MECHCOMP3 - International Conference on Mechanics of Composites 4-7 July 2017 – University of Bologna, Italy Cellular thermoplastic manufactured using 3D printing: experimental characterization and finite element modeling of internal structure Sunil Bhandari and Roberto A. Lopez-Anido Advanced Structures and Composites Center University of Maine Abstract: Polyetherimide (PEI) test coupons with cellular internal structure enclosed by PEI solid outer walls were 3D printed using fused deposition modeling. Material experiments were carried out using ASTM standard test procedures to measure the elastic modulus, Poisson’s ratio, and the shear modulus in different material directions. The observed behavior was compared with typical cellular materials. A space frame lattice and shell finite element analysis was implemented to model the cellular internal structure. The linearly elastic response of the material was predicted using finite element analysis. The results form finite element analyses were correlated with the experimental results. This approach to predict linear elastic properties of 3D printed cellular material using finite element analysis provides an efficient procedure for designing and optimizing the geometry of the cellular structure of 3D printed parts. Smeared linear elastic properties were calculated for a representative continuum model of the cellular structure. These smeared properties were used to predict the linear elastic behavior of a larger structure with the same cellular internal structure.
Research Motivation Use 3D printing to create cellular parts in a short time with iterative design changes. Design lightweight molds that meet mechanical and thermal requirements for thermoforming or vacuum forming of composite materials. R&D
Research Objectives Study mechanical properties of internal cellular structure by Fused Deposition Modeling (FDM) or Fused Filament Fabrication. Create a lattice (space frame) finite element model to determine the elastic properties of internal structure. Create a continuum finite element model to determine the strains on the mold during initial stages of the forming. One common internal structure chosen for study Material change in mechanical properties with rise in temperature. A finite element model that is computationally cheap and reasonably accurate in linear elastic region. And use that to predict stains on mold.
3D Printer The 3D printer uses Fused Deposition Modeling (FDM) to deposit layers of molten filaments one over another to create the part. The system prints accurate, repeatable parts as large as 914 x 610 x 914 mm. The system can use a wide range of thermoplastics with advanced mechanical properties Computer numerically controlled (CNC) extruder head: The CNC extruder head has two degrees of freedom. It can move in global X and Y directions in the horizontal plane. The extruder head has a heated tip to melt the thermoplastic material. The computer controlling the system moves the head to correct positon, heats up the material loaded at the tip and extrudes necessary amount of material to deposit the required height and width. The tip attached to the head and the flow rate of the extrudate controls the width of the deposit partially. Motion table: The motion table is free to move in Z direction and thus has one degree of freedom. The computer moves the table to the required height for deposition during manufacturing. A build sheet, which is a thin sheet (2 mm) of plastic (proprietary material sold by Stratasys) over which the first layers of deposits are made, is secured by the vacuum being applied through the holes on the table. Stratasys Fortus 900 mc printer, Advanced Structures and Composites Center, University of Maine
Material selection The thermoplastic material adopted is a blend of Polyetherimide (PEI) and Polycarbonate (PC) The commercial name is ULTEM 9085 and is supplied by Sabic Amorphous polymer; high peformance Glass transition temperature by Dynamic Mechanical Thermal Analysis: 180°C The material is provided as a filament with a nominal diameter of 1.75 mm For amorphous polymers, the glass transition temperature is important as there is a rapid decline in the storage modulus and hence the stiffness of the material. The elastic modulus is reduced by 50% at 150 C
Research steps for validation of part model Lattice Lattice Solid Space frame (lattice) model more computationally expensive. Coupon tests modeled with it. Coupon tests small size. Only linear elastic response considered. Continuum model is less computationally expensive. Useful for molds as they are larger in size compared to coupons.
Material characterization: test methods Material coupons were 3D printed for tension, compression, and shear tests. ASTM D638 (tension), ASTM D6641(compression) ASTM D7078 (shear) The samples exhibited brittle nature in tension which is consistent with the behavior of cellular solids The samples showed somewhat ductile behavior in compression. The stress-strain curves have an elastic region at low loading. The shear failures were all brittle failures. Compression failure Shear failure: loading in XY plane
Material characterization: parameters Parameters defining internal cellular (parse infill) structure: unit cell, raster, contour Internal structure of 3D printed material with two layers of deposition stacked one over another XY plane is the plane of deposition. Z is through the thickness. The printing parameters constitute the sequence of deposition, the path to be followed during deposition, the dimensions of the deposited material, and some properties of the material that is being deposited. Based on these parameters, the proprietary software for the 3D printer determines the movement path for the extruder head and the motion table, as well as the height of deposition and the correction for shrinkage of the material.
Internal Cellular Structure Y X X Z Internal Structure in XY plane Internal Structure in XZ plane X Y plane is the plane of deposition. Z direction is through the thickness. Broken tension samples Due to the geometry of the material, the mechanical properties are considered identical in X and Y directions (plane of deposition). The properties are different in Z direction (through the thickness).
Ultimate Strength (MPa) Experimental Results Ultimate Strength (MPa) Offset Strength (MPa) Elastic Modulus (MPa) Poisson’s Ratio ASTM D638 Tension X (or Y) 14.6 (4.51%) - 1140 (4.92%) 0.376 (2.15%) ASTM D638 Tension Z 13.3 (2.3%) 921 (2.9%) 0.242 (12.2%) ASTM D6641 Compression X (or Y) 23.6 (2.41%) 22.5 (3.1%) 925 (8.8%) 0.286 (10.8%) ASTM D6641 Compression Z 38.0 (2.0%) 31.97 (5.8%) 1090 (12.6%) 0.246 (18.9%) ASTM D7078 Shear XY 12.5 (5.12%) 789 (7.0%) ASTM D7078 Shear YZ 12.6 (4.0%) 814 (6.5%) ASTM D7078 Shear XZ 13.6 (2.5%) 796 (4.8%) These are not material properties, but the values observed in the experiments. These values are used to verify the finite element model presented later. One thing of note is the high coefficient of variation noted in the parenthesis. Three sources of variability were identified, the material (filament), the machine (3D printer) and the method of printing (internal structure of the 3D printed material – solid vs sparse). Subsequent tests were able to ensure that the variability from the material and the machine was minimal. The samples for tension in X direction broke in the transition region between the grip and gage regions. A new set of samples were created with the density in grip region and transition region double that of density in gage region. This was done to ensure that the failure occurred in gage region.
FE Model of the internal structure The layers are stacked one over another. The structure is modeled as space frames with connection regions working as columns. Lots of approximations here… beams are not really square. Not perfect alignment. The transition region between shell and space frame region not exact. The finite element model consists of an internal structure modeled as a space frame with outer walls modelled as shells.
Input Material Properties for Model The elastic modulus and the Poisson’s ratio were obtained experimentally. Elastic modulus was calculated from tension tests of the filaments. Poisson's ratio was calculated from ASTM D6641 compression test of 3D printed coupon with solid internal fill. Aramis non-contact digital image correlation (DIC) was used to measured strains in the compression tests.
Material Property Test Results The elastic modulus of the ULTEM 9085 material was found to be 2860 MPa with a COV of 3.18% The Poisson's ratio was found to be 0.285 with a COV of 9.04% Extensometer Gage region of filament sample (50.8 mm) Sample for compression test Cameras for the DIC system Fixture for compression test Poisson’s ratio was obtained from compression test. Add picture of compression test Filament Tensile Test Prismatic Coupon Compressive Test
FE Model of the internal structure Boundary condition of uz = 0 (zero vertical displacement) for all nodes with Z = 0. A single node at the center was assigned a boundary condition of ux =0, uy=0 and uz=0 for stability. Unit Load is applied at the center. Kinematic coupling in Z direction is used for all the nodes at the top (Z = 13mm) The space frame and the outer shell are connected by a tie constraint in regions where they come in contact Do you have other figures of the FEM model showing contour plots with stresses or strains? Finite element model for compression test with loading in Z direction
FE Model of the internal structure Elastic modulus is calculated as the 𝐸= 𝑃∗𝐿 𝐴∗𝑒 where, E = elastic modulus of the material (N/mm2) P= force(N) A = area perpendicular to force(mm2) L = length of specimen (13 mm ) e = displacement of the top face (mm) This value is compared with the value observed from the experiments. Elastic Modulus from other tension, compression and shear tests is modeled and compared with experimental values similarly. FE model displacement results for compression test with loading in Z direction
Correlation of Elastic Modulus Between Finite Element Model and Experimental Results Elastic Modulus from Modeling (MPa) Elastic Modulus from Experiments (MPa) % difference Compression in Z-direction 1160 1090 5.2 Compression in X-direction 949 925 3.6 Tension in X -direction 1203 1140 5.5 Tension in Z-direction 904 921 1.9 Shear in XY Plane 726 789 8.0 Shear in XZ plane 785 796 1.4 The values are close for the moduli. The results from FEM are comparable to the results form the experiments.
Poisson’s Ratio from Modeling Poisson’s Ratio From Experiments Correlation of Poisson’s Ratio Between Finite Element Model and Experimental Results Poisson’s Ratio from Modeling Poisson’s Ratio From Experiments % difference Compression in Z- direction 0.248 0.246 0.8 Compression in X- direction 0.235 0.286 17.8 Tension in X - direction 0.350 0.376 6.9 Tension in Z- direction 0.189 19.6
Male mold with various design features Part Design Features Blended edges to reduce friction with forming tapes Solid reinforcement to minimize bending at the center Male mold with various design features
Part Design Features Female mold with various design features Release pin holes Edge walls blended with parabolic profile to reduce friction Slot for transparent Polycarbonate sheet Ended up not using the polycarbonate sheet during the forming process because there was too much reflection of light. That affected the Aramis DIC system. Female mold with various design features
Finite element model for part Mold modeled with an internal orthotropic material for the cellular core and an isotropic material for the outer skin. The mechanical properties for internal orthotropic material for the cellular core obtained from virtual experiments on space frame (lattice) models. The mechanical properties of isotropic ULTEM 9085 used for the outer skin.
FE Model – Virtual Experiments FE model for predicting Gxy Determination of shear modulus Gxy Six virtual experiments carried out to determine the material properties for the orthotropic material for the cellular core
Virtual Experiments Results for Cellular Core Property Value Ex 132 MPa Ey Ez 186 MPa νxy 0.824 νxz νyz Gxy 5.27 MPa Gxz 34.3 MPa Gyz Correct typo Properties of internal cellular core material: The internal structure has higher modulus in X direction. The shear modulus in XZ direction is low. Poisson’s ratios are effectively zero.
Finite element solid model of parts Three parts: the male mold, the female mold, and the solid reinforcements. Internal structure is orthotropic material, outer skin is isotropic material. Solid reinforcement is isotropic solid. Loading of 3.45 MPa. No displacement in Z direction for all nodes at Z = 0. No displacement in X, Y and Z direction for a single node for stability. The parts have tie constraints.
FE Model results–part displacement Solid model with orthotropic internal structure Outer skin Deformations too high Applied load. Magnitude shown is the magnitude of the displacement vector (sqrt of the squares of displacement in x, y and z )
Experimental Validation of FE Model Non-contact Digital Image Correlation Region with deviation from FEM results Section for strain comparison Region with high tensile strain Tip region with highest compressive strains The figures show major in-plane strains in the central sine wave protrusion (tip).
Experimental Validation of FE Model The in-plane major strains from the finite element model and the experimental measurements are correlated Can only get in plane strains from the experiments. Major strains would incorporate strains in both axes. So, I thought the comparisons would be more valid with major strains.
Conclusions A space frame and shell finite element model can be used to predict the elastic properties of a 3D printed part with cellular internal structure. The tensile properties of a extruded filament can be used for input properties in the model. For parts with cellular internal structure, the geometry of the contact area (joint) in the plane of deposition (XY) can be simplified using beam-column elements. The finite element modeling approach could be used to optimize the internal structure of the part to meet design requirements for the molding process For parts with cellular internal structure, the geometry of the contact area (joint) in the plane of deposition (XY) can be simplified
Questions ???