Acta Polytechnica CTU Proceedings doi:10.14311/APP.2019.25.0052 Acta Polytechnica CTU Proceedings 25:52–57, 2019 © Czech Technical University in Prague, 2019 available online at http://ojs.cvut.cz/ojs/index.php/app EXPERIMENTAL INVESTIGATION AND SIMULATION OF 3D-PRINTED LATTICE STRUCTURES Eva Heiml∗, Anna Kalteis, Zoltan Major Johannes Kepler Universität Linz, Institute of Polymer Product Engineering, Altenberger Straße 69, 4040 Linz, Austria ∗ corresponding author: eva.heiml@jku.at Abstract. Lattice structures are currently of high interest, especially for lightweight design. They generally have better structural performance per weight than parts made of bulk material. With con- ventional manufacturing techniques they are difficult to produce, but with additive manufacturing (AM) fabrication is feasible. To better understand their behaviour under various loading conditions two lattice structures in different configurations were observed. For each structure three different test specimens were designed and manufactured using selective laser sintering (SLS). To investigate the mechanical performance under large deformations the specimens were made of a thermoplastic polyurethane (TPU), which shows a hyperelastic material behaviour. Beside the experimental observations also finite element analyses (FEA) were conducted to investigate the deformation behaviour in more detail. Keywords: Lattice structures, additive manufacturing, mechanical testing, finite element analysis. 1. Introduction Cellular structures are classified by their inner topol- ogy and are thus considered either as stochastic or as ordered. They can be further differentiated in open or closed cell types [1]. Ordered materials generally have better mechanical properties, high surface area densities and lower pressure drops when compared to stochastic structures. The biggest disadvantage of stochastic cellular materials is the lack of design free- dom. Therefore, ordered structures, especially lattice structures, are of higher interest [2]. Lattices have a trusslike structure with interconnected struts and nodes in a threedimensional space [3]. They consist of repeating unit cells, which have periodicity in three dimensions [1]. The differences in performance come from a different deformation behaviour. Foams are goverend by cell wall bending, whereas lattice cells stretch and compress [2]. This stretch dominated be- haviour means that the initial yield is followed by either plastic buckling or brittle collapse which leads to post yield softening and then at the densification strain the stress rises steeply [4]. Ashby [4] has defined three design variables which describe the properties of cellular materials. The first variable is the material from which the structure is made. The second variable states that properties are different for varying cell topology and shape. And the third design variable is the relative density, which is the relation between the density of the cellular structure and that of the bulk material. The aim of this work presented here is to model and investigate the behaviour of two lattice structures, manufacturedwithSLS, under tension and compression. The experimental data is compared to the results of the FEA.A further objective is to investigate this behaviour when the configuration of the specimen is changed. 2. Test Specimen Two lattice structures are chosen to be investigated more thoroughly. One is the octet structure, Fig- ure 1a, which consists of two regular tetrahedrons and one octahedron [5]. The second structure, Figure 1b, consists of a hexagonal array which forms the hori- zontal planes that are connected by spatial struts [6]. The models are created in NX 12.0 (Siemens PLM Software). To create the specimens the diameter of the trusses as well as the length of each unit cell are adapted. Therefore, the overall dimension and the volume stay the same for each configuration. The overall dimen- sions were constrained by the building space of the SLS-printer, which only allowed 60 mm in each di- rection and a minimum diameter of 1.2 mm. With three adjacent unit cells in each direction in space the basic lattice structure is created (Octet 3 × 3 × 3 , Hexagonal 3 × 3 × 3 ). To investigate the influence of increased number of unit cells another specimen with four cells is created (Octet 4 × 4 × 4 , Hexago- nal 4 × 4 × 4 ). The third structure consists of five unit cells in two directions in space and three cells in the third one (Octet 5 × 5 × 3 , Hexagonal 5 × 5 × 3 ). To enable a uniform distribution of forces onto the specimen, 2.0 mm thick plates are added at the top and bottom of each structure. For the third specimen type these plates only cover an area of three times three unit cells, so that the forces apply on the same configuration as in the first specimen type. A sum- mary of specimen data can be found in Table 1. For each specimen information about the dimension of the unit cell, including the diameter of the trusses d, the overall dimension and the area where the load is applied is given. To make production easier and to reduce stress con- 52 http://dx.doi.org/10.14311/APP.2019.25.0052 http://ojs.cvut.cz/ojs/index.php/app vol. 25/2019 Investigation of 3D-printed lattice structures Specimen Unit Cell Dimension Cube Dimension Load Face Area [mm] [mm] [ mm2] x y z d x y z Octet 3 × 3 × 3 20 20 20 3 60 60 60 3600 Octet 4 × 4 × 4 15 15 15 2.3 60 60 60 3600 Octet 5 × 5 × 3 12 12 12 1.8 60 60 36 1296 Hexagonal 3 × 3 × 3 11.5 11.5 19.91 3 34.5 34.5 59.75 1190.25 Hexagonal 4 × 4 × 4 8.6 8.6 14.89 2.3 34.4 34.4 59.58 1183.36 Hexagonal 5 × 5 × 3 6.9 6.9 11.95 1.8 34.5 34.5 35.83 428.49 Table 1. Specimen Data (a) . Octet Structure (b) . Hexagonal Structure Figure 1. Lattice Structures centrations radii are added at the strut connections. For the simulations they are removed, to enable a more regular mesh distribution. Test runs showed, that the influence of the radii on the outcome of the simulation is neglectable. The lattice structures have very complex geometries, thus, the chosen manufac- turing method is SLS. This is a powder bed based process, where a laser beam selectively sinters mate- rial particles. This method is especially interesting for manufacturing lattice structures, because the unused powder can function as support material [7]. 3. Mechanical Testing 3.1. Bulk Material Characterisation Before the testing of the lattice structures started, a basic characterisation of the TPU was undertaken. For this, tension tests of ISO 527-5b specimens at different test rates were carried out. The results for 0.1 mm · s−1 were then used to create the material model. Results for the bulk material characterisation are depicted in Figure 2. These results show the time dependence and the hyperelastic material behaviour. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Strain (-) 0 2 4 6 8 S tr es s (M P a) 10 mm/s 1 mm/s 0.1 mm/s 0.001 mm/s Figure 2. Bulk Material Characterisation 3.2. Lattice Structure Characterisation All compression and tension testing was carried out on a MTS 852 test system at room temperature. The test speed of the machine was set to 0.1 mm · s−1. For compression tests the machine was set up in a way that the specimens rested on one compression plate while the other one applied the force from the top. For tension tests additional support structures, manufac- tured with fused deposition modelling (FDM) using acrylonitrile butadiene styrene (ABS), were glued on the specimens. The clamps were then mounted on those support structures (Figure 3). Tension tests were conducted until either failure of the bonding layer or failure of the lattice occured. Compression tests were stopped after reaching a certain strain. For strain evaluation digital image correlation (DIC) was used. 53 E. Heiml, A. Kalteis, Z. Major Acta Polytechnica CTU Proceedings (a) . Compression Test (b) . Tension Test Figure 3. Test Setup 4. Finite Element Analysis 4.1. Material Model Generation The data from the bulk material tests at 0.1 mm · s−1 is used to generate a hyperelastic material model for the TPU, because the experiments were performed with this test rate. The true strain results together with the true stress are then used to create the mate- rial model in Abaqus 6.14 (Dassault Systèmes). The Ogden model (see [8]) at a strain energy potential of order 3 best describes the actual behaviour of the TPU and is therefore used in the simulation, see Figure 4. 4.2. Simulation Methodology The FEA is performed using Abaqus as well. For compression tests rigid plates are added to the top and bottom of each structure. Through these the boundary conditions are applied. A frictionless con- tact between the plates and the specimen is created. The deformation is the same as in the mechanical test- ing in order to compare the results of the simulations and experiments. For tension tests reference points above and below the support structures, connected via coupling, and kinematic constraints are used to apply the boundary conditions (Figure 5). The sup- port structures are included in the simulation, because they are made of ABS, which has a low stiffness as Figure 4. Material Model Generation well. With linear tetrahedral elements a free mesh is created, on the bounding faces a mapped mesh is used. Seed sizes are adapted for each structure, with at least four elements over the thickness. The strain-rate sen- sitivity of the bulk material is identified (see Figure 2), this effect is neglected for material model used during FEA. Because of the time-independence of the mate- rial model it is possible to describe the test-rate of the experiments also with the explicit dynamic solver, which is used to improve computational efficiency, ad- ditionally mass scaling is utilised. Since the generated material model is time independent the quasi-static tests can be represented with an explicit solver. To simulate the behaviour of the TPU the hyperelastic material model from Figure 4 is implemented. Both simulations are displacement controlled. 5. Results 5.1. Experiments The apparent tensile modulus and apparent compres- sive modulus is calculated with Equation 1 in the standardised strain region (ε1 = 0.05%, ε2 = 0.25%). E = σ2 − σ1 ε2 − ε1 (1) The apparent tensile stress is evaluated at 20 % strain, since that is the highest strain where all struc- tures can be compared. The apparent compressive plateau stress is evaluated for each structure as well (see Figure 6). These two values are normalized with the load face area. A summary of the results can be found in Table 2. The apparent tensile modulus increases for both structures when the number of unit cells is increased. The apparent compressive modulus shows the same behaviour for the octet structures. Both the appar- ent tensile stress and the apparent compressive stress increase for a higher number of unit cells. The Hexag- onal 5 × 5 × 3 specimen shows the highest values, except for the apparent compressive modulus. 54 vol. 25/2019 Investigation of 3D-printed lattice structures Specimen Apparent Tensile Modulus Apparent Tensile Stress at 20 % Strain Apparent Com- pressive Modu- lus Apparent Com- pressive Plateau Stress [MPa] [MPa] [MPa] [MPa] Octet 3 × 3 × 3 3.61 0.4614 1.31 0.35 Octet 4 × 4 × 4 4.32 0.5042 0.54 0.43 Octet 5 × 5 × 3 5.47 0.6640 0.11 0.47 Hexagonal 3 × 3 × 3 6.74 0.7717 0.79 0.49 Hexagonal 4 × 4 × 4 7.53 0.8755 1.81 0.65 Hexagonal 5 × 5 × 3 15.51 1.5060 1.77 1.76 Table 2. Experimental Results (a) . Compression Simulation (b) . Tension Simulation Figure 5. Simulation Setup 5.2. Simulation The experimental results are used to validate the sim- ulations. The results of a range of selected structures are further discussed in this section. Figure 7 dis- plays the behaviour of the Hexagonal 3 × 3 × 3 and Hexagonal 4 × 4 × 4 specimens under tension. For small strains both configurations show a linear elas- tic behaviour. For a higher number of unit cells the slope of the curves is higher, both for experiment and simulation. Especially for small displacements the results of experiment and simulation are in a good agreement. The problem of most tension tests was, that the 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Strain (-) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 S tr es s (M P a) Apparent Plateau Stress (a) . Compression Test 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Strain (-) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 S tr es s (M P a) Apparent Tensile Stress (b) . Tension Test Figure 6. Evaluation of Test Results bonding layer failed prior to the structure. Only for the specimens with five unit cells in x and y direction failure of the material occured. Figure 8 shows the re- sults of the mechanical test and the simulation of the hexagonal structure shortly before the struts connect- ing the lattice structure with the support structure rip. Until this point the experimental result and the result of the simulation are in a good agreement. Depicted in Figure 9 the struts start to rip at a dis- placement of around 7 mm and a force of 600 N. This 55 E. Heiml, A. Kalteis, Z. Major Acta Polytechnica CTU Proceedings 0 5 10 15 20 25 30 35 Displacement (mm) 0 500 1000 1500 2000 F or ce (N ) Hexagonal 3x3x3 Experiment Hexagonal 3x3x3 Simulation Hexagonal 4x4x4 Experiment Hexagonal 4x4x4 Simulation Figure 7. Tension Tests of Hexagonal 3 × 3 × 3 and Hexagonal 4 × 4 × 4 (a) . Finite Element Analysis (b) . Mechanical Test Figure 8. Tension Test of Hexagonal 5 × 5 × 3 is way less than what the other hexagonal structures endure, where the bonding layer failed at approxi- mately 30 mm displacement and a force of 1400 N. The force acts on the same number of unit cells as on the Hexagonal 3 × 3 × 3 specimen, but on a smaller area. For the same number of unit cells their size is an important factor for how much load they can bear. In Figure 10 the results for compression tests of the Octet 3 × 3 × 3 and the Octet 4 × 4 × 4 specimens are depicted. For small displacements the results of the 0 2 4 6 8 10 12 Displacement (mm) 0 200 400 600 800 1000 1200 F o rc e (N ) Hexagonal 5x5x3 Experiment Hexagonal 5x5x3 Simulation Figure 9. Tension Test of Hexagonal 5 × 5 × 3 mechanical tests show a linear behaviour and match with the simulation for both specimens. Then again for a higher number of unit cells the force progression is higher. At a displacement of around 10mm a force plateau is reached and at a later point the densification starts, which again happens earlier for Octet 4×4×4 . 0 10 20 30 40 50 Displacement (mm) 0 5000 10000 15000 20000 25000 F or ce (N ) Octet 3x3x3 Experiment Octet 3x3x3 Simulation Octet 4x4x4 Experiment Octet 4x4x4 Simulation Figure 10. Compression Tests of Octet 3 × 3 × 3 and Octet 4 × 4 × 4 6. Conclusion This paper investigates the behaviour of two different lattice structures with three different configurations under tension and compression. As it is described by Ashby [4] the geometry is a crucial factor for the behaviour of such structures. The specimens with three and four unit cells have the same volume for both structures respectively, thus the influence of the diameter on the apparent tensile modulus can be evaluated. As shown in Figure 11, the modulus increases when the diameter decreases. It is assumed that stiffening is a result of internal constraint from adjacent unit cells, which increases 56 vol. 25/2019 Investigation of 3D-printed lattice structures 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Diameter (mm) 2 3 4 5 6 7 8 9 A p p a re n t T en si le M o d u lu s (M P a) Octet Structure Hexagonal Structure Figure 11. Influence of the Diameter on the Apparent Tensile Modulus with the number of unit cells in the specimen. Spec- imens with smaller and thus more unit cells show a stiffer response. For the validation of this assumption further configurations have to be investigated. In a first step only a simple time-independent material model is implemented, which will be extended to con- sider the time-dependence of the material. The model created to describe the lattice structures, when tension and compression is applied, is in a good agreement with the experimental data. Since there is no failure criterion implemented, there are still some deviations, which can be resolved by expanding the model. With the method being validated by the experiments, it can be further developed for various loading conditions. Acknowledgements The specimens for the work conducted were manufactured at Bernstein Innovation GmbH. The mechanical tests were performed in the IPPE laboratory under the supervision of Michael Lackner. References [1] T. George. Carbon fiber composite cellular structures, 2014. PhD Thesis, School of Engineering and Applied Science, University of Virginia. [2] D. Rosen, S. R. Johnston, M. Reed. Design of general lattice structures for lightweight and compliance applications 2019. [3] G. Dong, Y. Tang, Y. Zhao. A survey of modeling of lattice structures fabricated by additive manufacturing. Journal of Mechanical Design 139, 2017. doi:10.1115/1.4037305. [4] M. F. Ahsby. Cellular solids - scaling of properties. In Cellular Ceramics: Structure, Manufacturing, Properties and Applications, chap. 1.1. Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim, 2005. doi:10.1002/3527606696.ch1a. [5] R. Fuller. Synergetic building construction, 1961. US Patent 2,986,241. [6] J. Aboudi, R. Gilat. Micromechanical analysis of lattice blocks. International Journal of Solids and Structures 42:4372–4392, 2005. doi:10.1016/j.ijsolstr.2005.01.008. [7] W. Tao, M. Leu. Design of lattice structure for additive manufacturing. pp. 325–332. 2016. doi:10.1109/ISFA.2016.7790182. [8] R. Ogden. Large deformation isotropic elasticity: On the correlation of theory and experiments for incompressible rubber-like solids. Proc Roy Soc Lond Ser A: Math Phys Sci 326:556–585, 1992. doi:10.1098/rspa.1972.0096. 57 https://doi.org/10.1115/1.4037305 https://doi.org/10.1002/3527606696.ch1a https://doi.org/10.1016/j.ijsolstr.2005.01.008 https://doi.org/10.1109/ISFA.2016.7790182 https://doi.org/10.1098/rspa.1972.0096 Acta Polytechnica CTU Proceedings 25:52–57, 2019 1 Introduction 2 Test Specimen 3 Mechanical Testing 3.1 Bulk Material Characterisation 3.2 Lattice Structure Characterisation 4 Finite Element Analysis 4.1 Material Model Generation 4.2 Simulation Methodology 5 Results 5.1 Experiments 5.2 Simulation 6 Conclusion Acknowledgements References