Anisotropic Finite Element Modeling of the Fused Deposition

Modeling Process.

Skyler Ogden1, Scott Kessler, P.E., Ph.D.2

1University of Colorado Boulder; 2510 Foresight Circle; Grand Junction, Colorado 81505, USA

2Colorado Mesa University, 2510 Foresight Circle, Grand Junction, Colorado 81505, USA

Keywords: FEA, 3D, Printing, FDM, Additive, Manufacturing, Plastic, ABSplus, Stratasys,

Modeling, DARPA, DRC, Mojavaton

Abstract

The exhibited material behaviors of 3D printed Acrylonitrile Butadiene Styrene (ABS) plastics

are highly dependent on the load direction with respect to print orientation. A database of

strength characteristics was generated to facilitate the construction of a Finite Element Analysis

(FEA) model. This model was used to predict the anisotropic material properties of ABS under

load conditions. It was demonstrated that an FEA model for 3D printed ABS plastic can be

created and verified by measuring the material properties of test specimens printed in multiple

orientations.

An accurate FEA model of the anisotropic material properties of ABS can be used to predict the

behavior of the part under load conditions. Anisotropic material properties become an issue

when printed parts are used as an end product. A load applied to a part parallel to the print

direction may not result in fracture, while the same load applied perpendicular to the print

direction may result in catastrophic failure. Predicting these behaviors is paramount when

designing parts designated for 3D printing, particularly when used as a fail safe to protect more

expensive components in a drivetrain as noted below.

Introduction

Industry has traditionally used Fused Deposition Modeling (FDM) as a method for rapid

prototyping but has devalued the output

product as a mere demonstration or proof of

concept. FDM processes have become

accurate, precise, and strong; allowing for a

conceptual shift from printing for prototyping

to printing for direct end use. End products are

produced quickly, may be highly complex, and

possess acceptable material strengths [1, 2].

The 3D printing processes employs the use of

thermally bonded thermoplastics. Fine ribbons

of thermoplastic are laid down layer by layer

through a computer controlled extrusion head

(see Figure 1). The thermoplastic is heated via

an electrical resistor to well above the melting

point. Anisotropic material properties inherent

due to material layering.

Figure 1. (1) Nozzle extruding molten

plastic. (2) Deposited material. (3)

Platform with x, y, and z translation

abilities.

Tensile tests were performed on thirty nine 3D printed plastic tensile specimens. Twelve

specimens were printed with print layers parallel to the load direction, hereinafter referred to as

horizontal specimens. Another twenty seven specimens were printed with layers perpendicular to

load direction, hereinafter referred to as vertical specimens.

Material properties were supplied by the manufacturer, Stratasys. However, data was reported

for specimens printed in the most advantageous print orientation (horizontal); not taking into

account the inherent anisotropic material properties. Mechanical properties were determined

from experimentally gathered stress-strain curves and compared against values reported by the

original equipment manufacturer (Stratasys) and a third party material properties reporting

company (MatWeb).

A representative stress-strain curve was chosen for each orientation using statistical analysis. The

representative curves were imported into an FEA analysis tool available through SolidWorks.

Computationally derived values from FEA were compared to experimentally gathered data for

model verification.

Methods

3D printing

FDM was used for manufacturing of all tensile specimens. Pre-print slicing of the 3D model was

performed using CatalystEX. The slicing software was set to the highest density and resolution

available. The software parameters were solid fill with a layer height of 2.54 mm.

A single Stratasys Dimension 1200es 3D printer was used for all 3D printing. All specimens

were extruded in ABSplus-P430 (ABS-430). 1200es was used as support during the printing

process and was fully dissolved using a Stratasys SCA-1200 support-removal system. Specimens

were printed within an actively heated envelope at the default temperature of 80oC. Model and

support materials were extruded at the default temperature of 300oC. ABSplus-P430 material

property data was acquired from Stratasys [3].

Specimen Prep and Testing

Specimen dimensions and testing procedures adhered to ASTM D638-10, Standard Test Method

for Tensile Properties of Plastics. A type II specimen was used due to the infrequency at which

samples broke within the intended gauge length (see Figure 2). Five hundred grit sand paper was

used to lightly sand the surface of the sample to slightly reduce the cross sectional area within

the gauge length encouraging an inter gauge fracture. All specimens were sanded equally [4].

Calculations

Tested tensile specimens exhibited little to no necking. Therefore, engineering stress was

considered viable. Experimental stress-strain curve data indicated linear behavior in the elastic

deformation area and was therefore modeled linearly. The modulus of elasticity was found by

taking the slope between two points = .005, and = .01, where and are strain and stress respectively. Yield strength was found at a 0.2% offset. Toughness was

calculated using the trapezoidal method of numeric integration (see equation 1).

Matlab

Matlab was used to:

1. Import data from .txt tensile test data dump.

2. Calculate mechanical properties.

3. Perform statistical analysis.

4. Plot resultant data.

5. Construct .dat stress-strain curve for use in the SolidWorks static FEA.

SolidWorks 2013 and FEA

Solidworks was used for 3D modeling of specimens and FEA simulations. A plasticity von

Mises model was chosen for FEA modeling. A single representative stress-strain curve was

selected for each print orientation tested. The representative curve was chosen based closeness to

average values for yield strength, toughness, and modulus of elasticity.

+ 2

(1)

Figure 2. ASTM tensile specimen type II used for all tests. W = 6mm, L = 57 mm, WO = 19 mm,

LO = 183 mm, G = 50, D =135, R = 76, and T = 7 mm.

Results

Horizontal Samples

Twelve tensile specimens were pulled in a tensile

testing machine (see figure 3). Six of the 12

specimens tested broke within the gauge length

(50.00% success). All six samples exhibited closely

grouped yield strengths with a standard deviation of

0.41 MPa (see Table I). The average yield strength

was 28.6 MPa. Specimens showed a considerable

amount of plastic deformation before breaking,

absorbing an average of 1223 kJ before failure.

During and after testing, plastic deformation was

visible in the form of white striations (see Figure 4).

Table I. Experimentally gathered mechanical property data for

horizontally printed specimens.

Vertical Samples

Twenty seven tensile specimens were pulled in a

tensile testing machine (see Figure 5). Five of the 27

specimens tested broke within the gauge length

(18.52% success). A low rate of success was

indicative of a group of specimens which failed

unpredictably. The average yield strength was 26.2

MPa with a standard deviation of 2.7 MPa (see Table

II). The vertical samples absorbed an average of

242.24 kJ almost exclusively in the elastic region,

indicated the specimen broke without warning and

without much, if any, plastic deformation.

Table II. Experimentally gathered mechanical property data for

vertically printed specimens.

Criteria Value Std.

Deviation

Error

(%)

Tensile Modulus (MPa) 1860 23 9.6

Ultimate Strength (MPa) 29.5 0.48 0.20

Yield Strength (MPa) 28.6 0.41 0.17

Breaking Strength (MPa) 28.5 0.52 0.21

Toughness (kJ) 1220 516 211

Criteria Value Std.

Deviation

Error

(%)

Tensile Modulus (MPa) 1820 44 20

Ultimate Strength (MPa) 26.5 2.7 1.2

Yield Strength (MPa) 26.2 2.7 1.2

Breaking Strength (MPa) 26.4 2.7 1.2

Toughness (kJ) 242 66 30

Figure 3. Stress-strain curve of six 3D printed tensile

specimens printed with layering parallel to load direction.

Values indicated are averages.

Figure 4. Result of tensile test on a horizontally printed

specimen. The visible white striations in the specimen

indicated a large amount of energy was absorbed via plastic

deformation.

Figure 5. Stress-strain curve of five 3D printed tensile

specimens printed with layering perpendicular to load

direction. Values indicated are averages.

Comparison between Horizontal and Vertical Samples

The average modulus of elasticity, yield strengths and ultimate strengths were not significantly

impacted by the print orientation. Horizontal specimens exhibited an average modulus of elasticity

only a 2% larger than vertical specimens. Horizontal specimens were stronger by only a small

margin. Most notable, the ultimate strength of the horizontal specimens was an average of 11%

larger.

Energy absorption was the distinguishing characteristic between vertical and horizontal

specimens. Vertical specimens absorb an average of 242 kJ of energy at fracture while horizontal

specimens absorbed an average of 1220 kJ of energy, nearly six times as much. The extra

toughness found in the horizontal specimens was a result of a much larger plastic deformation

region (see Figure 6).

Comparison of Experimental Data to Reported Data

Experimentally gathered mechanical properties for ABSplus printed horizontally were compared

to values reported by Stratasys and by MatWeb for extruded ABS. Values of concern were:

modulus of elasticity, ultimate strength and yield strength [3, 5].

Experimentally gathered average modulus of elasticity data or horizontal specimens was an

average of 22% lower than reported by Stratasys (see Figure 7). Experimentally acquired

ultimate strength was 25% lower than reported (see Figure 8) [3].

Similarly, material property values reported by MatWeb for extruded ABS were well above

average experimentally gathered values. The experimentally gathered average modulus of

elasticity was an average of 11% lower than reported by MatWeb (see Figure 7). Experimentally

gathered average ultimate strength was 32% lower than reported by MatWeb (see Figure 8) [5].

Figure 6. Toughness comparison between vertically printed specimens (light grey)

and horizontally printed specimens (dark grey). Indicated values are of

representative stress-strain curves determined through statistical analysis.

Horizontal Sample:

1220 kJ energy absorbed

Vertical Sample:

242 kJ energy absorbed

In both cases the reported strengths and modulus of elasticities far exceed what was gathered

experimentally. Engineers designing for reported specs would likely be over estimating the

capabilities of the material; leading to premature and catastrophic failures.

Finite Element Modeling in Solidworks.

Experimental results were compared to theoretical

results acquired via the SolidWorks FEA tool. Two

representative stress-strain curves were imported

into SolidWorks to define the material properties for

ABSplus; one for the horizontal specimens and one

for the vertical specimens. The analysis was

performed at average load force experienced

immediately after yielding.

Horizontal FEA

Average force at yield for the horizontal specimens

was 1112 N (tension). A maximum von Mises stress

of 27.1 MPa was found at the reduced cross section

(see Figure 9). FEA results were 5.54% lower than

average experimental yield strength. Calculated

yield stress fit well with experimental data which

ranged from 28.2 MPa to 29.3 MPa.

1860 1820

2300

2070

0

500

1000

1500

2000

2500M

od

ulu

s o

f E

last

icit

y (

MP

a)

Figure 7. Material property value comparison between

experimentally determined modulus of elasticity as compared to

reported values.

Hori

zonta

l

Str

atas

ys

Ver

tica

l

Mat

Web

26.528.6

26.5 25.9

36.038.7

41.4

0

5

10

15

20

25

30

35

40

45

(MPa) (MPa)

Ultimate Strength Yield Strength

Str

en

gth

(M

Pa

)

Figure 8. Material property value comparison between

experimentally determined ultimate strength and yield

strength compared to reported values.

Hori

zonta

l

Ver

tica

l

Str

atas

ys

Mat

Web

Ver

tica

l

Mat

Web

Hori

zonta

l

Figure 9. Results of FEA in SolidWorks using a

representative stress strain curve data for all

horizontal specimens.

Model name: Horizontal

Specimen

Study Name: Horizontal FEA

Plot type: Static nodal stress

Deformation scale: 11

Vertical FEA

The average force at yield for the horizontal specimens

was 1102 N. A maximum von Mises stress of 27.0

MPa was found in the reduced cross section (see

Figure 10). FEA results were 4.33% higher than

average experimental yield strength. The calculated

yield stress fits well with experimental data of 4 of the

5 specimens which ranged from 26.23 MPa to 27.85

MPa.

Conclusions

Experimental data indicated 3D printed ABSplus

thermoplastic exhibited anisotropic material behavior

under load conditions. Loads applied in parallel

(horizontal) to the print direction resulted in a larger

strength, more absorbed energy (toughness) and a more

predicable failure than loads applied perpendicularly

(vertical).

Material properties for ABSplus as reported by

Stratasys did not agree with values gathered

experimentally. In all cases the reported value was

larger than the experimental value, accounting for a

11%-25% discrepancy.

The FEA model created using SolidWorks plasticity

von Mises model can reproduce experimental values accurate to within 6%.

Recommendations

Further testing is required to determine the effects of print orientation on cyclical loading and

impact energy absorption. A flexural strength test and an Izod impact test are recommended to

expand the characterization of the material.

Designing parts for 3D printing

The strength of a 3D printed part will be determined by print orientation. Whenever possible,

care should be taken to ensure the maximum loading force is applied parallel to print direction. A

parellel print orientation will allow for a higher strengths. More importantly, the part will exhibit

larger amounts of plastic deformation before failure, assuming the part is not unreasonably shock

loaded. In general, any 3D printed part can only be as strong as the weakest print orientation.

Care must be taken to design a part with print orientaiton in mind.

Current Application

A humanoid robot has been developed for the Defense Advanced Research Project Agency

(DARPA) to compete in the DARPA Robotics Challenge in December, 2013 (see Figure 11).

The robot incorporates many 3D printed components which are inexpensive and easy to produce.

Precision servos are used to actuate all five joints in the arms. The servos are many orders of

magnitude more costly than the 3D printed components. Ideally, the printed components will fail

Figure 10. Results of FEA in SolidWorks using a

representative stress strain curve data for all

horizontal specimens.

Model name: Vertical

Specimen

Study Name: Vertical FEA

Plot type: Static nodal stress

Deformation scale: 11

before the servos. A 3D printed adapter disk is used to mate the hinge joints to the rotary joints in

the arms. The adapter disk is a simple component, which can be quickly and inexpensively

replaced. Concepts discussed in this manuscript have led to the development of an adapter disk

which will fail before the precision servos (see Figure 12).

Future Applications

All the limbs in the humanoid robot employ

a planetary gear system that translates

torque from the precision servos (see

Figure 13). The print orientation with

respect to the load direction is constantly

changing, complicating the FEA model. A

more comprehensive FEA model will be

developed to predict the dynamic internal

forces of the gear system.

Figure 11. A humanoid robot developed for the

DARPA robotics challenge in 2013. The robot

employs the use of 3D printed components which

are designed to fail before expensive servos.

Figure 13. 3D printed planetary gears used in every joint in the

humanoid robot. Such an integral part requires great confidence

in strength characteristics.

Figure 12. A 3D printed component of a robotic arm designed

to fail before more expensive components. Arrows indicated

failed regions.

References

1. D. Bak, Rapid prototyping or rapid production? 3D printing processes move industry

towards the latter, Assembly Automation, vol. 23, no. 4, pp. 340345, Dec. 2003.

2. DeGrange, J. "Materials Move Aerospace Additive Manufacturing from Prototypes to

Finished Products." Design News Sept. 2013: 46-48. Print.

3. ABSplus, Fortus 3D Production Systems FDM Materials | Stratasys. (n.d.). Retrieved

from http://www.stratasys.com/materials/fdm/absplus

4. ASTM Standard D638-10, 2010, "Standard Test Method for Tensile Properties of

Plastic," ASTM International, West Conshohocken, PA, 2010, DOI: 10.1520/D0638-10,

www.astm.org.

5. Overview of materials for Acrylonitrile Butadiene Styrene (ABS), Extruded. (n.d.).

Retrieved from MatWeb - The Online Materials Information Resource website:

http://matweb.com/search/DataSheet.aspx?MatGUID=3a8afcddac864d4b8f58d40570d2e

5aa&ckck=1