Establishing a finite element model to determine the tensile strength of additively manufactured PA2200 parts

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Establishing a finite element model to determine

the tensile strength of additively manufactured

PA2200 parts

EL Fourie

orcid.org/ 0000-0003-3983-5382

Dissertation accepted in fulfilment of the requirements for the

degree

Master of Engineering in Mechanical Engineering

at

the North West University

Supervisor:

Mr CP Kloppers

Examination:

May 2020

Student number:

24190918

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ACKNOWLEDGEMENTS

First and foremost, I thank my Father in Heaven. He is great and above all things, and He gave me the knowledge, resources and authority to finish my pre-graduate studies and to tackle a post-graduate degree. His son, Jesus Christ, saved me from being a slave to stress and fear, and He sent the Holy Spirit to uphold me throughout my life (Isaiah 41:10). Without Him I am nothing. Secondly, I thank Prof. Deon de Beer for making our research group possible and for organising our bursaries from the Collaborative Program in Additive Manufacturing (CPAM). Thank you to Johan Els, Operations Manager at the Centre for Rapid Prototyping and Manufacturing (CRPM), for supplying all my test specimens and for ensuring consistency and quality of all products. Thank you to my dissertation advisor Mr. CP Kloppers of the Faculty of Mechanical Engineering at the Potchefstroom campus of the North-West University. Thank you for making it possible for me to do my masters, that you always had time to discuss any queries that I had, and for teaching me that friendship is possible at the workplace.

I also acknowledge and thank all who made testing of the applicable specimens possible; this include the Laboratory technician, Sonia Visser, of the Faculty of Consumer Sciences, as well as Darnelle Hood, Special process Auditor, and Gertrude Makgatho, Head of Composite laboratory, of Aerosud. Thank you for always acknowledging the urgency of testing and for ensuring the accuracy and calibration of the testing equipment. I also want to thank Dr. Anine Jordaan, senior specialist at the laboratory for Electron Microscopy Chemical Resources Beneficiation (CRB) at the North-West University Potchefstroom campus for her enthusiasm and diligence in supplying me with the necessary SEM images for this study.

Lastly, I would like to thank my family and friends for supporting me throughout the two years of my masters. Thank you for bringing me food and coffee when I needed it, and for motivating my when I felt like giving up. And thank you to my wonderful boyfriend, Juan Aveling, for understanding when my patience started to run out, when frustration took over, and when I had too much coffee. Thank you for motivating me to take “just one more step” towards the end of my study.

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ABSTRACT

Selective laser sintering (SLS) is an additive manufacturing process that produces three-dimensional parts from computer aided design (CAD) models. This process aids in the production of parts that are singular complex and designed for a specific application, which decreases the time and cost of manufacturing components. Structures such as these are mostly optimised using finite element method (FEM) analysis where there is increased difficulty in designing a mathematical prediction model for each individual structure. Most software programs use FEM analysis for designing and optimising structures with isotropic material properties, but the layer-by-layer manufacturing of SLS causes the strength of its structures to be nonuniform in the x-, y- and z-axes; that is, the parts have a certain level of anisotropy. This brings to question the accuracy of simulating parts with anisotropic material properties through FEM analysis.

In achieving the aim of this study, a tensile material database was defined for PA2200 structures manufactured with the EOSINT P380 machine. This database was then used to simulate the global structural behaviour of specimens under tensile forces. The test specimens were specimens manufactured at 30° to the 𝑥-𝑦 plane of the print bed and specimens with varying cross-sectional areas in its gauge length. The second set of specimens were defined in two groups as symmetrical and asymmetrical about its longitudinal and lateral axes. The tensile material database displayed Young’s moduli which were very similar to one another, resulting in the conclusion that an isotropic material database can be assumed in the simulation models. The simulation model also defined a solid model with a specified density, which resulted in accurate simulation to experimental data. This indicates that the porosity of PA2200 SLS structures can be disregarded in similar simulations.

All specimens were manufactured and tested according to the simulation parameters, and the actual elongation values were compared to the predicted simulation values. The specimens manufactured at 30° to the print bed and the symmetrical structures were within a 10% error margin, which indicates accurate simulation predictions. That of the asymmetrical structures were, however, approximately 40% smaller than the experimental values. The variation in the simulation and experimental data of the asymmetrical structures were ascribed to the variance in 2D cross-sectional areas as determined by the slicing program; the smaller 2D cross-sectional areas tended to laminate from each other, causing high stress regions. The parameters that affect the simulation model accuracy as the complexity of the structures increase must be identified in future studies to better understand the polymer SLS process and the behaviour of the manufactured specimens.

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LIST OF TABLES

Table 2.2-1: Tensile strength and Young’s modulus of PA2200 ... 12

Table 2.2-2: Poisson’s ratio, shear modulus and mass density of PA2200 ... 12

Table 5.1-1: Test Results of 0° specimens ... 25

Table 5.1-2: Statistics of tensile tests of 0° specimens ... 25

Table 5.1-3: Analytical vs experimental elongation at 7MPa, 0° specimens ... 26

Table 5.1-4: Analytical vs experimental elongation at 14 MPa, 0° specimens ... 27

Table 5.1-5: Analytical vs experimental elongation at 21 MPa, 0° specimens ... 27

Table 5.2-1: Test results of 90° specimens ... 29

Table 5.2-3: Summary of yield strength and Young’s modulus of 0° and 90° test specimens ... 30

Table 5.2-4: Analytical vs experimental elongations at 7 MPa, 90° specimens ... 31

Table 5.3-1: Tensile material database used for NX simulations ... 35

Table 6.1-1: Analytical model elongation predictions ... 36

Table 6.1-2: Simulation model elongation predictions ... 39

Table 6.1-3: Analytical vs simulation results of 30° specimens ... 39

Table 6.2-1: Test results of 30° specimens ... 41

Table 6.2-3: Analytical model vs experimental elongation results of 30° specimens ... 42

Table 6.2-4: Simulation model vs experimental elongation results of 30° specimens ... 43

Table 7.2-1: Average and standard deviation in experimental data, symmetrical structure 1 ... 47

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Table 7.2-3: Average and standard deviation in experimental data, symmetrical structure 2 ... 49 Table 7.2-4: Simulation vs experimental data, symmetrical structure 2 ... 50 Table 7.3-1: Average, standard deviation and variation in experimental data, asymmetrical

structure 1 ... 52 Table 7.3-2: Simulation vs experimental data, asymmetrical structure 1 ... 53 Table 7.3-3: Average, standard deviation and variation in experimental data, asymmetrical

structure 2 ... 56 Table 7.3-4: Simulation vs experimental data, asymmetrical structure 2 ... 56 Table A.1-1: Raw data of tensile tests done on 0° specimens, data of specimen 1, 2 and 3 ... I Table A.1-2: Raw data of tensile tests done on 0° specimens, data of specimen 4 and 5 .... XXIX Table A.1-3: Raw data of tensile tests done on 90° specimens, data of specimen 1, 2 and

3 ... LIX Table A.1-4: Raw data of tensile tests done on 90° specimens, data of specimen 4 and

5 ... LXXVIII Table A.1-5: Raw data of tensile tests done on 30° specimens, data of specimen 1, 2 and

3 ... XCIX Table A.1-6: Raw data of tensile tests done on 30° specimens, data of specimen 4 and 5 . CXXII Table A.2-1: Raw data of tensile tests done on 1st_{symmetrical structure test specimens,}

data of specimen 1, 2 and 3 ... CXLIX Table A.2-2: Raw data of tensile tests done on 1st_{symmetrical structure test specimens,}

data of specimen 4 and 5 ... CLI Table A.2-3: Raw data of tensile tests done on 2nd_{symmetrical structure test specimens,}

data of specimen 1, 2 and 3 ... CLV Table A.2-4: Raw data of tensile tests done on 2nd_{symmetrical structure test specimens,}

data of specimen 4, 5 and 6 ... CLVII Table A.2-5: Raw data of tensile tests done on 1st_{asymmetrical test specimens, data of}

specimen 1, 2 and 3 ... CLXI Table A.2-6: Raw data of tensile tests done on 1st_{asymmetrical test specimens, data of}

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Table A.2-7: Raw data of tensile tests done on 2nd_{asymmetrical test specimens, data of}

specimen 1, 2 and 3 ... CLXVII Table A.2-8: Raw data of tensile tests done on 2nd_{asymmetrical test specimens, data of}

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LIST OF FIGURES

Figure 1.1-1: 3D printed scoliosis bespoke brace [1] ... 1

Figure 2.1-1: SL setup [8, p. 49] ... 4

Figure 2.1-2: FDM setup [8, p. 49] ... 5

Figure 2.1-3: SLS setup [10, p. 148] ... 6

Figure 2.2-1: Right-hand rule for part build orientation ... 10

Figure 3.1-1: Conventional and true stress-strain diagrams for ductile material [56] ... 17

Figure 3.2-1: Representation of a specimen printed at an angle between 0° and 90° to the print bed ... 19

Figure 4.1-1: ASTM D638-14 Type IV test specimen dimensions ... 20

Figure 4.1-2: Test specimens at 0° and 90° to the print bed ... 21

Figure 4.2-1: Test specimen at angle of 30° to the 𝒙-𝒚 plane ... 22

Figure 4.2-2: Cross-sectional area dimensions of symmetrical structures, (a) Structure No. 1 (b) Structure No. 2 ... 22

Figure 4.2-3: Trimetric view of topology-optimised structure 1 ... 23

Figure 4.2-4: Trimetric front and side view of topology-optimised structure 2 ... 23

Figure 5.1-1: Stress-strain diagram of 0° test specimens... 24

Figure 5.1-2: SEM images of 0° test specimens, (a)-(e) Specimen 1 to 5 respectively ... 26

Figure 5.1-3: SEM image of specimen 3, highlighting fracture origin, 0° specimens ... 27

Figure 5.1-4: Stress-strain diagram of analytical and experimental data, 0° specimens ... 28

Figure 5.2-1: Stress-strain diagrams of 90° test specimens ... 29

Figure 5.2-2: SEM image of 90° test specimens, (a)-(e) specimen 1 to 5, respectively ... 31

Figure 5.2-3: SEM image of specimen 3, highlighting fracture origin, 90° specimens ... 32

Figure 5.2-4: Stress-strain diagram of analytical and experimental data, 90° specimens ... 33 Figure 5.3-1: Percentage error of analytical and simulation models in relation to

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Figure 5.3-2: Percentage error of analytical and simulation models in relation to

experimental data, summary, 90° test specimens ... 35

Figure 6.1-1: Stress-strain diagram of analytical model predictions, 30° specimens ... 37

Figure 6.1-2: Gripping regions of simulation model ... 37

Figure 6.1-3: Divide face feature of Siemens NX ... 38

Figure 6.1-4: Constraint and load boundary conditions of the simulation model... 38

Figure 6.1-5: Stress-strain diagram of analytical and simulation model predictions ... 40

Figure 6.2-1: Stress-strain diagram of 30° test specimens ... 41

Figure 6.2-2: Stress vs elongation of 30° test specimens, analytical vs experimental ... 43

Figure 6.2-3: Percentage error of analytical and simulation models in relation to experimental data, summary, 30° specimens ... 44

Figure 6.2-4: Relation of elongation determined by analytical and simulation models to experimental data, 30° specimens ... 44

Figure 7.2-1: Isometric view of symmetrical structure 1 ... 46

Figure 7.2-2: Experimental results of symmetrical structure 1... 46

Figure 7.2-3: Load-elongation diagram of simulation and experimental data, symmetrical structure 1 ... 48

Figure 7.2-4: Isometric view of symmetrical structure 2 ... 48

Figure 7.2-5: Experimental results of symmetrical structure 2... 49

Figure 7.2-6: Load-elongation diagram of simulation and experimental data, symmetrical structure 2 ... 50

Figure 7.3-1: Trimetric view of asymmetrical structure 1 ... 51

Figure 7.3-2: Experimental results of asymmetrical structure 1 ... 52

Figure 7.3-3: Load-elongation diagram of simulation and experimental data, asymmetrical structure 1 ... 53

Figure 7.3-4: Simulation prediction of area of highest stress concentration, asymmetrical structure 1 ... 54

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Figure 7.3-5: Experimental results of fracture region, asymmetrical structure 1 ... 54 Figure 7.3-6: Trimetric front and side view of asymmetrical structure 2 ... 55 Figure 7.3-7: Experimental results of asymmetrical structure 2 ... 55 Figure 7.3-8: Load-elongation diagram of simulation and experimental data, asymmetrical

structure 2 ... 57 Figure 7.3-9: Simulation prediction of area of highest stress concentration, asymmetrical

structure 2 ... 57 Figure 7.3-10: Experimental results of fracture region, asymmetrical structure 2 ... 58 Figure A.1-1: Stress-strain graph of raw data of test specimen 1, 0° specimens ... LIV Figure A.1-2: Stress-strain graph of raw data of test specimen 2, 0° specimens ... LIV Figure A.1-3: Stress-strain graph of raw data of test specimen 3, 0° specimens ... LIV Figure A.1-4: Stress-strain graph of raw data of test specimen 4, 0° specimens ... LIV Figure A.1-5: Stress-strain graph of raw data of test specimen 5, 0° specimens ... LV Figure A.1-6: Percentage error of analytical model in relation to experimental data, 7 MPa,

0° specimens ... LV Figure A.1-7: Percentage error of analytical model in relation to experimental data, 14

MPa, 0° specimens ... LV Figure A.1-8: Percentage error of analytical model in relation to experimental data, 21

MPa, 0° Test Specimens ... LVI Figure A.1-9: SEM image of 0° test specimen, specimen 1 ... LVII Figure A.1-10: SEM image of 0° test specimen, specimen 2 ... LVII Figure A.1-11: SEM image of 0° test specimen, specimen 3 ... LVIII Figure A.1-12: SEM image of 0° test specimen, specimen 4 ... LVIII Figure A.1-13: SEM image of 0° test specimen, specimen 5 ... LVIII Figure A.1-14: Stress-strain graph of raw data of test specimen 1, 90° specimens ... XCV Figure A.1-15: Stress-strain graph of raw data of test specimen 2, 90° specimens ... XCV Figure A.1-16: Stress-strain graph of raw data of test specimen 3, 90° specimens ... XCVI

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Figure A.1-17: Stress-strain graph of raw data of test specimen 4, 90° specimens ... XCVI Figure A.1-18: Stress-strain graph of raw data of test specimen 5, 90° specimens ... XCVI Figure A.1-19: Percentage error of analytical model in relation to experimental data, 7

MPa, 90° specimens ... XCVII Figure A.1-20: Percentage error of analytical model in relation to experimental data, 14

MPa, 90° specimens ... XCVII Figure A.1-21: Percentage error of analytical model in relation to experimental data, 21

MPa, 90° specimens ... XCVIII Figure A.1-22: SEM image of 90° test specimen, specimen 1 ... XCVIII Figure A.1-23: SEM image of 90° test specimen, specimen 2 ... XCVIII Figure A.1-24: SEM image of 90° test specimen, specimen 3 ... XCIX Figure A.1-25: SEM image of 90° test specimen, specimen 4 ... XCIX Figure A.1-26: SEM image of 90° test specimen, specimen 5 ... XCIX Figure A.1-27: Stress-strain graph of raw data of test specimen 1, 30° specimens ... CXLVI Figure A.1-28: Stress-strain graph of raw data of test specimen 2, 30° specimens ... CXLVI Figure A.1-29: Stress-strain graph of raw data of test specimen 3, 30° specimens ... CXLVII Figure A.1-30: Stress-strain graph of raw data of test specimen 4, 30° specimens ... CXLVII Figure A.1-31: Stress-strain graph of raw data of test specimen 5, 30° specimens ... CXLVII Figure A.1-32: Percentage error of analytical and simulation models in relation to

experimental data, 7 MPa, 30° specimens ... CXLVIII Figure A.1-33: Percentage error of analytical and simulation models in relation to

experimental data, 14 MPa, 30° specimens ... CXLVIII Figure A.1-34: Percentage error of analytical and simulation models in relation to

experimental data, 21 MPa, 30° specimens ... CXLIX Figure A.2-1: Load-elongation graph of raw data of test specimen 1, symmetric structure 1 CLIV Figure A.2-2: Load-elongation graph of raw data of test specimen 2, symmetric structure 1 CLIV Figure A.2-3: Load-elongation graph of raw data of test specimen 3, symmetric structure 1 CLV

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Figure A.2-4: Load-elongation graph of raw data of test specimen 4, symmetric structure 1 CLV Figure A.2-5: Load-elongation graph of raw data of test specimen 5, symmetric structure 1 CLV Figure A.2-6: Load-elongation graph of raw data of test specimen 1, symmetric structure 2 CLX Figure A.2-7: Load-elongation graph of raw data of test specimen 2, symmetric structure 2 CLX Figure A.2-8: Load-elongation graph of raw data of test specimen 3, symmetric structure 2 CLX Figure A.2-9: Load-elongation graph of raw data of test specimen 4, symmetric structure 2 CLX Figure A.2-10: Load-elongation graph of raw data of test specimen 5, symmetric structure

2 ... CLXI Figure A.2-11: Load-elongation graph of raw data of test specimen 6, symmetric structure

2 ... CLXI Figure A.2-12: Load-elongation graph of raw data of test specimen 1, asymmetric

structure 1 ... CLXVI Figure A.2-13: Load-elongation graph of raw data of test specimen 2, asymmetric

structure 1 ... CLXVII Figure A.2-17: Load-elongation graph of raw data of test specimen 6, asymmetric

structure 1 ... CLXVII Figure A.2-18: Load-elongation graph of raw data of test specimen 1, asymmetric

structure 2 ... CLXXII Figure A.2-19: Load-elongation graph of raw data of test specimen 2, asymmetric

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Figure A.2-21: Load-elongation graph of raw data of test specimen 4, asymmetric

structure 2 ... CLXXIII Figure A.2-23: Load-elongation graph of raw data of test specimen 6, asymmetric

structure 2 ... CLXXIII Figure B.1-1: Elongation of 30° test specimen at 7 MPa ... CLXXIV Figure B.1-2: Stress distribution of 30° test specimen under tensile stress of 7 MPa ... CLXXV Figure B.1-3: Elongation of 30° test specimen at 14 MPa ... CLXXV Figure B.1-4: Stress distribution of 30° test specimen under tensile stress of 14 MPa ... CLXXVI Figure B.1-5: Elongation of 30° test specimen at 21 MPa ... CLXXVI Figure B.1-6: Stress distribution of 30° test specimen under tensile stress of 21 MPa .... CLXXVII Figure B.2-1: Elongation of symmetrical structure 1, at P = 100 N ... CLXXVIII Figure B.2-2: Stress distribution of symmetrical structure 1, at P = 100 N ... CLXXIX Figure B.2-3: Elongation of symmetrical structure 1, at P = 120 N ... CLXXIX Figure B.2-4: Stress distribution of symmetrical structure 1, at P = 120 N ... CLXXX Figure B.2-5: Elongation of symmetrical structure 1, at P = 150 N ... CLXXX Figure B.2-6: Stress distribution of symmetrical structure 1, at P = 150 N ... CLXXXI Figure B.2-7: Elongation of symmetrical structure 2, at P = 60 N ... CLXXXII Figure B.2-8: Stress distribution of symmetrical structure 2, at P = 60 N ... CLXXXII Figure B.2-9: Elongation of symmetrical structure 2, at P = 80 N ... CLXXXIII Figure B.2-10: Stress distribution of symmetrical structure 2, at P = 80 N ... CLXXXIII Figure B.2-11: Elongation of symmetrical structure 2, at P = 110 N ... CLXXXIV Figure B.2-12: Stress distribution of symmetrical structure 2, at P = 110 N ... CLXXXIV Figure B.3-1: Elongation of asymmetrical structure 1, at P = 80 N ... CLXXXV Figure B.3-2: Stress distribution of asymmetrical structure 1, at P = 80 N ... CLXXXVI

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Figure B.3-3: Elongation of asymmetrical structure 1, at P = 110 N ... CLXXXVI Figure B.3-4: Stress distribution of asymmetrical structure 1, at P = 110 N ... CLXXXVII Figure B.3-5: Elongation of asymmetrical structure 1, at P = 130 N ... CLXXXVII Figure B.3-6: Stress distribution of asymmetrical structure 1, at P = 130 N ... CLXXXVIII Figure B.3-7: Elongation of asymmetrical structure 2, at P = 80 N ... CLXXXIX Figure B.3-8: Stress distribution of asymmetrical structure 2, at P = 80 N ... CLXXXIX Figure B.3-9: Elongation of asymmetrical structure 2, at P = 110 N ... CXC Figure B.3-10: Stress distribution of asymmetrical structure 2, at P = 110 N ... CXC Figure B.3-11: Elongation of asymmetrical structure 2, at P = 130 N ... CXCI Figure B.3-12: Stress distribution of asymmetrical structure 2, at P = 130 N ... CXCI

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CHAPTER 1 INTRODUCTION

Over the past 30 years, additive manufacturing has developed and expanded into a large portion of what we know to be the fourth industrial revolution. This study focuses on the linear static finite element method (FEM) analysis of parts produced by selective laser sintering (SLS) and its tensile material properties. This chapter gives a background on the motivation to the study and defines its specifications.

1.1. Background

Selective laser sintering (SLS) is an additive manufacturing (AM) process that produces three-dimensional (3D) parts directly from computer aided design (CAD) models. This process enables manufacturing of a wide range of parts which were previously limited due to design parameter restrictions in traditional manufacturing techniques. The layer-by-layer manufacturing process enables an increase in design complexity, thus producing parts that are more lightweight than their traditionally manufactured counterparts. The SLS process aids in the production of parts that are singular complex and designed for a specific application, which decreases the time and cost of components like patient-specific designs. These types of designs are in high demand in aerospace and medical industries.

One of the areas in the medical industry in which SLS is used is in the production of patient-specific scoliosis braces. This process is used for its ability to manufacture complex designs that combine advancements in design technology and fashion. Dr. James Policy of Stanford University and Robert Jensen created a 3D-printed bespoke brace (Figure 1.1-1) that is visually appealing and more comfortable, thus resulting in patients being more receptive to wearing the brace and thereby improving the medical efficiency of the brace [1], [2]. This brace features a scanned-to-fit design and results in a lightweight, comfortable, SLS-printed device.

Figure 1.1-1: 3D printed scoliosis bespoke brace [1]

In medical cases like these, the patient’s health progress is dependent on whether the patient follows the treatment according to the specifications of a physician or not [2] [3]. The need hence arises for the design and accurate analysis of the strength and behaviour of complex structures.

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Structures such as these are mostly optimised using FEM analysis where there is increased difficulty in designing a mathematical prediction model for each individual structure.

Software programs use FEM analysis extensively for designing and optimising structures made from processes that produce parts with isotropic material properties. There is, however, a shortage of data on the accuracy of FEM analysis on structures with any level of anisotropy in its material properties. It is therefore necessary to focus on and determine the accuracy of FEM analysis when applied to parts manufactured by the SLS process.

1.2. Problem statement

The SLS process creates a large window of opportunity for the medical industry in the use of scoliosis braces. The layer-by-layer manufacturing of these parts affects the strength in the x-, y- and z-axes to be nonuniform; that is, the parts have a certain level of anisotropy. This brings to question the accuracy of simulating such parts through FEM analysis.

Given the rapid growth of AM technology in providing new potential in design freedom and manufacturing of complex shapes, the effect of anisotropic material properties on design specifications must be identified. The prediction of the behaviour of AM materials is not as advanced as their isotropic counterparts. A comprehensive study by [4] summarised the compressive strength of PA2200 (Polyamide-12 from EOS GmbH) SLS parts. Thus, the problem lies in identifying a tensile material database of PA2200 and testing the accuracy of a finite element (FE) model of the tensile strength of SLS parts.

1.3. Research aim

To contribute to the assessment of the accuracy of a FEM analysis on structures with anisotropic material properties.

1.4. Research objectives

The objectives of this dissertation are:

1. Defining and validating a tensile anisotropic material database for Polyamide-12 (PA2200).

2. Applying the material database in a FEM analysis to predict the global structural behaviour of test specimens.

3. Determining the accuracy of the FEM analysis predictions by comparing them to the actual behaviour of the structures.

1.5. Research methodology

To achieve the aim of this study, it was necessary to first define a tensile material database by applying tensile tests on polyamide-12 (PA2200) specimens which were manufactured with the longitudinal dimension parallel and perpendicular to the print bed, respectively. The summarised material database was then used to simulate the behaviour of test specimens manufactured at

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other angles to the print bed. The actual elongations of the specimens were determined using both experimental and analytical models.

The validated material database was then used to simulate the global structural behaviour of symmetrical and asymmetrical structures when under a tensile force. The second set of tests consisted of depicting the simulation parameters on a test bench while measuring the actual elongations of the symmetrical and asymmetrical structures with the testing rig. These results were then compared to the simulation predictions to determine the error margin of the simulation model.

1.6. Contributions and limitations

This study will contribute to the research community by attributing to the parameter definition of SLS components as simulated by the Siemens NX software program; this will enable engineers to better understand the regions in which to design polymer SLS parts.

The available testing rigs for this study were the MTS tensile testing machine, the Zwick Z2.5 materials testing machine, and the Lloyd materials testing machine. The MTS tensile testing machine has a load cell of 100 kN, thus indicating accuracy from the point of 1 kN; this is not applicable to polymers and could not be used for the PA2200 test specimens. The Zwick Z2.5 tensile testing machine had a load cell of 2.5 kN, which was accurate enough for this study. This machine was, however, has been used at another working station and had limited access. The final available tensile testing machine was the Lloyd materials testing machine, which had a load cell of 250 N and as available at any time.

1.7. Chapter layout of report

Chapter 2 contains a literature review on the SLS process and material properties of PA2200 and the use of FEM to predict the behaviour of parts with anisotropic material properties. Chapter 3 consist of the theory used to obtain the necessary parameters to create a material database from engineering stress-strain graphs, which was used to determine the displacement of test specimens under tensile loads. The experimental and simulation procedures of this study follow in Chapter 4.

Chapter 5 summarises the tensile material database as obtained by tensile tests, while Chapter 6 discusses the verification and validation of this database when applied to a simulation model. Chapter 7 contains a further analysis of this simulation model followed by the conclusions and recommendations in Chapter 8. The appendices containing all the test and simulation raw data follow the References.

Chapter 1 introduced the problem statement, aim, objectives, methodology, and the contributions and limitations of this dissertation followed by a short summary of the chapter layout of this report.

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CHAPTER 2 LITERATURE STUDY

This chapter consist of a literature study into the background of the most common additive manufacturing methods used today, followed by an in-depth study of the material properties and its affecting parameters on polymer selective laser sintered (SLS) parts. A description is then given on previous studies that used FEM models to simulate the behaviour of these parts, after which the chapter ends with a section that focuses on previous studies that used the 3D-DIC system as optical measuring device. This chapter, lastly, summarises the conclusions found in the applicable studies for application to this study.

2.1. Overview of relevant additive manufacturing processes

One of the main factors in the fourth industrial revolution is additive manufacturing (AM), otherwise known as rapid prototyping (RP). Processes included in AM are stereolithography (SL), fused deposition modelling (FDM), and selective laser sintering (SLS) [5].

In 1987, AM made its first appearance in commercialisation with stereolithography (SL) from 3D Systems [6]. The stereolithography (SL) process is based on the principle of curing (hardening/solidifying) a liquid polymer, or photopolymer, into a specific shape. The platform is moved in the vertical direction by a mechanism connected to a vat that lowers and raises the print platform as necessary. The vat is then filled with a photocurable liquid-acrylate polymer, which is a combination of oligomers (polymer intermediates), acrylic monomers and a photoinitiator (a composite which reacts to light) [7].

Figure 2.1-1: SL setup [8, p. 49]

The SL process setup is displayed in Figure 2.1-1. When the print platform is at its highest position, a thin layer of liquid is present on the platform. The software of the printer then scans a laser generating an ultraviolet (UV) beam on a specified surface area of the photopolymer and moves in the 𝑥-𝑦 plane to form the first layer of a selected 3D model. The laser beam hardens (cures) that portion of the photopolymer and thereby fabricates a solid model. The print platform lowers or raises (depending on the type of SL printer being used) by one increment (the height of

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the layer setting) covering the cured polymer with a single layer of uncured polymer, and the sequence is repeated.

Four years after SL emerged, three AM technologies were commercialised: fused deposition modelling (FDM) from Stratasys, laminated object manufacturing (LOM) from Helisys and solid ground curing (SGC) from Cupital [6]. FDM extrudes thermoplastic materials (produced in filament form) to produce plastic parts layer by layer, LOM uses a digitally guided laser to bond and cut sheet material while SGC floods UV light through masks made of electrostatic toner on a glass plate, thereby curing full layers of UV-sensitive liquid polymer.

In the FDM process, a robot-controlled extruder nozzle moves in the 𝑧- and 𝑦-axis direction over a heated print bed that moves in the 𝑥-axis direction as needed (Figure 2.1-2). A thermoplastic filament is then extruded through a heated die. The initial layer of the filament is extruded at a constant rate while the extruder nozzle moves in the needed 𝑦-direction and the heated print bed moves in the 𝑥-direction. The path of extrusion is determined by a software which slices a three-dimensional (3D) model into two-three-dimensional (2D) layers. When the first layer is complete, the extruder nozzle raises by a single layer height so that the subsequent layers can be constructed.

Figure 2.1-2: FDM setup [8, p. 49]

In the requirement of more complicated parts, manufacturing difficulties could occur due to the support needed for areas where the part has an overhang greater than 45°. When these parts are built up to a certain layer, the next 2D layer would require the placement of filament where no material exist beneath it. This will cause the melted thermoplastic to be extruded in the air. To avoid this, a support material is extruded from the modelling material. The support structure is manufactured from the initial layer and has a less dense layer spacing so that it is strong enough for support but weak enough for fast and effective removal after manufacturing.

The layers of FDM models can vary from 0.05 mm to 0.2 mm. This thickness represents the achievable tolerance in the vertical direction, where 0.05 mm gives a good surface finish and

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0.2mm reduces the time interval of production. Of these settings, a layer height of 0.15 mm is most common for commercial use. The dimensional accuracy in the 𝑥-𝑦 plane can, however, be as fine as 0.025 mm, which is as long as the filament can be extruded efficiently (this also depends on the size of the extrusion nozzle) [7], [8].

Selective laser sintering (SLS) is the youngest technology in the field of AM, as well as the process which is most popular for its commercial use [9]. SLS is a form of powder bed fusion (PBF), which is one of the seven categories of AM processes defined in ASTM F2792. SLS from DTM (now part of 3D Systems) became available in 1992. This process uses heat from a laser to fuse powder materials. 3D Systems and Ciba commercialised their first epoxy resin product in 1993, after which SLS came into popular demand for end-use parts in the aerospace sector by Boeing and NavAir for supplying low pressure ducting for the Boeing FA-18 aircraft [6], [10].

The SLS process allows the production of complex 3D models by selective fusion of consecutive layers of powdered materials; the layout of this process is displayed in Figure 2.1-3. The process consists of feedstock powders which are loaded into heated delivery chambers or feed bins. The part piston lowers by a predetermined increment (0.06 mm - 0.12 mm) and a recoater (roller) spreads the powder from the feed bins over the part bed. The part bed is then heated to just below melting temperature to minimise the required laser energy density, which decreases internal stresses in the manufactured part that can lead to distortion of the part during cooling. A computer-controlled carbon dioxide (CO2) laser scans over the area, as it heats and fuses the

powder particles into a specified shape corresponding to a cross-sectional area given by a processed CAD model. The part piston lowers by one increment, the recoater applies a new layer of powder over the melted cross-sectional area, and the process repeats itself for all layers of the part until fully fabricated.

Figure 2.1-3: SLS setup [10, p. 148]

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part and surrounding material in the build chamber is cooled below the glass transition and oxidation temperatures, it can be removed from the chamber. The unsintered powder material (aged powder) which acts as support during the build process is then brushed away from the completed part [4], [7], [9], [11].

2.2. Polymer SLS

Advantages of polymer SLS include that SLS does not require a support structure for overhangs and thin walls in a part, as is the case with many other additive processes, nor does it require a binder, which can add post-processing steps. A binder can raise the toxicity concerns, especially with parts used in medical applications. Polymer SLS cannot match the resolution of stereolithography, but the produced parts are tough and more stable. Improving the resolution is, however, possible with further research into micro-LS systems. It is this potential and its ability to process a wide range of materials that makes laser sintering an exemplary candidate for further research.

When comparing SLS to its alternative competitor, injection moulding (IM), it becomes evident that both methods produce parts with similar yield strengths, while SLS parts generally have a lower ductility as shown by [4] and [12]. This outcome is ascribed to the significant difference in microstructure of IM and SLS parts. Problems identified in these processes are that the cooling process of IM cause aligned lamellar crystalline regions and intertwined molecular chains, while SLS forms porosity [10].

The porosity between powder layers of SLS results in the presence of particle cores of a different crystal structure than that of the surrounding structures, leading to varying material properties [4], [11], [13–15]. Powders that are deposited and melted into layers give rise to anisotropic material properties, where the part tends to be weaker between layers due to the porosity that aligns in this plane.

Anisotropic material properties caused by porosity and coring in SLS must be identified and analysed when testing for the mechanical properties of a specific SLS powder material. The anisotropy of the material depends not only on the powder used for production but also on the SLS machine.

2.2.1. Isotropic vs anisotropic material properties

The strength of parts produced by AM depends on the orientation direction of the part layers. To incorporate the linear elastic model into a material database for SLS materials, the direction dependence of the material must first be determined. The most general formations of linear elasticity are defined to determine their relevance to the structure of a SLS-manufactured material. These include, but are not limited to, orthotropic linear elasticity, transversely isotropic elasticity and isotropic linear elasticity.

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The generalised Hooke’s law states that each stress component depends (linearly) on all strain components. Full anisotropic elasticity is defined by six directions, three translational and three rotational components. When an element undergoes shear strain, it will also be subjected to normal stress. This can be written in a 6X6 matrix, thus resulting in 36 unknown variables [16]. This great number of elastic constants makes it difficult to model fully anisotropic materials, but fortunately, many materials have some type of symmetry which simplifies the number of unknown material variables.

2.2.1.1. Orthotropic linear elasticity

An orthotropic material has three orthogonal planes of microstructural symmetry. An example of this is glass-fibre. The material has thousands of slender, long glass fibres which are bound together in bundles. This relates to the material composition of FDM materials where the polymer is extruded in rows onto the print bed.

Three mutually perpendicular planes of symmetry can be passed through each point in the model, thus creating material directions in the 𝑥-, 𝑦-, and 𝑧-axes. This symmetry reduces the number of unknown material variables to nine. An important factor of the orthotopic material is that the shear is independent of the material axes. This means that normal stresses will only cause normal strains and shear stresses only shear strains [16].

2.2.1.2. Transversely isotropic linear elasticity

A transversely isotropic material has a single material direction with an isotropic response in the plane that is orthogonal to this direction. Many materials belong to this class, including but not limited to wood, fibre-reinforced composites and laminated steel. This type of elasticity can also be related to SLS materials.

The characteristic material direction is the 𝑧-axis and the material is isotropic in any plane parallel to the 𝑥-𝑦 plane. The material properties are the same in all directions which are transverse to the fibre direction. This extra symmetry reduces the number of unknown material variables to five [16].

2.2.1.3. Isotropic linear elasticity

The final type of linear elasticity to consider is isotropic linear elasticity. An isotropic material has a material response which is independent of orientation; this indicates that the material properties are constant in all directions. The symmetry of such a material further reduces the unknown material variables to two [16].

The anisotropic nature of materials produced by SLS has a significant effect on the material properties. For this reason, the mechanical properties of the manufactured part must be determined in the 𝑥, 𝑦 and 𝑧 directions. The current information on mechanical properties and the

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standards used for testing of SLS materials are investigated to determine the anisotropic material properties of the machine and material which are used in this study.

2.2.2. Material properties of PA2200

A database of the material properties of laser sintered PA2200 is needed for the accurate predictive simulation of models. Polyamide (PA)-based laser sintering materials (PA11 and PA12) are strong enough and sufficiently durable to be used as functional prototypes, but the limit in knowledge and range of their mechanical properties restricts engineers in creating optimised designs.

PA2200 (PA12 from EOS GmbH) is a white material powder with a wide variety of applications due to its well-balanced property profile, which is why it is the most widely used polymer in the industry [11], [14], [17]. This polymer is popular due to its wide thermal processing window (the temperature between the melting temperature (TM) and crystallisation temperature (TC)), which is

a particularly favourable characteristic for laser sintering. This characteristic indicates that small deviations in optimum processing conditions have a negligible effect on the material properties of the manufactured parts [10], [17–19].

In addition to its wide processing window, PA2200 is also popular for its powder availability, low tendency to warp, and low initial zero-shear velocity. According to EOS [20], this material is a multipurpose material with balanced property profile, good chemical resistance, high strength and stiffness, excellent long-term constant behaviour, high selectivity and detail resolution, and various finishing possibilities (i.e. metallisation, stove enamelling, vibratory grinding, tub colouring, bonding, powder coating, or flocking). This material is also bio compatible according to EN ISO 10993-1 and USP/level VI/121 °C and is approved for food contact in compliance with the EU Plastice Directive 2002/72/EC (with an exception in high alcoholic foods) [20]. Jain et al. [9] also states that the most common applications of this material is that of functional parts, medical applications (like prostheses), high quality, fully functional plastic parts, substitute typical injection moulding plastics and realisation of movable part connections. For these reasons, this material is ideal for use in an industrial setting.

2.2.2.1. Build parameters that influence material properties and anisotropy

Further industrialising the laser sintering process requires parts with higher strength, durability and accuracy, which can be attained by optimising the mechanical integrity of the manufactured part. The mechanical properties (and in turn the mechanical integrity) of a part are affected by a certain number of factors, which include but are not limited to (a) supplied energy density (laser power), (b) scan spacing (the distance between two laser scan lines in a sintered area), (c) part build orientation (with relation to the three principle axis of the machine), (d) material type, (e) powder consistency (ratio of used powder to virgin powder), (f) feed/part bed temperatures, and (g) layer thickness. Of these, the supplied energy density (ED), part build orientation, and the bed

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temperature (Tb) have the largest impact on the mechanical structure and properties of a sintered

part [5], [9], [10].

The ED (power) of the CO2 laser directly affects the mechanical structure and properties of a part,

with higher energy inputs increasing the melting within the part. This measure decreases porosity and anisotropy, which improve the overall part strength and ductility [10], [15]. An ED level above 0.299 J/mm2_{can, however, lead to a decrease in the strength and modulus values; this can be}

attributed to the powder particles becoming damaged or burnt by excess heat [7], [10]. Studies indicate that a constant ED level between 0.012 J/mm2_{and 0.299 J/mm}2_{will achieve optimum}

part density for parts manufactured with PA2200 [5], [10], [12], [21], [22].

The part build orientation is further crucial for the creation of optimum parts. The part build orientation is the angle at which the part is manufactured in relation to the print bed; this angle is defined according to the right-hand rule (Figure 2.2-1). A 0° build orientation (the longest dimension of the specimen is parallel to the 𝑥- and 𝑦-axes) results in a greater fracture/ultimate tensile strength (UTS), while a 90° build orientation (the longest dimension of the specimen is parallel to the 𝑧-axis and perpendicular to the 𝑥- and 𝑦-axis) leads to greater elongation at break (EAB) [5], [9], [11], [23], [24]. Further studies indicate an optimum ultimate tensile strength (UTS), Young’s modulus, and EAB at an orientation of 30° to the 𝑦-axis [9], [24].

Figure 2.2-1: Right-hand rule for part build orientation

When determining the material properties of PA2200 it is necessary to test the properties of each batch of powder due to the reuse of unsintered powder. Some of the powder is not melted (sintered) during production of SLS parts; this powder is mixed with unused (virgin) powder in a 50/50 ratio to insure that the viscosity build-up and molecular weight of the used (aged) powder particles are within standard specifications [17], [19], [25]. The viscosity of the melted polymer depends mostly on laser ED and Tb [13], [26]. A higher bed temperature requires less energy to

melt the powder, but the Tb should be low enough so that the powder does not reach the melting

temperature. Too low a Tb can however result in warping and insufficient melting. According to

+Z

+X +Y

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Goodridge et al. [11], Tb is usually set between 3°C and 4°C below the melting temperature for

semi-crystalline polymers.

2.2.2.2. Material properties of PA2200

The relationship between the fabrication parameters (delay time, build orientation and powder properties) and the mechanical properties is identified in the studies of Goodridge et al. [11], Jain et al. [9] and Gibson et al. [27]. These studies indicate that both orthotropic and isotropic material models can be used to define the level of anisotropy found in PA2200 [26], [28]. The effect of using different LS machines and reusing powder is taken into account by Stitchel et al. [28] and Zarringhalam et al. [25]. Lastly, studies using tensile and compressive tests to create finite element method (FEM) simulations include that of Ajoku et al. [4] and Helou et al. [29].

Gibson et al. [27] comprehensively analysed the relationship between powder properties, fabrication parameters and the mechanical properties of SLS parts. This study measured the effect of fabrication parameters on the tensile strength, density and hardness of PA12 specimens. Jain et al. [9], in turn, studied the effect of delay time on the part strength. The delay time is, however, dependent on part build orientation, and for this reason this study developed and implemented an algorithm that calculates the optimum part build orientation (in the 𝑥- and 𝑦-axes) for improving tensile strength.

Zarringhalam et al. [25] investigated the effect of powder reuse on the mechanical properties of PA2200 as produced by different LS machines. The effects of the difference in processing of each machine on the microstructure of the parts were identified. Stitchel et al. [28] also analysed the mechanical properties of powders fabricated by different machines by observing the efficiency of the machines in relation to the build direction. The mechanical tensile tests displayed a high variability in the ductility of the samples among the machines and a distinctive anisotropic response to the adjustment in build direction.

Faes et al. [26] concluded that the elastic properties of SLS PA-12 are best described using an isotropic material model by identifying and quantifying the variability and heterogeneity in the quasi-static response of SLS PA-12 components, after which the anisotropy in this quasi-static response was studied.

Goodridge et al. [11] scripted a review paper on the main factors that influence the selection and processing of polymers and identified research on laser sintering that has been carried out to date. This study also examines the limitations of current laser sintering systems in the processing of polymer materials.

Ajoku et al. [4] applied compression and tensile tests to Nylon-12 laser sintered and injection-moulded parts, in order to compare experimental results to the predictions of FEM simulations. This study identified that the laser-sintered nylon-12 has a modulus that is 10% below that of

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injection moulding. The tensile strength of the laser-sintered specimens was, however, higher than the injection-moulded specimens. Helou et al. [29] validated FEM simulations of cellular structures by using data from compression tests. The cells were evaluated through simulations and compared to the test data from laser-sintered specimens.

The mechanical properties determined by these studies are displayed in Table 2.2-1 and Table 2.2-2, and reflect the optimal values of each study. The UTS of polyamide-12 stays relatively constant, while the yield strength varies remarkably. This difference can be ascribed to the system’s sensitivity to the identified build parameters and other environmental factors.

Table 2.2-1: Tensile strength and Young’s modulus of PA2200

Ajoku et al. [30]

Faes et al. [26] Jain et al. [9] Zarringhalam et al. [25]

Goodridge et al. [11]

Min UTS (MPa)

x 46.9 46 43.8 42 50.36 y 38.5 45 42.4 - - z 39.9 42 - 38 - Min ET (MPa) x 2014.3 1680 - 1600 1782.6 y 1803.6 1660 - - - z 1806.9 1620 - 1400 -

Other parameters, such as Poisson’s ratio, the shear modulus and mass density of PA2200, were also identified. These parameters are a necessity in defining a material database for simulation purposes. The values are displayed in Table 2.2-2.

Table 2.2-2: Poisson’s ratio, shear modulus and mass density of PA2200

2.2.2.3. Standards used for mechanical testing of PA2200

To determine the mechanical properties of PA2200 produced by the laser sintering process, the standards used in previous studies and the current standards according to BS EN ISO and ASTM

Helou et al. [29] Faes et al. [26] Gibson et al. [27] Goodridge et al. [11] Poisson’s ratio 0.4 0.387 - 0.409 - - Shear modulus (MPa) - 587 - 600 - - Mass density (g/cm3₎ 0.93 0.96 - 0.98 0.9 - 1 0.95 - 1

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are identified. Two standards on the determination of tensile properties of plastics are identified, namely BS EN ISO 527 and ASTM D638.

The ISO 527 standard states the general principles on determining the tensile properties of plastics and plastic composites. This standard defines several different types of test specimens that suit different types of material. These test specimens are used to determine the tensile strength, tensile modulus, and other aspects as needed for material property characterisation [8], [12], [14], [23]. The ASTM D638 standard also describes the principles used in determining the tensile properties of plastics. This testing standard states that all samples must be prepared under identical circumstances because plastics have a high degree of sensitivity to straining and environmental conditions. This standard covers the test methods used in determining the tensile properties of reinforced and unreinforced plastics and defining the method of determining Poisson’s ratio at room temperature [5], [8], [9], [13], [19], [31]. This standard addresses the same subject material as BS EN ISO 527.

2.3. Finite element modelling of anisotropic material properties

In this study, the accuracy of an area of Nastran®_{is tested on Siemens NX software. The}

predictions of the Nastran®_{FEA engine are compared to elongations as determined by an}

experimental setup, and the error margin between these values is determined. The software programs used in previous studies are discussed in this section together with their conclusions.

2.3.1. Available simulation programs

Simulation and analytical models defined in previous studies used either the discrete element method (DEM) or the finite element method (FEM) to predict the mechanical performance of SLS structures. The simulation programs referenced in this section include ANSYS®_Academic

Teaching, COMSOL Multiphysics®_{, ABAQUS, Vega FEM, MSC Nastran}®_{and Solidworks}®_.

Numerical simulations are used by [26] and [32] to determine the reliability of a model. In the study of [26], a virtual fields method (VFM) is used to determine the variability in the elastic tensor of PA2200, while [32] used the discrete element method (DEM) to test the reliability of a model in terms of representing real phenomena (shrinkage predictions) and the thermal history experienced by the material. The phenomenon of the effect of the thermal cycles on the material powder present during manufacturing is extensively studied for both polymer and metal AM [33– 36]. These studies identified the thermal finite element framework during heating and cooling of the powder, including the fusion depths achieved in the SLS process. The software used for these analyses are ANSYS®_{Academic Teaching [35] and COMSOL Multiphysics}®_{[34], [36].}

In other studies, the mechanical performance of SLS structures under compressive and tensile forces were predicted using FEM analyses [4], [29], [37–41]. [29] and [40] used ANSYS®_{as FEM}

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lower-leg prosthesis components under compression forces, respectively. In simulating the global structural behaviour of a cellular structure/scaffold, [39] created a 1D model on ANSYS®_which

mimicked the expected level of porosity in an SLS structure. The behavioural predictions of orthotropic scaffolds under compression or tensile loads can also be analysed using programs such as ABAQUS [37], [42] and Vega FEM [38].

In analysing the mechanical behaviour of parts using MSC Nastran®_{as finite element analysis}

(FEA) engine, two studies were identified. The mode of deformation occurring in specimens under compression loads is predicted by [4] using MSC Patran/Marc. In another study [39] applied a 3D FEM analysis on cellular structures using Solidworks®_{to predict the global structural behaviour}

when tensile loads are applied. These studies indicated that the FEM analysis reached the yield point sooner than the experimental data [4], and a lower ultimate tensile strength was predicted through Solidworks®_[39].

2.3.2. Level of anisotropy in material models

With the assessment of the results and recommendations made by the identified FEA studies, it is necessary to consider the assumptions made on the level of anisotropy in the material models. The material models are the input parameters of the FEM analysis and therefore greatly influence the outcome of the predicted results. Two categories of material models were assumed in these studies, namely, isotropic [4], [29], [39] and transverse isotropic [37], [38] models.

In assuming an isotropic material model for polymer SLS structures, [29] concluded that simulations in ANSYS®_{do not converge to a solution that estimates the experimental data. This}

study indicates that the shortcoming can be ascribed to the porosity of the structures and the program’s inability to solve non-solid objects. The studies of [4] and [39] also assumed isotropic material models, and both studies concluded that the proposed FEM models only serve to identify areas in which the SLS structures would fail and, as such, does not give an accurate indication of the structure’s strength parameter. These models led to predictions of a smaller elastic region and a lower ultimate strength, which indicated that the material properties of SLS structures are not congruent with the behaviour of traditional FEA and that isotropic theories fail when applied to these structures.

Using ABAQUS as a simulation program, [37] assumed and confirmed a transverse isotropic material model for PA2200. This analysis led to a higher predicted Young’s modulus than that found in the experimental data. The study assumed that the change in moduli can be attributed to the effect that the surface roughness has on the experimental data due to the scaffolding shapes that are used. In assuming a transverse isotropic material model, [38] identified that shearing is more present in models containing an increase in anisotropy and that this parameter is not taken into account when an isotropic material model is assumed. [40] concluded that a

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transverse isotropic material model is more accurate than an isotropic material model, but that the variation in material properties of polymer SLS still yield less reliable FEM simulation results.

2.3.3. Conclusions on simulation parameters

The variation in material properties of polymer SLS is mostly ascribed to the inability to have perfect control over the manufacturing process. Better control of this process will lead to reduced porosity in the structure and smaller variations in the structure’s properties. The limited access in editing the printing parameters of SLS machines requires a focus on identifying simulation parameters that will lead to improved predictions of the mechanical behaviour of SLS parts. To accommodate shearing experienced in non-isotropic structures, [38] suggests tetrahedral meshing, which better resolves shear. The shearing between layers will however be affected by the porosity of the structure, which is directly influenced by the level of melting of the SLS powder. This parameter is very difficult to incorporate into a linear FEM analysis due to the porosity being non-uniform, so, the density of the material will have to suffice [29].

According to [29], ANSYS®_{and Nastran}®_{assume that the analysed specimen is homogeneous,}

defining the object as solid. The density of the material will therefor still indicate to the program that the object is solid and will not incorporate the effect of porosity on the mechanical properties of the structure. When observing the porosity in the structure, the surface roughness and micropans can also be identified, which has a remarkable influence on the mechanical properties of a SLS structure [37].

Chapter 2 discussed the literature found on the available material database parameters for PA2200 SLS structures, and the simulations thereof. Chapter 3 consist of the theory in obtaining the material database and defined an analytical model for elongation predictions of PA2200 structures.

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CHAPTER 3 THEORY

This chapter consists of the theory pertaining to this study and defines the method used to analyse the mechanical properties from a stress-strain diagram and the analytical model used for elongation predictions.

3.1. Calculations on stress-strain diagrams

The aim of this study is to specify the accuracy of displacement simulation models as determined by the Siemens NX software tool. One of the main parameters in creating accurate FEM simulation models is the material properties of the specimen. The properties of some materials, such as PA2200, depend on the company that produces the material and the machine used for manufacturing. For this reason, it is necessary to identify the material properties of the batch of material powder used to produce the specimens tested in this study. These material properties are compared to that found in literature to identify parameters that cannot be measured using the available apparatus, such as Poisson’s ratio.

The data gathered by a tensle test can be used to quantify a set of parameters defined by the stress experienced by a specimen and the accompanying strain. The stress and strain experienced by each specimen is plotted and the necessary data is read from the graph. The curve that results from this data set is called the stress-strain diagram and there are two ways of defining this data, namely the engineering stress-strain curve and the true stress-strain curve. The engineering stress-strain curve assumes that the original cross-sectional area of the test specimen remains constant while the tensile test is executed, while the true stress-strain curve takes into account the change in cross-sectional area. Measuring the change in cross-sectional area is time-consuming and a limited process for most materials. These two curves are essentially constant over an elastic region, and for this reason the engineering stress-strain curve is used.

3.1.1. Engineering stress-strain curve

For the engineering stress-strain curve, it is assumed that the nominal or engineering stress and strain are constant throughout the region between the gauge points. The nominal stress is determined by dividing the applied load, P, by the original cross-sectional area of the specimen, A0:

𝜎 = 𝑃 𝐴0

The nominal or engineering strain is measured with a strain gauge and represents the ratio of the change in gauge length, 𝛿, to the specimen’s original gauge length L0:

𝜖 = 𝛿 𝐿0

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The nominal stress is plotted to the corresponding nominal strain for each specimen, which is known as the conventional stress-strain diagram.

Hibbeler [56] describes the four areas in which the stress-strain curve is divided and the parameters that can be obtained by analysing these regions. The four regions of a stress-strain diagram are explained by assessing the engineering and true stress-strain diagrams of steel, as displayed in Figure 3.1-1.

Figure 3.1-1: Conventional and true stress-strain diagrams for ductile material [56]

The stress-strain curve can be divided into four regions: the elastic region, the region of yielding, the region of strain hardening before necking, and lastly, the region of localised necking [57].The elastic region is indicated by the light brown region in Figure 3.1-1; the gradient of this region is known as the Young’s modulus (E), and is mathematically represented by

𝐸 = 𝜎 𝜖

This gradient indicates the rate at which a material will deform as the stress over the material is increased. At the end of the linear elastic region the material will start to yield and deform plastically. The maximum stress that can be applied to a material before it starts to deform, is defined as the yield stress, 𝜎𝑌. The yield stress is determined by drawing a 2% offset line parallel

to the linear elastic curve. The 2% offset yield strength is indicated by 𝜎𝑌=

𝑃𝑠𝑡𝑟𝑎𝑖𝑛 𝑜𝑓𝑓𝑠𝑒𝑡=0.002

𝐴0

When the yield point is reached, the material will continue to strain without an increase in load as indicated by the dark-shaded brown region in Figure 3.1-1. After yielding has occurred, a load can be further applied to the material, which will result in a curve that rises continuously with a decreasing gradient until it reaches a point of maximum stress, also known as the ultimate tensile strength (UTS), 𝜎𝑢.

Establishing a finite element model to determine the tensile strength of additively manufactured PA2200 parts