ptfe modeling of sealing components 17th isc template english

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Numerical Simulation of PTFE Sealing Components Bastías, Pedro, Ph.D. Trelleborg Sealing Solutions, R&D 547 North Mount Juliet Rd., Mount Juliet, Tennessee 37122, USA Fayaz Mogal, M.Sc. Trelleborg Sealing Solutions, R&D 2531 Bremer Rd., Fort Wayne, Indiana 46803, USA Larry Castleman, M.Sc. Trelleborg Sealing Solutions, R&D 2531 Bremer Rd., Fort Wayne, Indiana 46803, USA Abstract The sealing industry has relied on fluoropolymers (PTFE’S) for many applications on a wide variety of fields ranging from life saving medical devices to mission critical, i.e. extreme temperature and pressure, oil and gas fields. The mechanical response of these materials is highly complex and characterized by non-linear phenomena influenced by strain- rate and temperature dependencies. Behavior like extrusion, deformation under high pressure, load reversals, and other non-linear behavior challenge traditional material models to accurately predict the mechanical response of PTFE seals. Trelleborg Sealing Solutions has introduced numerical material models which more accurately reproduce the physics of PTFE’s when used in sealing applications. The paper will briefly describe the rheological representation of the model and its constitutive theory, as well as the validation of the model for several PTFE’s compounds. Early results are encouraging as, highly complex, seal phenomena such as extrussion deformation under extreme pressures, and the effect of load reversal can be more faithfully reproduced. 1. Introduction Fluoropolymers are a class of polymers defined by the presence of carbon and fluorine that have many unique mechanical and chamical properties such as a lower friction coefficient than almost any other solid material, the chemical resistance and thermomechanical stability. In many applications, the use of a fluoropolymer is the only reasonable option, due to operational requirements or environmental conditions. For example, fluoropolymers have found many applications in gaskets and liners for vessels and pipes in applications where chemical resistance is of importance, in high pressure seals

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Numerical Simulation of PTFE Sealing ComponentsBastías, Pedro, Ph.D.Trelleborg Sealing Solutions, R&D547 North Mount Juliet Rd., Mount Juliet, Tennessee 37122, USA

Fayaz Mogal, M.Sc.Trelleborg Sealing Solutions, R&D2531 Bremer Rd., Fort Wayne, Indiana 46803, USA

Larry Castleman, M.Sc.Trelleborg Sealing Solutions, R&D2531 Bremer Rd., Fort Wayne, Indiana 46803, USA

AbstractThe sealing industry has relied on fluoropolymers (PTFE’S) for manyapplications on a wide variety of fields ranging from life saving medicaldevices to mission critical, i.e. extreme temperature and pressure, oiland gas fields. The mechanical response of these materials is highlycomplex and characterized by non-linear phenomena influenced by strain-rate and temperature dependencies. Behavior like extrusion, deformationunder high pressure, load reversals, and other non-linear behaviorchallenge traditional material models to accurately predict the mechanicalresponse of PTFE seals. Trelleborg Sealing Solutions has introducednumerical material models which more accurately reproduce the physics ofPTFE’s when used in sealing applications. The paper will briefly describethe rheological representation of the model and its constitutive theory, aswell as the validation of the model for several PTFE’s compounds. Earlyresults are encouraging as, highly complex, seal phenomena such asextrussion deformation under extreme pressures, and the effect of loadreversal can be more faithfully reproduced.

1. IntroductionFluoropolymers are a class of polymers defined by the presenceof carbon and fluorine that have many unique mechanical andchamical properties such as a lower friction coefficient thanalmost any other solid material, the chemical resistance andthermomechanical stability. In many applications, the use of afluoropolymer is the only reasonable option, due tooperational requirements or environmental conditions. Forexample, fluoropolymers have found many applications ingaskets and liners for vessels and pipes in applications wherechemical resistance is of importance, in high pressure seals

for the automotive industry and petrochemical industries, incoatings in various cookware applications, in medicalapplications, and in architectural fabrics for stadiums andairport roofs. Due to its high cost compared to otherpolymers, the use of fluoropolymers is always motivated by oneor more of its specific properties, which sets it apart frommost materials, specifically other polymers.

It is known that unmelted PTFE can have a degree of crystallinity that is higher than 90%, and that the degree of crystallinity of FEP is typically half that of PTFE [10]. For temperatures above 19 _C, the crystal structure of PTFE is hexagonal, and individual molecules are arranged in helical conformations [9]. These features of the microstructure, together with the broad range of usable temperature, makes the characteristic material response of fluoropolymers particularly challenging to model. The current understanding of how to predict the thermomechanical response of fluoropolymers under thermomechanical loads are for these reasons far from complete. Only recently have more advanced constitutive models for fluoropolymer material models been developed [2-5,8,10]

These models have enabled finite element predictions of the large strain behavior of fluoropolymeric. In spite of their availability, a broad section of the sealing industry continues to use material models that fail to capture all the physics involved in the deformation of the fluoropolymers. Thegoal of this work was to implement one of these new and more accurate material model, i.e. Three-Network Model (TNM), thatcan be used to predict the behavior of fluoropolymers subjected to multiaxial large-deformation thermomechanical loadings. The model, its theory, validation and predictive capabilities of the new constitutive model are presented in the following sections.

2. Three-Network Model

The three network model (TNM) is a material model specificallydeveloped for thermoplastic materials. It has many featuresthat are similar to the hybrid model [5, 6], but is designedto be more numerically efficient. The TNM is also aspecialization of the more general parallel network model,

which was developed to predict the large strain time-dependentbehavior of ultra-high molecular weight polyethylene (UHMWPE)[6,7].

Readers are encouraged to review Bergström’s work for themathematical details of the model. In brief, the kinematics ofthe TNM consists of three molecular networks working inparallel, see Figure 1.

Fappl=FFth

Figure 1 Rheological equivalent of the Three Network Model. Thedeveloper suggest for Network A to be stiffer and yield earlier than

network B. That is: A > Bi > Bf, and A < B

The TNM model requires a fairly extensive set of the materialparameters, which are listed in Table 1. The state variablesthat are used by the TNM are summarized in Table 2.

Table 1 Material parameters used by the Three Network Model

Index Symbol Unit Description1 A MPa Shear modulus of network A2 T Temperature factor3 L - Locking stretch4 MPa Bulk modulus5 A MPa Flow resistance of network A6 a - Pressure dependence of flow7 mA - Stress expoenential of network A8 n - Temperature exponential9 Bi MPa Initial shear modulus of network B10 Bf MPa Final shear modulus of netowkr B11 - Evolution rate of B

12 B MPa Flow resistance of network B13 mB - Stress exponential of network B

14 C MPa Shear modulus of network C15 q - Relative contribution of I2 of network C16 T-1 Thermal expansion coefficient17 0 T Thermal expansion reference

Table 2 State variables used by the Three Network model

Index State Variable Name1 Viscoelastic strain magnitude2 Viscoelastic strain magnitude3 Chain strain4 Failure flag

5-13 Viscoelastic deformation gradient FvA

14-22 Plastic deformation gradient FvB

23 Shear modulus of network B:B

The material parameters for a large number of PTFE compounds,shown in Table 3, were determined by means of an optimizationprogram [14] based on the Nelder-Mead method. The programtakes experimental data for a large number of testingconditions and determines the best set of parameters.

3. Experimental Program

The tests conducted at room temperature for each materialwere: a) Uniaxial tension to failure at different strainrates, b) Uniaxial compression at different strain rates, c)Saw-tooth strain amplitude relaxation, d) Stepped strainamplitude relaxation with different schedules.

Table 3 Compounds Evaluated for this Study

Property Test ConditionsStanda

rdUnit

PTFE Compound

A B C D E

Specificgravity

23 CASTMD792

g/cm3 2.16 2.08 2.01 3.07 2.31

Tensilestress at

23 C ASTM MPa 38 23 24 29 22

break D4894

Tensileelongationat break

23 CASTMD4894

% 350 215 260 280 175

Shore D 23 CASTMD2240

Shore D 58 66 61 64

Deformationunder load

23 C – 24 hr 13.8MPa

ASTMD621

% 9.7 3.7 4.0 7.2

Creep23 C – 24 hr 13.8

MPa – 1.5 hrASTMD621

% 5.6 2.2 2.7 4.8

Coefficientof LinearExpansion

-75 C to +25 C

ASTME831

mm/mm/K

1E-4 9E-5 1E-4 1E-4

+15 C to +25 C 2E-4 2E-4 3E-4 2E-4

+25 C to +125 C 1E-4 1E-4 2E-4 1E-4

Compounding material Virgin CarbonCarbonFiber

BronzeMinera

lFiber

Crystallinity 40 – 60%

Uniaxial tension to failure of micro-tension specimen (ASTMD1708) pulled to three different crosshead speeds, i.e. 0.2, 1and 10 mm/sec, which results in three different strain rates,i.e. 0.01, 0.044 and 0.44/sec. Figures 2 shows the typicalengineering stress versus engineering strain response for PTFEcompound type “A” tested in tension and compression. Asexpected and in agreement with what has already reportedelswewhere [15], this type of materials are strongly strainrate sensitive as well as plastically anisotropic [15,16]. Thestrain rates in tension are: 0.01 (green curve), 0.044 (blue)and 0.44/sec (red). Test conducted on ASTM D1708microspecimens skived from bar stock. The compression testswere run on cylindrical specimens 10 mm diameter x 10 mmheight at two different strain rates, i.e. -0.1 (red curve)and -1/sec (blue)

a) Monotonic tension to failure atdifferent strain rates

b) Monotonic tension to failureshowing the lower strain range,

i.e. < 60%

c) Very low strain range, i.e. <10%, in monotonic tension tests

d) Monotonic compression tests atdifferent strain rates

e) Direct comparison of the completemonotonic tension and compression

curves

f) Low strain, i.e. < 50%,comparison of the monotonic

tension and compression curvesFigure 2 Tension and compression tests run at room

temperature on compound A.

Relaxation test - The different relaxation tests seek to reveal the viscoplastic response of the material when

subjected bo different variations of strain. Figures 8 presents a summary of the resulting engineering stress-strain curves and engineering stress versus time for different variations of engineering strain versus time for compound A tested at room temperature.

Figure 8 Relaxation tests on compound A at room temperaturefollowing three different schedules. The figures show from

left to right, for each row, variation of strain as a functionof time, variation of stress as a function of time, and

resulting engineering stress-strain curve. These tests wererun on micro-tensile specimens.

It needs to be pointed out that the experimental tension test data was obtained using crosshead displacement and micro-tensile specimens. That means that the actual strain in the tension test specimen is inhomogenous and the strain in the gauge section is higher than the recorded experimental strain.

To overcome this shortcoming the model calibration is performed in a two step process, first the recorded experimental tension strain is converted to the approximate

strain in the gauge section. To a first order, the strain in the gauge section is approximately 1.35 times the strain basedon the crosshead displacement; Figure 9 shows comparisons of the uncorrected and corrected data. This data is, then, used for an initial calibration of the material model. The initial calibration is refined by performing a reverse FE calibration using the exact experimental setup used in the experiments. Itshould be pointed out that both calibrations are performed using Mcalibration [14].

(a) (b)Figure 9 Comparison of a predicted engineering stress-strain curvefor compound A at room temperature using a one element Mcalibrationand a full blown finite element, i.e. ABAQUS, model. (a) uncorrected

(b) corrected data.

The calibration on compound A indicated that more weight should be given to the monotonic and cyclic compression tests results during the material calibration phase.Cyclic compression experiments at different strain rates were run for all the other compounds. Figure 10 shows the results for cyclic compression at different rates for all the other compounds.

Compound B Compound C

Compound D Compound EFigure 10 True stress-strain curves for the cyclic compression

tests run for different compounds.Using all the experimental data enable us to obtain the calibration constants for all the compounds for room temperature response. The values are shows in Table 4.

Table 4 Constants for the Three Network Model for compounds A – Efor loading at room temperature

A B C D EMM 11 11 11 11 11

ODE 0 0 0 0 0

JAC 0 0 0 0 0

ERRM 0 0 0 2 0

TWOD_S 0 0 0 0 0

VER 1 1 1 1 1

B VTIM

E 0 0 0 0 0 VELE

M 0 0 0 0 0VINT 0 0 0 0 0

ORIENT 0 0 0 0 0

NPROP 33 33 33 33 33

NHIST 23 23 23 23 23

GMU 1 1 1 1 1

GKAPPA 500 500 500 500 500

FAILT 0 0 0 0 0

FAILV 0 0 0 0 0

muA 120312.477

380.958

179.092

239.693

thetaHat 999 9E+09 9E+09

9.00E+09 9E+09

lambdaL

5.47811

5.47277

5.46993

5.35512

5.10822

kappa 1000 1000 1000

1746.6 1000

tauHatA

5.84853

6.1967

5.41317

5.95739

2.38408

a 0.5

0.328163

0.328163

0.650195

0.648459

mA

6.80214 10

10.0029

14.0027

18.9125

n 0 0 0 0 0

muBi30.2295

69.5638

108.298

69.9119

218.278

muBf

10.7021

118.224

69.1923

25.2596

58.1019

bet 7.89 34.23 37.80 27.00 75.73

a 834 97 58 59 38 tauHat

B8.92975

10.5829

9.87237

6.50335

4.54384

mB

7.90621 10

12.7002

26.2935

17.3012

muC

4.27446

13.5076

10.577

5.16595

7.85424

q 0 0 0 0 0

alpha 0 0 0 0 0

theta0 293 293 293 293 293

4. Validation

The validation of the numerical model consists of two steps. Comparing the actual experimental data for the simple deformation modes with the predictions of the model for the same loading conditions and using the results of an experimentwith a more complex state of stress and strains with the FE results for this type of problem. Figures 11 shows comparisonsbetween experimental results and predicted values using the TNM for compound A. Figure 12 does the same for compound C.

1. Cyclic tension 2. Short term relaxation 3. Long term relaxation

4. Monotonic tension 5. Monotonic compression (-1.0/sec)

6. Monotonic compression(-0.1/sec)

Figure 11 – Comparison between experiments and modelprediction for different tests of compound A at room

temperature: a) Cyclic tension, b) Short term relaxation, c)Long term relaxation, d) Monotonic tension (0.1/sec), e)

Monotonic compression (-1.0/sec) and f) Monotonic compression(-0.1/sec)

(a) Cyclic compression (b) Long term relaxation

Figure 12 Comparisons between test and numerical simulation for compound Ctested at room temperature: a) Cyclic compression test, at two different

rates, i.e. -0.01 and -0.1/sec and a long term relaxation test for compoundC, b) Long term compressive relaxation.

In order to further verify the accuracy of the material models, a cyclic indentation test was implemented to verify the accuracy of the calibrated constants. The test consisted of running a cyclic indentation on a 40 mm diameter x 30 mm height cylinder of the compound under study. The cylinder was mounted on a rigid base and indented with a polished steel ball of 12.7 mm diameter. The cyclic indentation was run understroke control but between fixed load limits, and consisted of10 cycles between -800 N and -100 N, followed by an additional10 cycles between -1600 N and -100 N. The load and displacement of the indentor were recorded for each load cycle.

This procedure was repeated, using new specimens, for each compound at three different loading rates. The lower loading rates, i.e. 0.01 mm/sec and 1.0 mm/sec were the same for all the compounds. The fastest loading rates varied due to some limitations of the testing equipment; it was equal to 10 mm/min for compound A and equal to 6 mm/min for all the other compounds. Figure 13 shows this type of results for compoundsA, C, D and E.

Compound A Compound C

Compound D Compound E

Figure 13 Cyclic indentation tests under stroke control andbetween fixed load limits, i.e. 10 cycles between -100 N and -

800 N and 10 cycles between -100 N and -1600 N, at threedifferent indentation rates and room temperature for

compounds A, C, D and E

The second step in our validation process involved comparing the results of the indentation with numerical prediction usingFE. All the analyses were run using the implicit solver of ABAQUS Version 6.11 [1]. A simulation was run using the widelyused elastic - isotropic hardening plastic material model (EP), the results are shown in Figure 14.

Figure 14 Compressive force versus indentation depth tests runat different compression rates: 0.01 mm/min (green curve), 1.0mm/min (blue) and 10 mm/min (red). The dashed red line with

the red circles indicate the result of the numerical analysisusing the traditional, isotropic plasticity material model.

The insert shows the components of the numerical model and anactual specimen.

Although the EP model appears to reproduce the fast loading indentation test accurately there are several problems with this model. The main one, perhaps, is that the ten load cyclesare supperimposed on top of each other. This is a significant shortcoming of this model, i.e. the yield surface expands, reflecting hardening of the material with the attending and subsequent unloading/loading taking place in an elastic like behavior.

The indentation test reveals, however, that there is an acculation of plastic deformation with each subsequent compressive loading cycle. This ratchetting has been studied for PTFE’s [17] and shown to be a function of the mean stress and stress amplitude. Moreover, the ratchetting would due to the viscous plastic flow and hysteretic behavior of the material, which is also responsible for extrussion of PTFE seal through the e-gap. There is obviously a need for a betterway to model this effect.

Figure 15 shows the result of applying the Three Network Modelto the indentation problem for two loading rates, i.e. 0.01 mm/min and 10 mm/min, in compound A. It is clear than this model is better suited to describing the cyclic response of the material.

Figure 15 Compressive force versus indentation depth tests oncompound A. Dashed lines are the experimental results, solidlines are the numerical results of using the Three NetworkModel. Red lines are for the 10 mm/min load case, the green

line is for 0.01 mm/min.

The isotropic plasticity model is not able to capture the different yielding that these materials show in tension or compression. It should be also pointed out that the Drucker-Prager model, in theory capable to accounting for the plastic anisotropy, has been shown not to be able to reproduce the unloading response under compressive loading. This material model, morever, requires more extensive, complicated and costly testing programs.

5. Implementation

In order to demonstrate the advantages of using the Three Network material model and the cylic indentation experimental

approach to verify and help calibrate the material model, two actual sealing problems are shown here: a)

6. References

[1] ABAQUS Version 6.11, 2011, Dassault Systèmes.

[2] Arruda, E. C., and Boyce, M. C., . A three-dimensionalconstitutive model for the large stretch behavior ofrubber elastic materials. J. Mech. Phys. Solids.,41(2):389{412, 1993.

[3] Bergström, J.S., Boyce, M.C., 1998. Constitutivemodeling of the large strain time-dependent behavior ofelastomers. J. Mech. Phys. Solids, Vol. 46, 931–954.

[4] Bergström, J.S., Boyce, M.C., 2000. Large strain time-dependent behavior of filled elastomers. Mech. Mater.,Vol. 32, 620–644.

[5] Bergström, J.S., Boyce, M.C., 2001. Constitutivemodeling of the time-dependent and cyclic loading ofelastomers and application to soft biological tissues.Mech. Mater. Vol. 33, 523–530.

[6] Bergström, J.S., Kurtz, S.M., Rimnac, C.M., Edidin,A.A., 2002. Constitutive modeling of ultra-high molecularweight polyethylene under large-deformation and cyclicloading conditions. Biomaterials, Vol. 23, 2329–2343.

[7] Bergström, J.S., Rimnac, C.M., Kurtz, S.M., 2003.Prediction of multiaxial mechanical behavior forconventional and highly crosslinked UHMWPE using a hybridconstitutive model. Biomaterials, Vol. 24, 1365–1380.

[8] Bergström, J.S., Hilbert Jr., L. B., 2005, Aconstitutive model for predicting the large deformationthermomechanical behavior of fluoropolymers, Mechanics ofMaterials, Vol. 37, 899-913.

[9] Blanchet, T.A., 1997. Handbook of Thermoplastics. MarcelDekker, Inc.

[10] Ebnesajjad, S., 2000. Fluoroplastics. Non-Melt Processible Fluroplastics, vol. 1. Plastics Design Library.

[11] Khan, A., Zhang, H., 2001. Finite deformation of a polymer: experiments and modeling. Int. J. Plast., Vol. 17, 1167–1188

[12] Kletschkowski, T., Schomburg, U., Bertram, A., 2002. Endochronic viscoplastic material models for filled PTFE.Mech. Mater. 34, 795–808.

[13] Kletschkowski, T., Schomburg, U., Subramanian, S., 2000. Experimental investigations on the plastic memory effect of PTFE compounds. J. Mater. Process. Manuf. Sci.,Vol. 9, 113–130

[14] MCalibration – Version: 1.7.2 – Veryst Engineering, LLC, Needham, MA 02494, USA.

[15] Rae, P.J., Brown, E. N., 2005, The properties of ply(tetrafluoroethylene) (PTFE) in tension, Polymer, Vol.46, 8128-8140.

[16] Rae, P. J. and Dattelbaum, D.M., 2004, The properties of poly (tetrafluoroethylene) (PTFE) in compression, Polymer, Vol. 45, 7615-7625.

[17] Xu Chen and Shucai Hui, 2005, Ratchetting behavior of PTFE under cyclic compression, Polymer Testing, Vol 24, 829-833.