1. 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.

2. 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

3. 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.

4. 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

5. 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

6. 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.

7. 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

8. 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.

9. Internal Cellular StructureY 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).

10. 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.

11. 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.

12. 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.

13. Material Property Test Results
The elastic modulus of the ULTEM 9085 material was found to be MPa with a COV of 3.18%
The Poisson's ratio was found to be 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

14. 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

15. 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

16. 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.

17. 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

18. 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

19. 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

20. 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 used for the outer skin.

21. 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

22. 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.

23. 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.

24. 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 )

25. 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).

26. 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.

27. 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

28. Questions
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