thickness supplies the specimen with a great cross-section, see Figure 3.37, so it is expected to be stronger than the other ones. The hollows are in the faces of the triangles, see Figure 3.38.

Figure 3.37: J3 middle cross-section, top view Figure 3.38: Detailed J3 hollow for powder extraction

3.2. Experimental work

3.2.1.Compression test

3.2.1.1. Introduction

This test is not based on any standard because the aim of it was to study in the same test the effect of a simple vertical displacement in the specimens plus the designs to study could not be found in any regulation. Therefore, the purpose of this test is to find the elastic modulus and the maximum stress of the previously elaborated designs.

To compare the different specimens, a ratio will be made with the results of the test, the weight, and an evaluation of how difficult is to extract the powder, which is explained in subchapter 3.2.1.4. In the end, the best 4 specimens will be selected to proceed with the thesis with the shear test.

39 3.2. Experimental work

At the time that the tests were made, it has been possible to see different aspects or defects in the designs that were solved, for this reason, three compression tests have been required to evaluate all the different specimens.

3.2.1.2. Methodology

The design is collocated on the machine base, where previously a metal sheet has been put to have a flat surface under the specimen. The specimens must have been printed the flattest as possible to avoid eccentricities. A top flat tool then moves vertically downwards until the specimens fail due to bonding or compression. No gags have been necessary to do the test because the same top sheet has been able to press the specimens until fail.

The MTS machine has a load cell used of 25 kN and the speed test for all specimens has been the same, 1 mm/min with 10 Hz.

Is possible to see the parts of the machine in Figure 3.39. Those are a) Load cell. b) Top utensil. c) Specimen. d) Bottom sheet.

(a)

(b) (c) (d)

Figure 3.39: Parts of the compression test

For the specimens with an area of 60x60 mm2, it was necessary to use a bigger top flat tool, as there were not such as big tools in the laboratory, a flat metal sheet was glued to the previous utensil to have a bigger tool area., see in Figure 3.40: Top utensil for bigger areas: a) Tool for smaller specimens. b) Flat metal sheet.

40 3. Methodology

(a)

(b)

Figure 3.40: Top utensil for bigger areas

3.2.1.3. Specimens

For the compression test were required three different tests due to some improvements and new designs were elaborated. Although almost all the specimens have the same dimensions, some have a bigger cross-section because they were lighter. At first, all specimens were developed with a 60x60 mm2 section but were stronger than the load’s limit of the machine, so it was necessary to cut the already printed specimens and the following ones were designed with a section of 30x30 mm2. In Figure 3.41 there are the standards dimensions of them. Where 푡푠 is the top and bottom sheet thickness, ℎ푐 is the high of the core and b is the specimen’s side. See Table 3.3 for the values of the dimensions of the compression specimens.

Figure 3.41: Compression test dimension’s specimens

41 3.2. Experimental work

Table 3.3: Dimension's values

푡푠 2,5 mm ℎ푐 15 mm b 30 / 60 mm

As three different tests were necessary, the specimens are divided into 3 groups corresponding to each test.

First specimens

The first compression test has a total number of 18 specimens to test, where the designs Honeycomb in-plane (HCI) and the Square Pyramid (SP) are bigger (b =60) because they have a poor cross-section while the rest are smaller (b = 30). See them in Table 3.4 the designs Honeycomb out-of-plane (HCO), Honeycomb in-plane (HCI), Re-entrant Honeycomb out-of-plane (RHCO), Re-entrant Honeycomb in-plane (RHCI), Open Honeycomb and Square Pyramid (SP).

Table 3.4: Number and section of the first compression test

Design HCO HCI RHCO RHCI OHC SP Number 4 1 4 4 4 1 Area [mm2] 900 2400 900 900 900 2400

Second specimens

The second compression test has a total number of 16 specimens. The honeycomb out-of- plane has been modified to make it easier the cleaning dust, before the hollows were in the diagonal direction in the plane X2-X1, while the second version has them in the X1 direction. Also, new designs were made and tested, the iso grid designs. See in Table 3.5 the designs Honeycomb out-of-plane version 2 (HCO-2), Iso grid 1 (J1), Iso grid 2( J2) and Iso grid 3 (J3).

Table 3.5: Number and section of the second compression test

Design HCO-2 J1 J2 J3 Number 4 4 4 4 Area [mm2] 900 900 900 900

42 3. Methodology

Third specimens

The third compression test has a total number of 13 specimens. Where the studied specimens are the second version of the Open-Honeycomb (OHC-2), where the hollows to clean the powder are wider and the walls are thinner and this time the specimen is bigger (b = 60) because it has a poorer cross-section, and the buckling can be worse. Also, a second version of the J1 and J3 are presented with thinner walls because for the first time the powder cleaning was quite hard. In the end, the tetrahedron (TETRA) is tested, which can be considered as an improvement of the Square Pyramid design. See the specimens in Table 3.6.

Table 3.6: Number and section of the third compression test

Design OHC-2 J1-2 J3-2 TETRA Number 1 4 4 4 Area [mm2] 2400 900 900 900

3.2.1.4. Results

The objective of this test is to select the best designs to carry on with the shear test. For this reason, the elastic modulus and the maximum stress are searched. The machine takes the load and the position data, from where is possible to find the nominal Young’s modulus and the nominal maximum stress of the structure.

The compression stresses are obtained directly from the ultimate load, as is seen in equation (3.9)

푃 𝜎푐 = ⁄퐴 (3.9)

Where 𝜎푐 is the compression stress in MPa, 푃 is the load in N and 퐴 is the area of the specimens in mm2, which can be found in Table 3.4, Table 3.5, and Table 3.6.

The strains, in %, are obtained from the increment of the position of the top sheet over the initial longitude, which is 20 mm, see equation (3.10) to understand:

∆퐿 휀푐 = ⁄ · 100 (3.10) 퐿0

43 3.2. Experimental work

Referring to the elastic modulus, it is obtained from the slope of the graph stress-strain, where is possible to do a linear regression or from the Euler equation (3.11)

𝜎퐼퐼 − 𝜎퐼 퐸퐶 = (3.11) 휀퐼퐼 − 휀퐼

Where points a and b are selected manually in the graph, with the criteria to select the straightest segment possible, which are usually in the first graph part. In this context, 𝜎퐼퐼 and 𝜎퐼 are the stresses of points I and II, and 휀퐼퐼 and 휀퐼 are the strains of points I and II.

Once Young’s modulus and the maximum stress are achieved is necessary to do a ratio to compare the different designs to choose the best. For this reason, the following ratio is presented in equation (3.12)

퐸퐶 𝜎푐 푟푎푡𝑖표 = 휔 · ( ) + (1 − 휔) · ( ) (3.12) 𝑔 𝑔

Where 휔 is a coefficient between 0 and 1, thanks to it is possible to give more importance to the slope or the stress. For this master’s thesis, it is considered a value of 0,5, so the slope and the stress have the same importance in the designs. The 𝑔 is the weight in grams of the specimens which is known through the software Solidworks.

Also, the difficultness of the powder cleaning is evaluated in three criteria: easy, normal, or difficult. The design ratio and the structure’s ability to clean the powder have the same importance. With the test, some designs were really strong and stiff, but it was difficult or impossible to clean all the powder, so they have been discarded.

In the end, the best specimens are chosen according to the ratio and the powder criteria, as can be seen in Table 3.7. The values of stress and elastic modulus are the averages of each design.

Whereas the Open honeycomb version 2 has not a good ratio, the innovation is taken to do the design it has been considered, for this reason, it is also taken to do the shear test. The most promising specimens are J3-2 and Tetrahedron, the first one because it has the biggest strength-to-weight ratio and it was not so difficult to clean, and the second one because it has a good strength-to-weight ratio, but it was very easy to clean. Also, J1-2 has been chosen, for the same reasons as J3-2 even though the ratio is not so high.

See in Annex B all the stress-strain diagrams for each design, thus the values of Table 3.7 are just averages.

44 3. Methodology

Table 3.7: Results of the compression test.

Ratios w [grams] 𝜎푐 [MPa] 퐸퐶 [MPa] Stress E Final Powder extraction RHCO 42,78 23,61 494,24 0,552 11,553 6,052 hard RHCI 41,45 11,37 286,24 0,274 6,906 3,590 normal HCO 30,90 11,40 296,24 0,369 9,586 4,977 hard HCO-2 30,96 12,67 299,16 0,409 9,663 5,036 hard HCI 32,33 4,45 101,44 0,138 3,138 1,638 normal SP 25,03 2,61 60,868 0,104 2,432 1,268 easy TETRA 33,81 10,37 254,3 0,307 7,522 3,915 easy OHC 35,15 13,67 326,84 0,389 9,299 4,844 hard OHC-2 27,55 4,13 103,57 0,150 3,759 1,955 normal J1 34,03 8,18 276,30 0,240 8,120 4,180 hard J1-2 33,30 8,47 278,30 0,255 8,358 4,306 normal J2 43,51 10,92 314,72 0,251 7,233 3,742 hard J3 44,48 24,42 448,44 0,549 10,083 5,316 hard J3-2 38,69 16,63 394,61 0,430 10,199 5,314 normal

3.2.2.Shear test

3.2.2.1. Introduction

From the compression test 4 designs have been chosen: OHC-2, TETRA, J1-2, and J3-2. Since not all of them will do the bending test, it is necessary to perform a shear test to have a criterion for choosing one or another. Also, the name of them has changed to distinguish between the different tests, see Table 3.8.

Table 3.8: Shear specimens

Old name TETRA OHC-2 J1-2 J3-2 New name TS OHCS J1S J3S Number 1 1 1 1

Namely, during the bending test, a transverse load that produces a bending moment is applied, so it may happen that the specimen is forced until the breakthrough a shear load. Consequently, a shear analysis is needed.

This test is not based on any standard design that could be found in any regulation. Therefore, as in the compression test, the purpose of this test is to find the maximum stress that designs can afford, the best one will be chosen for carrying on with the bending test.

45 3.2. Experimental work

3.2.2.2. Methodology

It has not been easy to develop a shear test for the designs made. to the core should support the full load, not the top or bottom face sheet, for this reason, the specimen has suffered some changes.

On the bottom of the machine, the flat surface has been changed by a tool that can support the specimens from the corners. The specimen is subjected to a load applied at the centre. This load is transmitted through a sharp top utensil moving vertically downwards until the specimens fail. No gags have been necessary due to the same bottom tool holds the designs. See in Figure 3.42 all the parts: a) Load cell. b) Sharp top utensil. c) Shear specimen. d) Bottom holder tool.

The MTS machine used has a 25 kN load cell the speed test for all specimens has been the same, 1 mm/min with 10 Hz.

(b) (a) (c)

(d)

Figure 3.42: Parts of the shear test

3.2.2.3. Specimens

For the shear test it was enough to do one test. They have changed from the compression to study the properties of the core design, see Figure 3.43. In this case, there are two cores united by a full layer of PA12, with a thickness of 4 mm wider than the top sharp utensil. The cores have the same thickness as before, 15 mm. Whereas the total design is 39 mm wide while the lateral section is 40x40 mm2, see Table 3.9.

46 3. Methodology

Table 3.9: Dimension's values

푡푠 2,5 mm ℎ푐 15 mm p 4 mm b 40 mm

Figure 3.43: Shear test dimension’s specimens

3.2.2.4. Results

The objective of this test is to select the best design to be tested under a bending study. For this reason, the maximum stress value is searched. The machine takes the load and the position data, from where is possible to find the stress-strain diagram. In this case, is not necessary to obtain the young’s modulus due is only interesting the maximum load, consequently, the maximum stress.

The shear stresses are obtained directly from the ultimate load over 2 because in the shear diagram the force applied at the centre so the two cores are equal to half of the total load applied, as it is seen in Figure 3.44, consequently equation (3.13) (3.9) is used to obtain the shear stress:

Figure 3.44: Shear diagram

47 3.2. Experimental work

푃/2 (3.13) 휏푠 = ⁄퐴

Where 휏푠 is the shear stress in MPa, 푃 is the load in N and 퐴 is the area of the specimens in mm2, which is 40x40 mm2. The cores are not standard, they are irregular, so it is very complicated to find the proper crossed section for each one of them. For this reason, the area chosen is the full area of the specimen, thanks to it, is possible to simplify calculus. Of course, there will be some deviation from reality, but it is enough for a criterion to pick the best design.

The strains, in %, are obtained from the increment of the position of the top sheet over the initial longitude as in the pasted test, but the shear formula differs from the compression strain, see Figure 3.45.

Figure 3.45: Shear strain

According to Figure 3.45, see equation (3.14) to understand from where the shear strain is obtained:

∆퐿 tan (훾) = ⁄ℎ (3.14)

Where ∆퐿 is the position increment and h is equal to the core thickness plus half of the p thickness and half of 푡푠, giving a total value of 18.25 mm, see equation (3.15)

푡 푝 ℎ = ℎ + 푠 + = 18,25 푚푚 푐 2 2 (3.15)

From equation (3.14) is possible to take the shear strain, which has been divided by two, see equation (3.16)

48 3. Methodology

−1 ∆퐿 훾 tan ( ⁄ℎ) 휀 = ⁄ = (3.16) 휏 2 2

So, with the stain and the stress defined is possible to obtain the graphic and compare the maximum values of stress for the specimens under study.

After analysing the data obtained from the test, it has been possible to make the stress- strain diagram for every design. Where the J3-2 design showed the most promising values, so it has been chosen to proceed with the bending test. See Table 3.10 for the maximum values for each specimen. The open honeycomb version 2 was the second stronger design, but not for far and it was still hard to clean inside. On the other hand, the J1-2 has a similar design to the J3-2, to give an added value to this master’s thesis it has been considered to study in bending test the Tetrahedron with the J3-2. In addition, Tetrahedron design is the easiest one to clean the stocked inside powder for these reasons, even it is not so strong as the J3-2, it has been also chosen for the bending test.

Table 3.10: Shear test results

Design Max 휏푠 [MPa] Max Strength [N] J1S 1,57 5028,07 J3S 3,72 11900,33 OHCS 1,67 5353,43 TS 1,39 4459,48

3.2.3.Bending test

3.2.3.1. Introduction

As in the other test, this one is not based on any standard because the designs to study are not able to be found in any norm. Nevertheless, is possible to do this test using two different procedures.

The first one is the three-point bending test, where a load is applied to the specimen’s centre, which rests isostatically at its ends, causing simple bending along with the design. The generated bending moment diagram has a triangular shape with the maximum moment at the application’s point of the load. The maximum tension occurs in this central section too, see Figure 3.46.

On the other hand, the second bending test type is the four-point test, where two equal charges are applied at an equal distance from the specimen’s centre. This test is more

49 3.2. Experimental work suitable for materials that contain surface imperfections, as there is a constant distribution for moments between the two points of application of the load and the breakage can occur at any point within this distance, see Figure 3.46.

Figure 3.46: Moment's diagram. a) Three-point test. b) Four-point test

The chosen designs do not present huge surface imperfections after a visual inspection and are not wide enough to use the four-point bending test, for these reasons it has been decided to carry on with the three-point test. Even though on the application point can appear stress concentrations, two specimens of each design will be tested to reduce the possible errors.

3.2.3.2. Methodology

The specimen, i.e a panel supported by two supports, is subjected to a displacement imposed at the central point at a constant speed until it breaks, the speed is 1 mm/min. During this procedure, the force applied to the design and the displacement is measured.

It was necessary two do different methodologies study, because the boundary conditions were replied in the fatigue test, but specimens broke at the supports, so the results could not be considered as valid. See in Table 3.11 the values of the cylinder diameters and the longitude between supports of both methodologies followed.

Although it was presumed that the specimens are held by two simple supports, that is not true, as they are subjected to gripped supports. But to simplify calculus it has been decided to study them as simple supports. Furthermore, the central tool that applies the load, is applied to a grip to avoid little deformations or movements of the specimen when is under testing.

Finally, these supports transmit the load to the MTS machine bottom through two metal pieces subjected to the machine. See the first methodology boundary conditions in Figure 3.47, and the second methodology boundary conditions in Figure 3.48 where a) Load cell.

50 3. Methodology b) Specimen. c) Top utensil. d) Gripped supports. The parts are all same, the only changes are the gripped supports of the designs.

First test

At the first methodology followed, the gripped supports are made by a cylinder with a U profile, the one that carries out the load has the cylinder over the profile, the ones that hold the specimen is the opposite, the U profile is over the cylinder. In this way, it is looked to apply a clean bending load. The width of the profiles is 15mm as the diameter of the cylinders. So, the distance between the two supports is 105mm, which is equal to a minus two times the distance from the centre of the cylinder support to the edge.

Second test

The second methodology followed, is the same as the first test, but the only thing that changes are the gripped supports made by 20 mm diameter cylinders, these directly subjected the specimens. The distance between supports is 80 mm.

Table 3.11: Diameter supports and longitude between them

Test Support ∅ [mm] Longitude [mm] First 15 105 Second 40 80

(a)

(b) (c)

(d)

Figure 3.47: Parts of the bending test, first Figure 3.48: Parts of bending test, the second methodology methodology

51 3.2. Experimental work

3.2.3.3. Specimens

The designs to study are the Tetrahedron and the J3-2, as it has been possible to select with the shear test and the compression test. But they have been required some modifications to make the bending test, see Table 3.12. The designs are the same as in the compression test but with different areas. This time the area is bigger to make look more like a true sandwich panel, see Figure 3.49. Bigger specimens require more material and consequently more hours to be produced, so every 4 specimens printed needed 1 week.

As the specimens are different from the shear test, the name has changed in order to identify them better. J3S is in this test J3B and TS is now TB. The bending specimens’ names are followed by two numbers, the first one refers to the methodology used, the second one the number of the specimen, e. g., TB 11 refers to the Tetrahedral bending design, first methodology, first design.

Figure 3.49: Bending test dimension’s specimens

Table 3.12: Constants’ values

푡푠 2,5 mm ℎ푐 15 mm a 120 mm b 90 mm

First test

Due to the residual thermal stresses, the specimens had been printed with curve deformation on the top, see Figure 3.50. To avoid the effect produced by them, all the irregular shapes have been cut for the designs of the first methodology. So, in the end, the specimens have rectangular shapes, see Figure 3.51, with the same values as Table 3.12, but the constant b is different depending on the specimen, on Table 3.13 the final b dimension are shown for each design. As every specimen has different curve deformation the final b value is different.

52 3. Methodology

Table 3.13: b values

Design b [mm] TB 11 80 TB 12 85 J3B 11 85 J3B 12 85

Figure 3.50: Curve deformation, specimen Figure 3.51: Straight edges, specimen after the before the cut cut

Second test

For the second methodology used, the specimens have been printed with supports to absorb the effects of residual thermal stresses.

This solution was proposed to avoid cutting specimens, even though it was not enough thus curved shapes also appear in the top of the specimen printed with supports. On this occasion, the deformation was not so big as in the past test, but it also required a cut of around 2 mm. As in the bending specimens, it was necessary to cut the areas of the curve made by the temperature gradient inside the powder bed.

These supports have not been enough to consider the residual thermal stresses neutral. In Figure 3.52 and Figure 3.53 the supports are shown.

53 3.2. Experimental work

Figure 3.52: Printed support profile

Figure 3.53: Printed support front

3.2.3.4. Results

The objective of this test is to draw a force-displacement diagram from where it is possible to obtain the yield force. The fatigue test will be based on this force, for this reason, is not necessary to do the stress-strain diagram, plus is not possible to treat the data to obtain it thus the geometry of the sandwich panel is very irregular.

So, the force-displacement is obtained directly from the MTS 25 kN machine and no treatment is needed. TB is the tetrahedron designs for bending and J3B are the J3-2 designs for this test. All the designs have been brittle, in other words, they do not present a clear plastic regime, thus the majority of the deformation presents an elastic shape. See Table 3.14 the pic force values.

Specimens TB21 and J3B21 are the ones tested with the second methodology implemented. The second bending test is performed after the second fatigue test. With the new boundary conditions the load is applied by a line instead of a surface like the first methodology. So, applying the same force through a line makes more stress concentrations that tends these specimens to break earlier than before.

54 3. Methodology

Table 3.14: Bending test results

Design Distance supports [mm] Max Force [N] Max Displacement [mm] TB 11 105 5000,3 3,654 TB 12 105 5501,5 3,288 TB 21 80 5515,1 2,949 J3B 11 105 7644,4 4,287 J3B 12 105 7265,7 3,817 J3B 21 80 7096,2 2,208

3.2.4.Fatigue test

3.2.4.1. Introduction

Finally, the last test is presented, the fatigue test. The studied designs can be subjected to repeated loads, also called cyclic loads, and the resulting cyclic stresses can lead to microscopic physical damage to the materials involved. Even at stresses well below a given material's ultimate strength, this damage can accumulate with continued cycling until it develops into a crack or other damage that leads to failure of the component.

All the past tests lead to this one. It is expected to obtain the force-cycle plot from the specimens J3 and Tetrahedron. In Table 3.15 find the specimens tested, where the Tetrahedron design has the name of TF and the J3-2 is called J3F, to differentiate them from the other’s tests specimens.

Table 3.15: Fatigue test specimens

Old name TETRA J3-2 New name TF J3F Number 2 2

Due to some unexpected results during the test performed, three different tests have been required to obtain results that could be considered valid.

3.2.4.2. Methodology

The specimen, hold as a panel on two supports, is subjected to a cyclic displacement imposed at the central area until it breaks. The frequency imposed is 1 Hz for the peak force applied, and for the other points of the plot it is used 2 Hz to reduce test time. During this procedure, the peak limit force is applied to the design, and the peak displacements are measured.

55 3.2. Experimental work

Finally, these supports transmit the load to the MTS machine bottom through two metal pieces subjected to the machine. See them in Figure 3.48 on page 51.

As it is explained in the bending methodology, the boundary conditions suffered changes due to the test performed, so the same two bending methodologies are implemented to do the fatigue test. See them explained in subchapter 3.2.3.2 on page 50.

3.2.4.3. Specimens

The specimens used in this test are the same as the bending test, but with the difference that all these have been printed with the supports explained in the second test specimens of the bending.

3.2.4.4. Results

First test

The first test corresponds to the one done with the same boundary conditions as the first bending test. As it is explained in subchapter 3.2.3.2, cylinders with U profiles are used to support the design and transmit the load in it.

As the specimens showed a very elastic behaviour, the criterion selected in order to perform the test is the 80% of the ultimate strength obtained in the first bending test to the maximum force applied, and to the minimum is 5 % of the maximum load allowed. See in Table 3.16 the values obtained from static test and the values applied in this fatigue test.

Table 3.16: First fatigue test inputs

Bending Fatigue Design F max [N] F max [N] F min [N] J3F 7455,079 5964,06 298,20 TF 5250,894 4200,71 210,04

The results showed that the specimen broke through the supports, meaning that the boundary conditions applied were wrong, so it was necessary to change them. For this reason, a second test was needed.

Second test

In this test, the boundary conditions used are from the second methodology presented in the bending test. This time, the U profile is substituted by 20 mm cylinders. This means the load limits with new boundary conditions need to change because the distance between supports had changed.

56 3. Methodology

In order the have the same maximum moment, see Figure 3.54, even with the changed longitude between supports, the following procedure is followed.

Figure 3.54: Maximum moment at application area

Using equation (3.17) the new load for the new boundary conditions is obtained:

퐹 · 퐿 푀푚푎푥 = (3.17) 4

Where for the first test L is 105 mm and for the second L is 80 mm, to obtain the moment at the centre, first is obtained from the load of the bending results, then the moment keeps constant and the L longitude changes, as the result the incognita is the new load, then the 80% is selected to be the maximum load permitted and the minimum is the 5% of it, see Table 3.17 where the results are shown.

Table 3.17: Second fatigue test inputs

Bending Fatigue Design F max [N] M [N mm] F [N] F max [N] F min [N] TF 5250,89 137835,96 6891,80 5513,44 275,67 J3F 7455,08 195695,82 9784,79 7827,83 391,39

Applying these force limits conducted to J3F to fail after only 2 and a half cycles, which means the loads were too high for the designs. This is because the effect of applying the load through a line instead through a surface was not considered when doing the load recalculation. The second methodology uses cylinders that transmitted the load with more stress concentrations than the U profile. It has been clear that less load was needed to perform the test.

57 3.3. Finite element simulations

So, it has been decided to do another bending test with the cylinder boundary conditions to obtain a better load for the fatigue test. It has been after the second fatigue test that the second bending test has been performed.

Third test

To do this test, the second methodology for the bending test has been required because the second fatigue test showed that the procedure followed was not good. So, a second bending test was performed, and the results showed that the maximum load enabled by the designs does not change much with the different supports length. So, the average values of maximum bending force for each design are obtained, from it, the first load of the fatigue test has been selected, which was about the 80% of the bending average load, for J3B the average of static load is 7335,5 N and for TB is 5339 N. The loads applied in every fatigue test is in Table 3.18. For other points, the load has been decreased to obtain more cycles.

Table 3.18: Third fatigue test results

Fatigue Design F max [N] F min [N] N [cycles] LOG10(N) J3F 11 5964 298 13088 4,116873 J3F 12 5200 260 32948 4,517829 J3F 13 4800 240 93537 4,970981 TF 11 4201 210 8592 3,934094 TF 12 3500 175 24799 4,394434 TF 13 3200 160 36890 4,566909

As the procedure and the results are valid, this test has been considered valid to study the designs under fatigue load. From Table 3.16 is possible to draw the force-cycles plot. From where it is possible to obtain from which load and cycles the design is supposed to fail.

3.3. Finite element simulations

The purpose of this chapter is to compare experimental values with the finite element software Abaqus. The designs have not standard shapes from which it is not trivial to analyse the data, quite the opposite, they have very irregular geometries from which is not possible to treat the data properly. For this reason, they are treated in a simple way to obtain the stress-strain diagram. Nevertheless, is possible to obtain the real chart using finite element software such as Abaqus, but the results will differ so much from the ones calculated previously.

58 3. Methodology

Consequently, in this chapter the data to compare is the force-displacement diagram because in this type of chart the values are closer to reality thus they are obtained by the MTS 25 kN machine directly, so the values are closer to reality

The studies are divided by each type of test, from where all the Abaqus process and post- process are explained. Data is contrasted with the results obtained experimentally from the tests made. Every step of the program is explained as well as the tools used.

3.3.1.Abaqus

On one hand, there are four different specimens (J1S, J3S, TS and OHCS) studied under a shear load, and on the other, there are two different designs (J3B and TB) for the bending test. So, the following procedure is used the same way for all specimens excepting the subchapters Part and Step, where the principal difference between the shear and the bending designs is the shape, and, consequently, the boundary conditions implemented.

3.3.1.1. Part

Shear

As calculus is time-consuming, it requires a lot of computer power, so it has decided to cut the specimens into four equal pieces, corresponding to two symmetric planes. This is only possible because the designs are symmetric in Y and Z directions. So, in Figure 3.55 there are the symmetry planes that the specimens have been reduced to. Even though J3 is not symmetric on Z direction, so for this specimen it has only reduced on Y direction.

Therefore, is possible to spend less time doing the calculation, otherwise submitting the model to run could last more than 12 hours. See Figure 3.56 an example of the reduced specimens, corresponding to the J1S design.

Figure 3.55: Symmetry planes Figure 3.56: Reduced specimen

For obtaining the final part, the following procedure has been used.

59 3.3. Finite element simulations

First, the step file from Solidworks has been imported to the part. Then to cut the design into two planes it has been necessary to use the tools:

Partition face: Use the shortest path between two points. This tool has allowed cutting the specimen into 4 pieces.

Remove faces: After cutting the specimen it has been necessary to delete the not use parts of it with this tool.

Partition face: Sketch. To set up the boundary conditions on the support and where the load is applied, it has been necessary to divide the top and bottom surface, to get the surface that is truly under the effort.

Bending

The bending J3 specimens have been reduced in 4 equal parts as well as the shear specimens. But the symmetric axes have changed due to the geometries are different, in this case, the symmetric axes are X direction and Z direction. See the axes planes in Figure 3.57 and see a reduced specimen in Figure 3.58. It is important to say that Tetrahedral design is only symmetric on Z direction, so It only has reduced to two parts.

Figure 3.57: Symmetry planes bending Figure 3.58: Reduced bending specimen

3.3.1.2. Property

The section is assigned to the part, which previously has been created as well as the material that has been characterized.

The material used is the same as the one that the SLS printer uses, polyamide 12. So, to characterize this material has been introduced two behaviours: elastic and plastic. All the data was previously demonstrated experimentally by Sacchetti, G. on his master’s thesis “Topology optimization for structural strength and durability of 3D printed curved beams made of polymer and metal materials”[17].

Create material: On one hand, the isotropic elastic zone allowed to define the Young’s Modulus (1210 MPa) and the Poisson’s Ratio (0.41). On the other hand,

the plastic zone has been defined as isotropic with the true stress and the true

60 3. Methodology

plastic strain average [17], thanks to it the deformations of the specimens during the test can consider giving a more realistic test to the Abaqus simulations. See the values for the true stress and true plastic strain in Annex B

Create Section: With this tool, the material previously created is loaded to be under a section as a homogeneous solid.

Assign Section: After creating the section, it is given to the part to study, to tell the software which type of structure is the design.

3.3.1.3. Assembly

When a part is created, it exists in its coordinate system, independent of other parts in the model. In contrast, the Assembly module to create instances of the parts and to position the instances relative to each other in a global coordinate system, thus creating the assembly. The position part instances by sequentially applying position constraints that align selected faces, edges, or vertices or by applying simple translations and rotations.

Create the instance: By applying this tool, a global coordinate system is given to the part. Just selecting the desired part to study is enough to complete this step. If everything is correct, the design will change the color to blue and a yellow coordinate system will appear, see Figure 3.59

Figure 3.59: Assembled part

3.3.1.4. Step

One initial step comes always predefine in the model, the initial step. It is a special step that Abaqus create at the beginning of the model’s step sequence. In which is possible to define boundary conditions, predefined fields, and interactions that are applicable at the very beginning of the analysis.

After the initial step, a second one is added to apply the displacement on the surface top corner. See Figure 3.60.

61 3.3. Finite element simulations

Figure 3.60: Model steps

Create step: The second step is created by this tool. It must go after the initial and the procedure type is generally static. The nonlinearity of the geometry must be on, to consider the effect of deformation in the design. The period is 1. And the maximum number of increments is 100. That means that Abaqus will divide the total time period for the step into 100 increments. The initial, minimum, and maximum increment size is defined to 0,1.

Create Field Output: This tool is needed to obtain the results of the contact surface load, to extract the results in that part. To do that, a previous set of the desired surface must be done. Then the domain defined in the tool is the made set. From where the stresses, strains, displacements, forces, and contacts are selected.

Create History Output: With this tool, the total energy of the model can be obtained in the results.

3.3.1.5. Load

Shear

As the same recreation of the test is needed, the boundary conditions applied will be the same ones as in the test. To do that, a displacement is applied on the top corner surface, and at the bottom opposite surface, all movements are restricted to recreate the support. Not all the top corner surface is selected to be under displacement because the utensil used to transmit the load was smaller than all the surface, for this reason, the area selected to be under the displacement is 1,5 x 60 mm2, as the used tool was 3 mm thick and the total is 4 mm thick.

Moreover, as two different symmetry planes are applied in the Z and Y direction, it is mandatory to apply boundary conditions on the same symmetry faces. On the Z face plane, it is applied ZSYMM where the movement on Z is restricted as well as the rotations respect Y and Z (U3 = UR2 = UR3 = 0). On the Y face plane, it is applied YSYMM where the movement on Y is restricted as well as the rotations respect X and Z (U2 = UR1 = UR3 = 0).

Create boundary condition: All the different boundaries conditions are created by this tool, where first of all the type is selected, for the designs, it has been only required Symmetry or Displacement.

62 3. Methodology

In the end, the following boundary conditions must be created, see Figure 3.61 and Figure 3.62. Only the load should be created in the second step (Loading), the other ones should be created on the initial and propagated to the loading.

Figure 3.61: Boundary conditions

Figure 3.62: BC in the model

Bending

It should be recalled that two bending tests were necessary with different counter conditions. One with a support spacing of 105 mm and the other with a support spacing of 80 mm. To get a more realistic view of the comparisons between theory and experiment, the two types of tests were recreated.

Thus, a line with the restricted movements in the direction of the applied load has been drawn on the support site. On the other hand, at the upper central edge, an area of 1 mm amplitude has been used with the same edge to apply the displacement that will cause the bending load.

Also, two symmetry planes are applied, this time in X direction XSYMM where the movement on X is restricted as well as the rotations respect Y and Z (U1 = UR2 = UR3 = 0). And on the Z face plane, it is applied ZSYMM where the movement on Z is restricted as well as the rotations respect Y and Z (U3 = UR2 = UR3 = 0).

In this way, it has been possible to recreate the bending tests carried out previously.

3.3.1.6. Mesh

The mesh allows obtaining more or less accurate results, depending on the size. As it is divided into more parts, the mesh will be more realistic.

63 3.3. Finite element simulations

Seed part: First of all, it is required to select the maximum size of the elements that will be divided into the specimen. So, approximate global size of 0.5 has been

selected, to have as many accurate results as possible.

Assign Mesh Controls: Secondly, the shape of the elements that will compose the mesh needs to be selected. For very irregular geometries it is recommended to use tetrahedral forms, but for regular geometries, it is enough with hexagonal forms. For this reason, the core design is studied under the tetrahedral form. The tetrahedral form uses mapped tri meshing on bounding faces where is appropriate, this is an algorithm that enables the optimization of the mesh where is needed. The geometric order selected is quadratic.

Mesh part: This tool generates the final mesh, see an example in Figure 3.63

Figure 3.63: Design's mesh

3.3.1.7. Job

Once the mesh is already applied, is possible to start the calculation. To do it is necessary to make a job, from where the calculus will be saved. Then the data is checked and finally is possible to begin. Some jobs require a huge quantity of time to process all the data, it depends on the geometry, the number of elements generated, and the number of iterations selected.

Create Job: Within this tool, the job is generated. Then the data must be checked to avoid possible mistakes during the simulation.

After creating the job, and checking the data, the simulation can be submitted that can be supervised by the job manager.

64 3. Methodology

3.3.1.8. Visualization

If the boundary conditions were well applied the maximum displacement should be in the load area and the support there must be non, see Figure 3.64 where the colour red is referred to the maximum displacement and the blue is to the minimum.

Figure 3.64: Shear specimen displacement

Plot contours on deformed shape: This allows to see graphically the effect of the reactions that were selected previously in the step. The data to treat in this case will be the force-displacement chart, to see the displacement of the design, U in Magnitude must be selected on the top bar of the screen.

Create XY data: Used to generate plots from the desired data of the model. One node of the load section is selected, from it, the displacement is obtained as an ODB field Output, the variable is unique nodal, and the U displacement is selected (depending on the load direction, is possible to select U1, U2, or U3) The method is node label, from where is possible to select the wanted node. Then the reaction forces of every element of the load section need to select and summed to have the real force in the area. It is obtained by ODB history output, where the selected variables are the sum of reaction forces on the displaced area. Then plot the is generated by combining the reaction forces of the loading surface and the displacement of the node.

3.3.2.Results

3.3.2.1. Shear

After all the 4 shear designs were simulated in the finite element software Abaqus, the results obtained enable an insight into which design is stronger and stiffer. As expected, the design that stands out from the others is the J3, which has a much higher slope and strength than the other models. Furthermore, the other three designs have very similar behaviour, see Figure 3.65.

65 3.3. Finite element simulations

At first glance, it may seem that the general behaviour of the graph obtained by Abaqus appears to be similar to the behaviour of the results obtained from the stress-strain test. However, it is still necessary to compare the reactions and displacements of the two methods, to conclude whether the procedure followed has been good or not.

It can be seen that the curves show two behaviours: elastic and plastic. This is since the material characterized in Abaqus has these behaviours, so the results of this theoretical test also show them.

Abaqus Shear 12000

10000

8000

6000 Force Force [N]

4000

2000

0 0 1 2 3 4 5 6 Displacement [mm]

J1 J3 TETRA OHC

Figure 3.65: Abaqus shear results, force-displacement plot

3.3.2.2. Bending

It is important to note that the experimental bending test was done with two methodologies, the first one with U-sections and a spacing of 105 mm, and the second one with cylinders and a spacing of 80 mm.

As the second one has been the most useful in the bending and fatigue tests, it has been considered only to simulate the test performed with this methodology.

66 3. Methodology

At first sight, it is very similar to the experimental test since, again, the J3 design turns out to be the stiffer and stronger. As in the shear test, the graphs clearly show elastic and plastic behaviour, where the TETRA design seems to present a more plastic behaviour than the J3, see Figure 3.66. But it still needs to be checked with experimental values to decide whether these simulations can be considered valid or not.

The biggest drawback of the use of the Abaqus software has been the time required to simulate the tests, as many hours and a very powerful computer were needed, since the calculations were very large, even with the simplifications implemented.

Abaqus Bending 9000

8000

7000

6000

5000

4000 Force Force [N]

3000

2000

1000

0 0 1 2 3 4 5 6 Displacement [mm]

J3_80 Tetra_80

Figure 3.66: Abaqus bending results, force-displacement plot

4. Results and discussion

4.1. Experimental tests

4.1.1.Compression

This test is the first of 4 different tests that allow characterizing the designs to see which one is the best candidate to be selected as the best design. Both in terms of its ability to withstand different stresses and its geometry to facilitate the removal of excess material from the 3D printing process.

After testing 47 different specimens under compression loading and developing 14 different designs. It was possible to obtain the 4 best candidates for the shear test.

The candidates were chosen based on two criteria. The first was a ratio between the ultimate stress, the modulus of elasticity, and the weight of the design. The second criterion was the ease with which it was possible to clean the inside of the designs of polyamide powder.

The following summary Table 4.1 shows the values obtained for each of the different designs produced and tested. It can be seen that the chosen designs were the TETRA, OHC-2, J1-2, and J3-2.

Although there are specimens with better strength and slope ratios, it was also more difficult to extract the excess powder from the inside, which is why they were discarded. Like the design J3 and OHC, both presented extraordinarily strength against the compression load but when they were broken, it could be possible to see how full of polyamide powder were, so it was necessary to do some modifications in the design to obtain be able to remove more dust from the inside. It is important to note that unused material can be reused for future printing.

69 4.1. Experimental tests

Table 4.1: Criteria of compression test

Ratios Stress E Final Powder extraction RHCO 0,552 11,553 6,052 hard RHCI 0,274 6,906 3,590 normal HCO 0,369 9,586 4,977 hard HCO-2 0,409 9,663 5,036 hard HCI 0,138 3,138 1,638 normal SP 0,104 2,432 1,268 easy TETRA 0,307 7,522 3,915 easy OHC 0,389 9,299 4,844 hard OHC-2 0,150 3,759 1,955 normal J1 0,240 8,120 4,180 hard J1-2 0,255 8,358 4,306 normal J2 0,251 7,233 3,742 hard J3 0,549 10,083 5,316 hard J3-2 0,430 10,199 5,314 normal

4.1.2.Shear

The treated specimens do not have a common form, therefore it is not possible to find any standards explaining how to test them. That is why we had to find a method to perform the test. The specimens have been modified in such a way that in the centre of the specimen a flap has been placed which separates the interior into two.

In this way, it was possible to produce a design with a duplicated core. This sheet has received the stress of the machine and has made it possible to transmit the stress to the geometries of the cores. The specimens were clamped at the bottom corners to be able to shear test the cores. The purpose of this methodology was to find the clean shear stress.

Table 4.2 shows the values obtained and Figure 4.1 shows the stress-strain curves of the 4 tested designs. The J3S design stands out from the others because it is very strong and has a very pronounced elastic modulus. It has therefore been selected for the bending test. As the other designs have very similar behaviour, it has been decided to continue with the TS design as it is the easiest to clean the polyamide dust from the inside.

Table 4.2: Shear test results

Design Max 휏푠 [MPa] Max Strength [N] J1S 1,57 5028,07 J3S 3,72 11900,33 OHCS 1,67 5353,43 TS 1,39 4459,48

70 4. Results and discussion

SHEAR TEST 4,0

3,5

3,0

2,5

2,0 STRESS [MPA] STRESS 1,5

1,0

0,5

0,0 0 1 2 3 4 5 6 7 8 9 10 STRAIN [%]

TS J1S J3S OHCS

Figure 4.1: Shear test stress-strain diagram

4.1.3.Bending

After having done two tests with different boundary conditions, the results of Table 4.3 could be obtained. All designs show a high elastic behaviour because the straight lines show a fairly uniform slope, see Figure 4.2. However, it is not easy to know where the change between Hooke's regime and the plastic zone lies.

Thus, it can be seen from the two tests that the ultimate loads are very similar for each design. On the other hand, the tests carried out with less distance between the supports have a greater slope and consequently break with less displacement. The reason is that the second methodology used has cylinders as boundary conditions that transmit the load through a line instead of the first methodology, that used a U profile which transmited the load through a surface. So with second methodology, there were more stress concentrations that enable the design to be stiffer but consequently, they achived the same load with less displacement.

71 4.1. Experimental tests

Due to the large volume of the specimens, the printing time was very long, around 147 hours for the six designs studied in this trial.

Table 4.3: Bending test results

BENDING TEST 9000

8000

7000

6000

5000

Force Force [N] 4000

3000

2000

1000

0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 Displacement [mm]

TB 11 TB 12 J3B 11 J3B 12 TB 21 J3B 21

Figure 4.2: Bending test force-displacement diagram

72 4. Results and discussion

4.1.4.Fatigue

After 3 tests, in which a total of 6 designs were tested, it was possible to obtain valid results against a cyclic load.

The results of the static bending test have been used to obtain the point of maximum fatigue load, from there on, the other points have been obtained by reducing this value, consequently the cycles to failure increase and a load-cycle line can be obtained, see Figure 4.3. In Table 4.4 the values for the different points of the line are shown, specifying the load applied in the test to obtain the different number of cycles.

Table 4.4: Fatigue test results

Fatigue test 7000

6000

5000

4000 Force Force [N] 3000

2000

1000 3,5 3,7 3,9 4,1 4,3 4,5 4,7 4,9 5,1 Log10(N)

Tetra J3

Figure 4.3: Force-cycles plot

73 4.2. Tests contrasted with Abaqus

All the tests carried out lead to this, from the compression test, which served to have a selection criterion among the more than 10 different designs created, passing through the shear test where the 2 final designs to be studied under flexure and fatigue could be obtained. 4.2. Tests contrasted with Abaqus

As the studied geometries are very complex, it is not possible to compare the stress-strain diagram because the crossed sections are so irregular. Only considering them as fully solid, without any spaces in the core, it could be possible to get stresses similars to reality but in this manner, the Abaqus results are not valid to contrast. The real data possible to compare is the force-displacement plot. The performed tests allow getting real force and displacement which is valid to contrast with Abaqus simulations.

Abaqus results are distinguished from each kind of design and contrast with the corresponding specimen test.

4.2.1.Shear

The shear force in a bending test is very important to consider because it provokes the moment that breaks the specimen. In this context, it is mandatory to do a shear test to carry on with the bending test. For this reason, the test must be well performed, to avoid mistakes in choosing different designs. Contrasting experimental values with theoretical ones enable to obtain the searched design properties better.

4.2.1.1. J1

The first compared design is J1S. As the plot demonstrates the two methods, experimental and theoretical, have a good correlation meaning that the performed tests are very close to reality, see Figure 4.4. From the Abaqus curve, it is obtained a polynomial trendline of 3rd grade to obtain the equation. In it, it is selected the deformation where the design broke to obtain the force in Abaqus when the specimen failed. As can be seen in Table 4.5 the difference between the two values is about 5%. On the other hand, the slope at the Hooke's regime of the curve differs only 6,86 % from the test. So, both studies are almost equal in this space.

Table 4.5: J1S Test vs Abaqus

Force [N] Displacement [mm] Slope Test 5028,07 1,52 3449,24 Abaqus 4789,04 1,52 3686,00 Stdev 169,02 167,41 Variance [%] 4,75 6,86

74 4. Results and discussion

J1 Shear 8000 y = 120,7x3 - 1182,7x2 + 4630,6x + 52,314 7000 R² = 0,9995

6000

5000

4000 Force Force [N] 3000

2000

1000

0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 Displacement [mm]

Test Abaqus Poly. (Abaqus)

Figure 4.4: Force-displacement J1S charts comparison

4.2.1.2. J3S

The second compared design is J3S. With this specimen, the Abaqus values do not fit as well with the J1S design, see Figure 4.5. From the Abaqus curve, it is obtained a polynomial trendline of 3rd grade to obtain the equation. In it, it is selected the deformation where the design broke to obtain the force in Abaqus when the specimen failed. Table 4.6 reflects the values of the contrasted loads and slopes. The variance at the moment when the specimen failed in the experimental test with the load obtained from Abaqus is about 27 %, and the slope at the elastic zone difference is about 19 %. Even the values to the first millimeter are very similar, from that point on they differ quite a lot.

Table 4.6: J3S Test vs Abaqus

Force [N] Displacement [mm] Slope Test 11900,33 3,154 5968,67 Abaqus 8693,87 3,154 4845,12 Stdev 2267,31 794,47 Variance [%] 26,94 18,82

75 4.2. Tests contrasted with Abaqus

J3 Shear 14000

y = 112,57x3 - 1305,9x2 + 5708,1x + 149,65 12000 R² = 0,9985

10000

8000

6000 Force Force [N]

4000

2000

0 0 1 2 3 4 5 6 Displacement [mm]

Abaqus Test Poly. (Abaqus)

Figure 4.5: Force-displacement J3S charts comparison

4.2.1.3. TS

The third compared design is TS. With this specimen, the values obtained presents great similarities, see Figure 4.6. From the Abaqus curve, it is obtained a polynomial trendline of 3rd grade to obtain the equation. In it, it is selected the deformation where the design broke to obtain the force in Abaqus when the specimen failed. Table 4.7 shows the values of the contrasted loads and slopes. Unlike the past comparisons, in this design, the load at failure differs by 14,76 %, and the slope of the elastic zone of the curve deviates by 7,38 %. Thus, the two studies are very similar in the elastic zone of the Abaqus model.

Table 4.7: TS Test vs Abaqus

Force [N] Displacement [mm] Slope Test 4459,48 1,293 3508,39 Abaqus 3801,41 1,293 3249,61 Stdev 465,33 182,98 Variance [%] 14,76 7,38

76 4. Results and discussion

TETRA SHEAR 7000

y = 155,95x3 - 1260,3x2 + 4303,9x + 6,523 6000 R² = 0,9998

5000

4000

Force Force [N] 3000

2000

1000

0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 Displacement [mm]

Test Abaqus Poly. (Abaqus)

Figure 4.6: Force-displacement TS charts comparison

4.2.1.4. OHCS

The fourth compared design is OHCS. Like the other specimens, this one presents greats similarities, see Figure 4.7.

Comparing the data obtained by the experimental test with a polynomial trendline of 3rd grade of the Abaqus data is possible to describe the differences at the moment of break. This time, the variance between loads is about 18 % and the slope at the more elastic zone only differs a 5,71 %, see Table 4.8.

Table 4.8: OHCS Test vs Abaqus

Force [N] Displacement [mm] Slope Test 5353,43 1,58 3643,76 Abaqus 4393,18 1,58 3435,80 Stdev 678,99 147,05 Variance [%] 17,94 5,71

77 4.2. Tests contrasted with Abaqus

OHC SHEAR 6000 y = 239,16x3 - 1650,7x2 + 4828,6x - 58,401 5000 R² = 0,9998

4000

3000 Force Force [N] 2000

1000

0 0 0,5 1 1,5 2 2,5 3 Displacement [mm]

Test Abaqus Poly. (Abaqus)

Figure 4.7: Force-displacement OHCS charts comparison

4.2.2.Bending

Applying a bending load on the specimens allows to obtain the maximum possible load to perform the fatigue tests. This is why it is necessary to check the results obtained with finite element software and perhaps it could be useful for future research. The data contrasted is from the second methodology where the distance between supports was 80 mm.

4.2.2.1. J3B

The first bending design compared is the J3. The followed to contrast the results is the same as the shear designs, where a 3rd grade polynomial trendline is used to contrast loads at the moment of failure in experimental test, see Figure 4.8. This time the results differs a bit more than the shear ones, with a difference of 29,02 % of force and with a 27,22 % of slope in the straigthest area, see Table 4.9.

Table 4.9: J3B Test vs Abaqus

Force [N] Displacement [mm] Slope Test 7096,17 2,208 3472,04 Abaqus 5036,57 2,208 2526,90 Stdev 1456,36 668,32 Variance [%] 29,02 27,22

78 4. Results and discussion

J3_ 80 Bending 9000

3 2 8000 y = 28,372x - 476,53x + 3220,1x - 55,541 R² = 0,9997 7000

6000

5000

4000 Force Force [N]

3000

2000

1000

0 0 1 2 3 4 5 6 Displacement [mm]

Test Abaqus Poly. (Abaqus)

Figure 4.8: Force-displacement J3B charts comparison

4.2.2.2. TB

The last design constrated is the TB. Where the load at the design fail differs about a 26 % between the experimental test and the data obtained from Abaqus. The trendline is also 3rd grade polygonal. On the other hand the slope differs 21,28 % from the straightes part of the graphs, see data on Table 4.10 and graph on Figure 4.9.

Again, it seems that throught the first displacements the results are so similar but as the displacement increases it also does the difference between the two procedures.

Table 4.10: Test vs Abaqus

Force [N] Displacement [mm] Slope Test 5515,13 2,95 2216,53 Abaqus 4105,31 2,95 1744,80 Stdev 996,89 333,56 Variance [%] 25,56 21,28

79 4.2. Tests contrasted with Abaqus

TB_80 Bending

6000 y = 15,96x3 - 343,67x2 + 2284,4x - 52,244 R² = 0,9996 5000

4000

3000 Force Force [N]

2000

1000

0 0 1 2 3 4 5 6 Displacement [mm]

Test Abaqus Poly. (Abaqus)

Figure 4.9: Force-displacement TB charts comparison

5. Conclusions

Finally, with the present thesis, more than 10 different sandwich panels have been designed, 3D printed with SLS technology, and subjected to different efforts to choose the ones with the best mechanical properties but also the most feasible to be printed in this additive manufacturing technology. Thus, the findings have been:

1) It has been possible to understand how SLS printing works, thanks to the research and interpretation of the different articles and books that have been found.

2) Different sandwich panel core geometries have been designed and studied in this thesis. This objective has not been trivial since it has been necessary to think always about the printing method and its disadvantages, but in the end, the result has been complex geometries printable with SLS.

3) The obtained results indicate that it has been possible to design two different sandwich panels that have passed compression, shear, flexural, and fatigue tests. Initially, more than 10 designs have been designed, of which the different tests carried out have allowed the selection of the two designs with the highest possible mechanical properties and the easiest to print. The final two sandwich panel designs have been Iso grid 3 and Tetrahedral, the first present stronger and stiffer properties while the second presents easier behaviour to get cleaned inside.

4) Experimental results were compared with simulations carried out in the finite element software Abaqus. Only the shear and bending tests have been compared, but they have been sufficient as both show the same behaviour. On the one hand, the elastic part of the two methods has turned out to be very similar. But on the other hand, large discrepancies in the plastic regime could be observed. It is believed that this is since the boundary conditions could not be perfectly recreated in Abaqus, as it is almost impossible to recreate the behaviour of these conditions during the test. It has also been shown that the data on which the Abaqus simulations have been modelled are from a different batch of PA12, and the tests carried out with their specimens have lower residual thermal stresses due to the smaller volume of their designs.

82 5. Conclusions

The present thesis has allowed combining the selective laser sintering additive manufacturing with the elaboration of a light-weight structure as the sandwich panel, with a wide-open range of different uses.

Recommendations for future research

Different improvements can be considered in future studies of the present thesis, these have not been included as they are beyond the scope of a master thesis.

More specimens should be tested in the future, as the more tests that are carried out, the more accurate the results will be. In this case, time was limited, and it was not possible to print and test more designs.

The effects of residual thermal concentrations on the printed specimens should also be studied further, as additive manufacturing technology is a key factor in the properties of the panels. On the other hand, the same panels should also be studied with other types of printing that do not generate such a high thermal gradient in the printed designs, such as injection moulding technologies.

To be able to use the sandwich panels in the industry, be it automotive or aerospace, the properties of these printed panels with different curvatures should be studied. Also, the effect of using smaller or larger panels, and then bonding them together with some kind of adhesive to create larger structures that can be produced industrially.

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[10] W. Krenkel, “Carbon fiber reinforced CMC for high-performance structures,” Int. J. Appl. Ceram. Technol., vol. 1, no. 2, p. 13, 2004.

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[13] S. Chauhan, “Study of Polymer Matrix Composite with Natural Particulate / Fiber in PMC : A Review,” Int. J. Adv. Res. Ideas Innov. Technol., vol. 3, pp. 1168–1179, 2017.

[14] E. Spini, “Long molecular chain polyamides - Plastix World,” Radici Group. https://www.plastix-world.com/long-molecular-chain-polyamides/ (accessed Dec. 30, 2020).

[15] Sinterit, “PA12 Smooth - Technical Datasheet,” p. 100, [Online]. Available: https://www.sinterit.com/wp-content/uploads/2014/05/PA12-Specification.pdf.

[16] Sinterit, “Sinterit Studio 2019 manual.” .

[17] G. Sacchetti, “Topology optimisation for structural strength and durability of 3D printed curved beams made of polymer and metal materials,” 2020.

[18] P. Mercelis and J. P. Kruth, “Residual stresses in selective laser sintering and selective laser melting,” Rapid Prototyp. J., vol. 12, no. 5, pp. 254–265, 2006, doi: 10.1108/13552540610707013.

[19] M. He and W. Hu, “A study on composite honeycomb sandwich panel structure,” Mater. Des., vol. 29, no. 3, pp. 709–713, 2008, doi: 10.1016/j.matdes.2007.03.003.

[20] I. G. Masters and K. E. Evans, “Models for the elastic deformation of honeycombs,” Compos. Struct., vol. 35, no. 4, pp. 403–422, 1996, doi: 10.1016/S0263- 8223(96)00054-2.

[21] W. Becker, “Closed-form analysis of the thickness effect of regular honeycomb core material,” Compos. Struct., vol. 48, no. 1, pp. 67–70, 2000, doi: 10.1016/S0263- 8223(99)00074-4.

[22] L. Yang, O. Harrysson, H. West, and D. Cormier, “Mechanical properties of 3D re- entrant honeycomb auxetic structures realized via additive manufacturing,” Int. J. Solids Struct., vol. 69–70, pp. 475–490, 2015, doi: 10.1016/j.ijsolstr.2015.05.005.

[23] L. J. Gibson and M. F. Ashby, Cellular solids. Structure and properties, Second. Cambridge Solid State Sciences Series, 1999.

[24] K. Zied, M. Osman, and T. Elmahdy, “Enhancement of the in-plane stiffness of the hexagonal re-entrant auxetic honeycomb cores,” Phys. Status Solidi Basic Res., vol. 252, no. 12, pp. 2685–2692, 2015, doi: 10.1002/pssb.201552164.

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86 7. Annex

7. Annex

ANNEX A: Elastic modulus and demonstration of honeycomb structures

Undeformed honeycomb Unit cell in X1 direction: 2 푙 푐표푠 휃

From the unit, cell is possible to obtain the edge with the loads and moments applied, and the stress obtained is the following:

푃 𝜎 = 1 (ℎ + 푙 · 푠𝑖푛휃) · 푏

훿 푠𝑖푛휃 휖 = 1 푙 푐표푠휃

The diagram the moment and shear diagrams that can be obtained from the edge of the honyecomb

푙 3 푃 푠𝑖푛휃 ( ) 2·푃푙3푠𝑖푛휃 푃푙3푠𝑖푛휃 훿 = 2 · 2 = = 3퐸푆 퐼 24 퐸푆 퐼 12 퐸푆 퐼

Where:

푡3 퐼 = 푏 12

Combining:

3 ∗ 𝜎1 푃 푙 푐표푠휃 푃 푙 푐표푠휃 푡 퐸1 = = · = · 3 2 · 12 퐸푠 푏 퐸1 (ℎ + 푙 · 푠𝑖푛휃) · 푏 훿 푠𝑖푛휃 (ℎ + 푙 · 푠𝑖푛휃) · 푏 푃 푙 sin 휃 12

3 3 ∗ 푡 푐표푠휃 4 푡 퐸1 = 퐸푠 ( ) · = · 퐸푠 ( ) 푙 (ℎ/푙 + 푠𝑖푛휃) sin2 휃 √3 푙

ANNEX B: Compression tests

B.1 Honeycomb out-of-plane. HCO 16

8 Stress Stress [MPa] 6

0 0 5 10 15 20 25 Strain [%]

HCO11 HCO12 HCO13 HCO14 HCO21 HCO22 HCO23 HCO24

Ultimate stress [MPa] E [MPa] HCO 11 11,44 306,56 HCO 12 10,49 281,66 HCO 13 11,77 314,08 HCO 14 11,94 292,98 Average 11,41 298,82 Standard deviation 0,65 14,39 HCO 21 14,25 324,18 HCO 22 12,70 294,80 HCO 23 12,17 296,39 HCO 24 11,58 281,28 Average 12,67 299,16 Standard deviation 1,15 18,00

B.2 Honeycomb in-plane HCI 5,0

4,5

4,0

3,5

3,0

2,5

Stress Stress [MPa] 2,0

1,5

1,0

0,5

0,0 0 1 2 3 4 5 6 7 8 Strain [%]

HCI

Ultimate stress [MPa] E [MPa]

HCI 4,5 101,4

B.3 Re-entrant honeycomb out-of-plane RHCO 30

15 Stress Stress [MPa]

0 0 2 4 6 8 10 12 14 16 18 Strain [%]

RHCO1 RHCO2 RHCO3 RHCO4

Ultimate stress [MPa] E [MPa] RHCO 1 24,88 493,90 RHCO 2 24,12 478,23 RHCO 3 22,86 480,54 RHCO 4 23,85 523,95 Average 23,61 494,24 Standard deviation 0,66 25,76

B.4 Re-entrant honeycomb in-plane RHCI 14

Stress Stress [MPa] 6

0 0 1 2 3 4 5 6 7 8 Strain [%]

RHCI1 RHCI2 RHCI3 RHCI4

Ultimate stress [MPa] E [MPa]

RHCI 1 8,65 231,85 RHCI 2 10,56 271,37 RHCI 3 11,64 279,81 RHCI 4 11,90 307,53 Average 11,37 286,24 Standard deviation 0,71 18,92

B.5 Open honeycomb OHC 18

8 Stress Stress [MPa]

0 0 5 10 15 20 25 Strain [%]

OHC 11 OHC 12 OHC 13 OHC 14 OHC 21

Ultimate stress [MPa] E [MPa]

OHC 11 16,07 384,27 OHC 12 12,83 318,23 OHC 13 15,49 359,82 OHC 14 12,69 302,48 Average 13,67 326,84 Standard deviation 1,58 29,62 OHC 21 4,1 103,6

B.6 Square pyramid SP 3,0

2,5

2,0

1,5 Stress Stress [MPa]

1,0

0,5

0,0 0 2 4 6 8 10 12 Strain [%]

Ultimate stress [MPa] E [MPa]

SP 2,61 60,9

B.7 Tetrahedral

TETRA 12

6 Stress Stress [MPa]

0 0 2 4 6 8 10 12 14 16 18 Strain [%]

TETRA1 TETRA2 TETRA3 TETRA4

Ultimate stress [MPa] E [MPa] TETRA 1 10,46 247,73 TETRA 2 10,99 264,07 TETRA 3 9,63 242,93 TETRA 4 10,41 262,48 Average 10,37 254,30 Standard deviation 0,56 10,56

B.8 ISO GRID 1 J1 10

Stress Stress [MPa] 4

0 0 2 4 6 8 10 12 14 16 18 Strain [%]

J1 11 J1 12 J1 13 J1 14 J1 21 J1 22 J1 23 J1 24

Ultimate stress [MPa] E [MPa] J1 11 7,69 267,66 J1 12 8,68 285,66 J1 13 7,56 263,04 J1 14 8,30 280,21 Average 8,18 276,30 Standard deviation 0,57 11,80 J1 21 8,56 276,87 J1 22 8,49 270,96 J1 23 9,11 296,05 J1 24 7,82 267,88 Average 8,47 278,30 Standard deviation 0,65 15,46

B.9 ISO GRID 2

J2 14

Stress Stress [MPa] 6

0 0 2 4 6 8 10 12 14 Strain [%]

J21 J22 J23 J24

Ultimate stress [MPa] E [MPa] J21 12,02 243,65 J22 10,55 320,67 J23 10,56 296,49 J24 11,65 326,99 Average 10,92 314,72 Standard deviation 0,64 16,10

B.10 ISO GRID 3

J3 30

15 Stress Stress [MPa]

0 0 5 10 15 20 25 Strain [%]

J3 11 J3 13 J3 14 J3 21 J32 22 J3 23 J3 24

Ultimate stress [MPa] E [MPa] J3 11 22,66 457,05 J3 12 26,64 467,15 J3 13 21,36 460,13 J3 14 27,03 409,41 Average 24,42 448,44 Standard deviation 2,84 26,36 J3 21 15,72 372,18 J3 22 18,01 402,44 J3 23 15,46 387,72 J3 24 17,35 416,11 Average 16,63 394,61 Standard deviation 1,24 18,92

Annex C: PA12 True stresses and strains

True Stress [MPa] True Plastic Strain Average [mm/mm]

15,19384416 0 16,22440506 0,001087716 17,25775665 0,002208204 18,29532633 0,003433722 19,33691027 0,004736584 20,38328241 0,006142646 21,43561989 0,007691426 22,49973523 0,009620933 23,5656403 0,01145536 24,63626307 0,01332548 25,7261283 0,01579116 26,80118869 0,017509547 27,93108763 0,021063299 29,05523163 0,024153892 30,19132704 0,027418714 31,35971002 0,031486412 32,55600967 0,036134621 33,74255729 0,04018381 34,93420027 0,044118583 36,25387865 0,051345693 37,40852217 0,053710327 38,54352883 0,055429128 40,19864548 0,070075233