Mechanical property characterization and simulation of fused deposition modeling Polycarbonate parts

Mechanical property characterization and simulation of fused deposition modeling Polycarbonate

parts

Miquel Domingo-Espin a ,Josep M.Puigoriol-Forcada a ,Andres-Amador Garcia-Granada a ,Jordi Llumàc ,Salvador Borros b ,Guillermo Reyes a ,?

a

Grup d’Enginyeria de Productes Industrials,IQS,Universitat Ramon Llull,Spain b

Grup d’Enginyeria de Materials,IQS,Universitat Ramon Llull,Spain c

Dept.de Ciencia de Materials i Enginyeria Metal.lurgica,EUETIB,Universitat Politècnica de Catalunya,Spain

a r t i c l e i n f o Article history:

Received 26February 2015Revised 1April 2015Accepted 8June 2015

Available online 19June 2015Keywords:

Fused deposition modeling Mechanical behaviour Stiffness matrix Constitutive model Finite element analysis

a b s t r a c t

Building end-use functional parts with additive manufacturing (AM)technologies is a challenging task.Several factors in?uence their surface ?nish,dimensional accuracy,mechanical properties and cost.Their orientation inside the building chamber is one of the most signi?cant factors in AM processes.When using Fused Deposition Modeling (FDM)to build such parts,additional factors must be considered.This paper aims to accomplish two purposes:?nding a good model to simulate FDM parts and corre-lating a ?nite element analysis (FEA)simulation with physical testing.

The ?rst objective was achieved by experimental tensile test of specimens to determine the nine mechanical constants that de?nes the stiffness matrix of an orthotropic material.Three Young’s modulus,three Poisson’s ratio and three shear modulus were experimentally obtained as well as yield tensile and ultimate strength of each specimen.

A simple part was designed and manufactured in different orientations to be physically tested and sim-ulated to achieve the second objective.Polycarbonate (PC)was used as part https://www.360docs.net/doc/4717463246.html,bined loading including bending and torsion was used.Differences on mechanical response were observed during the physical test of the parts depending on the building direction.Conclusions comment results and the con-venience of using a different constitutive model depending on the design and use speci?cations.

ó2015Elsevier Ltd.All rights reserved.

1.Introduction

Nowadays additive manufacturing (AM)technologies are becoming useful techniques to produce parts due to the advan-tages they present in front of traditional manufacturing tech-niques.Some of them are:decrease in production cycle,high complexity and personalized parts [1].On the other hand using these technologies in order to achieve certain product speci?ca-tions is not a simple task.Some AM technologies have their own software that helps users to set few building parameters,with any or little quantitative information,according to cost and surface ?nish.Also,manufacturers often avoid information data about mechanical behaviour of AM processed materials.In order to build functional end-use parts using these technologies it is needed to know how different building parameters affect the mechanical behaviour of parts.The common practice among engineers when designing functional parts is to use ?nite element analysis (FEA)

to simulate a part under real loads and ?xtures.FEA materials data-base include isotropic materials,processed by traditional manufac-turing processes,but cannot model properly layered manufactured anisotropic materials.AM users need tools to evaluate virtual mod-els of a part with more precise and quantitative data to decide effectively prior to manufacturing the best building parameters.It is important for them to reduce manufacturing cost reaching geometrical and mechanical requirements when setting process parameters.

The manufacturing principle behind all those technologies is to slice a part and to build it layer by layer.Part orientation plays an important role in the surface ?nish [2–5],dimensional accuracy [6–10],cost [11,12]and mechanical behaviour.It has been reported a dependence of the mechanical behaviour of AM parts on its orientation in the building chamber.It indicates that its mechanical behaviour is not isotropic [13–20].Results may vary depending on the technology since bonding between layers depends on the material and the process [21].

Fused Deposition Modeling (FDM)presents also a great amount of other building parameters that affects parts features.It has been

https://www.360docs.net/doc/4717463246.html,/10.1016/j.matdes.2015.06.074

0264-1275/ó2015Elsevier Ltd.All rights reserved.

Corresponding author.

observed that the distance between extruded ?laments [9,10,19,20],its width [9,10,19,20,22],the pattern which the ?la-ments follow to ?ll each layer [9,10,19,20]and layer thickness [9,10,20,22],among others,have a great effect on quality and per-formance of a part.This implies that building strategy election has a signi?cant effect on the properties and the performance of a part.It is really important to characterize AM materials in order to sim-ulate properly end-use parts before manufacturing them.Some attempts to mechanically characterize FDM materials have been reported.The characterization of Acrylonitrile Butadiene Styrene (ABS)[23,24]and Ultem 9085[25]FDM materials has been per-formed in order to be able to simulate them with FEA.They all con-cluded that FDM parts presented different mechanical response depending on how the layers were placed regarding the direction of the load.Hence the building direction of the parts should be cho-sen according to boundary conditions.Physical models were also manufactured to compare simulation and real test data [24,25].The correlation presented was good under elastic deformation but not when the yield point was exceeded.

In this paper the mechanical characterization of Polycarbonate (PC)FDM material is performed assuming orthotropic behaviour in order to obtain the stiffness matrix.The mechanical response of a geometrically simple part is physically tested and FEA simu-lated.Conclusions from this work are useful for de?ning what is the best approach to simulate such parts.2.Constitutive orthotropic model

In order to use FEA simulations to predict the behaviour of FDM parts it is necessary to de?ne the constitutive model that govern its mechanical behaviour.The constitutive model presented here is assumed true under linear elastic deformations.

Linear elasticity is described by the Hooke’s law,which deter-mines that the relationship between stress and small strains is lin-early proportional.For orthotropic materials,de?ned as a material with three mutually perpendicular planes of symmetry,the com-pliance matrix has only nine unknown components (Eq.(1)).

e x e y e z c yz c xz c xy 0

B B

B

B B

B B B

@1C C C C C C C C A ?S 11S 12S 13000

S 22S 23000S 33000S 4400sym S 550S 66

0B B B B B B B

B @1

C C C C C C C C A ár x r y r z s yz s xz s xy 0B B B B B B B B @1

C C C C

C C C C A e1T

where e i is for unit elongation,c ij for unit shearing strain,r i for nor-mal stresses and s ij for shearing stresses.

Considering the conventional engineering constants in the three directions,Eq.(1)can be written in terms of Young’s modulus,Poisson’s ratio and shear modulus (Eq.(2)).

e x e y e z c yz c xz c xy 0

B B B B B B B B @1

C C C C C C C C A ?1=E x àm xy =E x àm xz =E x 0001=E y àm yz =E y 0001=E z

0001=G yz 00sym 1=G xz 01=G xy 0B B

B

B B

B B

B

@1C C C C C C C C A ár x r y r z s yz s xz s xy 0B B B B B B B B @1

C C C C C C C C A e2T

The equation used commonly in engineering is the product between the general stiffness matrix and the strain tensor (Eqs.(3)and (4)).

r ?áe

e3T

r x r y r z s yz s xz s xy 0

B B

B

B B

B B B

@1C C C C C C C C A ?C 11C 12C 13000C 22C 23000C 33000C 4400sym C 550C 66

0B B B B B B B

B @1

C C C C C C C C A áe x e y e z c yz c xz c xy 0B B B B B B B B @1

C C C C

C C C C A

e4T

where

C 11?eS 22áS 33àS 223TS ;C 22?eS 11áS 33àS 213TS ;

C 33?

eS 11áS 22àS 212TS ;C 12?eS 23áS 13àS 12áS 33TS ;C 13?

eS 12áS 23àS 22áS 13T;C 23?eS 12áS 13àS 11áS 23T

;C 44?1S 44;C 55?1S 55;C 66?1S 66

;

S ?S 11áS 22áS 33t2áS 12áS 23áS 13àS 213áS 22àS 223áS 11àS 2

13áS 33

e5T

To de?ne the mechanical behaviour of an orthotropic material,nine independent constants:three Young’s modulus (E i ),three Poisson’s ratios (m ij )and three shear modulus (G ij ),must be found.Five specimens built in six different orientations were tested to know those constants.According to Hooke’s law,Young’s modulus and Poisson’s ratio can be obtained from the tensile strength test as:

E 1?

D r 1e 1

e6Tm 12?à

e 2e 1

e7T

where 1is the pulling direction and 2perpendicular to the load.The in-plane shear modulus can be obtained from the test of a 45°-oriented unidirectional test specimen,according to the follow-ing equation:

G 12?E 1=2áe1tm 12T

e8T

where 1is the direction the load is applied and 2is the perpendic-ular direction.

3.Experimental procedure

The experimental procedure is divided in three parts.First,the

FDM Polycarbonate (PC)parts,printed under speci?c building parameters,are mechanically characterized in order to obtain the stiffness matrix.Then,a geometrically simple part is fabricated in different orientations and tested.Finally,using the previously obtained stiffness matrix,a FEA simulation is performed to model part behaviour.

3.1.Mechanical characterization

In order to obtain the nine independent constants values of the stiffness matrix,a total of thirty PC samples were built and tested in six different orientations (Fig.1).It corresponds to 5samples for each orientation.Since there are no standard tests for AM parts,the samples have been built and tested according to ASTMD638:Standard Test Method for Tensile Properties of Plastics.ASTM stan-dard was preferred instead of ISO because it is the standard used by the manufacturer of the specimen material and also for most of the authors studying the mechanical behaviour of AM part [14,17,21,24,26–34].

After orienting parts as shown in Fig.1,they were built using a Stratasys Fortus 400mc using the following building parameters:

M.Domingo-Espin et al./Materials &Design 83(2015)670–677671

Diameter nozzle:0.254mm;since it has been proved to give better results in dimensional accuracy,surface?nish and mechanical behaviour than the other possible diameters [6,9,20,35,36].The actual size of the extruded?lament is larger than the diameter of the tip due to swelling but it can be con-trolled[37].The size is set to0.508mm(in the control software) and is automatically regulated by the head speed and the drive wheels that adjust the material?ow rate[26,38].

Part interior style:Solid–Normal;which?lls the interior part completely with fully dense raster toolpaths.The extruded angle?laments in the XY plane are+45°/à45°alternating in each layer since it has been proved that parts with this interior style bear better combined loads[9,20,36,39].

Visible surface style:Enhanced;which uses independent con-trols for the visible surface rasters and the non-visible,internal rasters.The width of the visible raster is smaller than normal in order to improve the surface roughness and the visible appearance.

Support style:Breakaway;the removal is easier with this type of support and it is the most used when the parts present com-plex geometry.

Number of contours(1contour),visible surface style and sup-port style parameters have been selected to emulate what a user would set to manufacture a common part.

The tensile test has been performed using a Microtest EM2/20 equipped with an optical extensometer used to preform bi-dimensional measurement of specimen strain.Area reduction due to elongation was considered to measure real strains.

During the tensile stress test of the dog-bone samples,per-formed at1mm/min,the strain and axial and longitudinal elonga-tion were collected along with the stress.Elastic modulus,tensile stress and strain and ultimate stress and strain are presented in Table1according to the direction shown in Fig.1.

The results show that samples1and3present similar tensile strength but the fracture of the last one is fragile since there is not much plastic deformation observed(Fig.2).Specimens1and 2present a signi?cant plastic behaviour because the deposited?l-aments are arranged in the same direction that the sample is being pulled.Therefore,contour and raster are pulled longitudinally in those specimens.Sample3has a fragile fracture because it is pulled perpendicular to the layers,where the bonding strength is weaker than the strength of pulled contours.Samples2shows the highest value of both elastic modulus and tensile strength since there are more layers being pulled longitudinally.Consequently there are more contours that act as reinforcement?bers[36].

It is also noticeable that samples3present a wider variability (Fig.3)in Young’s modulus and tensile strength due to the fragile behaviour presented.

Data was processed using a MATLABòfunction to perform a least square interpolation in the linear part of the stress–strain curve.Young’s modulus,Poisson’s ratio and Shear modulus(Eqs.

(5)–(7))were calculated from a linear modeling of the curve in the domain of study.

The nine engineering constants obtained(Table2)de?ne the stiffness matrix in MPa(Eq.(9))using Eqs.(3)–(5).

C?

3:04á1032:13á1032:00á103000

3:45á1032:11á103000

3:16á103000

5:91á10200

sym6:33á1020

5:06á102 0

B B

B B

B B

B B

B@

1

C C

C C

C C

C C

C A

MPa

e9T

3.2.Physical testing of FDM parts

A geometrically simple part(Fig.4)was designed in order to present a complex stress state when tested.The design also consid-ered to?x the part during testing using a plate without holes for an easier simulation of constraints in FEA Analysis[24].The3D model was created using SolidWorksò.

The sample was designed in order to produce a stress in several directions,below the yield stress,with an acceptable deformation.

The designed part has six possible building orientations(Fig.4) because any of the six exterior surfaces can be used as building bases.Orientations using surfaces1or3,2or4and5or6are mechanically equivalents because the slicing process produces the same slices.Consequently,only three?nal building bases were considered(1,2and5).

The coordinate system of the building chamber sets the coordi-nate system of the part.As elastic modulus in X and Y are different, it was decided to build two different orientations for each building base:one of them with the cantilever aligned with the X-axis and the other one with the Y axis(Fig.5).A total of18parts of the model were printed.There are three parts for each

possible Fig.1.Orientations for tensile test samples.

orientation,using the same FDM technology and building parame-ters used for the tensile test parts.

During physical testing parts were?xed as shown in Fig.6left. All parts were tested in the same conditions:a vertical displace-ment of35mm was applied at1mm/min(same as the tensile test) at15mm from the end of the cantilever.The test was performed using:

MTS insight.

Load cell10kN.

Three point bending grip.

Parts were inspected after the test and all of them recovered its initial form due to the elastic material behaviour.Displacement and reaction force data was collected.Results also showed that the relation between force and displacement was linear.A least square interpolation MATLABòfunction was used to obtain the experimental data of the samples using the same building base were merged.Consequently only three different parts were consid-ered:1,2and5.

The same MATLABòfunction was used but now just considering building bases.The results are presented in Table4and Fig.7.They show that part orientation and building base election affects its mechanical response.Between building base1and2there is a dif-ference of5.77%and between1and5of2.15%.

The section that most in?uences the mechanical response(in

Table1

Average elastic modulus,tensile strength and strain and ultimate strength and strain for each orientation.

Fig.2.Average stress–strain curves for samples1,2and3.

Fig.3.Values of Young’s modulus and tensile strength for directions XY,YZ and XZ.

M.Domingo-Espin et al./Materials&Design83(2015)670–677673

Orientation2was the weakest because of the way that the con-tours were placed(Fig.8b).They did not act as reinforcement?bers and layers were moving relatively one above the other although being bonded.Orientation5presented the top and the bottom part of the end of the cantilever?lled with contours(Fig.8c).In this case,they acted as reinforcement?bers.This con?guration strengthened the end section,as it was proved.Slices are placed in a transverse direction with respect to the central axis form the end of the cantilever in orientation1.It results in the toughest ori-entation,stiffer than orientation5.The cantilever section is not square,so it can be said that the effect of bonding between slices stiffens more than that of contours acting as reinforcement?bers.

3.3.Simulation

The stiffness matrix for the orthotropic constitutive model was used to simulate the mechanical response of the same parts phys-ically tested.Data for that matrix was obtained from the mechan-ical characterization.Seven different simulations were made,one for each orientation physically tested and one considering the material isotropic,since it is the easiest way to carry out FEA sim-ulations of a part.The mechanical constants used in the isotropic simulation were obtained using the mean values of elastic modu-lus,Poisson’s ratio and shear in directions1,2and3.

ANSYSòMechanical15.0software was used to simulate the deformation of a part considering the building orientation.The boundary conditions for the FEA simulation were established according to the physical test conditions(Fig.6a).Since the load is not always applied in the same position due to bending,a con-tact was set for this area.The mechanical constants used in each simulation were set according to how the part was built.Linear and static cases were assumed in the?nite element model.The same hexahedral mesh(Solid185)was used for all the loading cases.Total element number of10476and total node number of 14008were used in the model.

The same?exural stiffness coef?cient(F/d)was calculated.The results for each orientation are presented in Table5and show that the differences between orientations using the same building base are small(maximum2.1%difference for building base2).This con-?rm that there is no important difference between orientations using the same building base,as it happened with the physical testing.

The simulated and the physical testing results were compared (Table6).The orthotropic simulation results similarity to the phys-ical test results depends on the building base orientation.Building

4.Dimensions of the sample for physical and FEA simulation test with possible building bases numbered.

Fig.5.Parts printed for physical testing sharing the same coordinate system.

base orientation 1was the most accurate.It has to be noted that FEA simulation is a simpli?ed model.It considers a part completely solid but it is made of joined plastic wires (contours and rasters)

with different bonding among ?laments in the same layer com-pared with bonding between layers.Then,a 7.30%average differ-ence (Table 6)can be considered a good approximation.

The results from isotropic mean simulations also presented ferent accuracy depending on the building bases,being the overall difference 7.12%(Table 6).It is very similar to the orthotropic model.Since the isotropic model is easier to use because there is no need to orientate the material properties,it should be used to simulate FDM parts under elastic stress conditions (like the studied case).On the other hand,if a part reaches the yield tension,the

for the physical test (left)and ANSYS òschematics of the simulation (right).Small displacement (a and b),and pictures Fig.7.Graphic results of force and displacement for each building base.

standard deviation (std),and standard deviation in %from experiment results.F /d std %std 1.410.036 2.551.430.019 1.351.360.014 1.031.330.039 2.961.410.0110.751.37

0.015

1.07

standard deviation (std),and standard deviation in %F /d std %std 1.420.028 1.991.340.027 2.031.39

0.022

1.58

Fig.8.Diagram of the different slices disposition in the cantilever for each building orientation (a)is orientation 1,(b)is orientation 2and (c)is orientation 5.

orthotropic model is more realistic.Therefore,depending of the building direction,a part could fail due to fragile rupture or could plasticize(Fig.2).

4.Conclusions

Anisotropic material properties should be considered when using FEA simulation of FDM parts exceeding the elastic region limit.However,regarding elastic deformations,the material can be considered isotropic using the mean values of the mechanical properties since the results are equivalent.An isotropic model is easier to use as there is no need to modify constitutive equations in the materials database of FEA software and to choose the right material orientation in the model.

When the yield strength is exceeded,it is important to choose the proper orientation to build a part.Parts should be oriented so that the greater tensile stresses are aligned with the direction of the longest contours to increase their strength.To avoid fragile fracture tensile stresses should not be aligned with the building direction,perpendicular to the layer’s planes.

FDM parts anisotropy depends not only on the building direc-tion.Manufacturing process such as nozzle diameter,slice height, and diameter of the extruded?laments can signi?cantly affect results so the mechanical properties reported in this article should be used carefully.

Acknowledgment

Miquel Domingo-Espin was supported by an IQS fellowship. Appendix A.Supplementary material

Supplementary data associated with this article can be found,in the online version,at https://www.360docs.net/doc/4717463246.html,/10.1016/j.matdes.2015.06. 074.

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Table5

Flexural stiffness coef?cient(F/d)for each simulated orientation.

Orientation F/d

1.01 1.35

1.02 1.32

2.01 1.26

2.02 1.29

5.01 1.38

5.02 1.39

Iso Mean 1.33

Table6

Comparison between physical test and simulated results for each orientation(the

orthotropic results are the mean value of the two simulations for each orientation).

Model type Test-simulation deviation for

orientations(%)

Mean deviation(%)

125

Orthotropic 4.22 6.6111.17.30

Iso mean 4.2210.61 6.527.12

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