16 Rubber & Plastics News * July 29 1996

TECH NICiU.

FEA support testing for elastomermodeling

TECHNICAL NUTE000KElfiteil by HaraW Herzlich

By Abraham PannikottuJoe Seller

and Jerry J. LeydenAkron flutter DevelopeienlLaboratory Inc.

Secondoftwo partsAll the major finite element analysis

codes like Ansys. Abaqus, MSC/Nastran, Cosmos/Mand Marc need Mooney-Rivlin constantsor Ogdenconstantsis inputs to run a non-linearanalysis.

Forerubber-like material, homogeneousdeformation modessufficientlydetermine the material constants.TheFEA codesaccept data from the following deformationmodes:

* Uniaxial tension Fig. 1* tltiiaxiol cernlpressiorl Fig. 21* ‘loner tension Fig. :1Note: The wide plonar s/sear sonspie

is physrcally constrained to not pull-inai t/r, edgesby i/se damps, so the sample will thin out hot out draw-in duringf/i,, -/oogo/uor. ‘l’!,,.x ansi,, of’ it’s/lug toll!p/ru.- tire ,;pr,. tn,,’u ‘0 Cr ml to, s/nor titer/i’

up to 100-percent eloogeiion.* Eqoi-biaxial tensionFig- 5* VolumetriccompressionFig. 6Thesemodesare shownin Fig. 6. The

most commonly performed exporimeertsare uniaxial tension,isnioxial corsipreasion. planartension and equi-bisxialtension. Combination of data fromthese four types of tests will result ingood characterizationof the behnviorofthe elastomer.

The superpositionof a tensileor compressivehydrostatic stresson a loaded,folly incompressibleolastic body resultsin different stresses,but doesnotchaugethe deformation. Fig. 7 showsthat different loading conditions areequivalent in their deformations,andthereforeoreequivalent in tests.

* Uniaxial tension = Equi-hiaxinl* compression

* Uniaxial compression= Equi-biaxialtensionIt may be difficult to satisfythis condition becstsseof the experimental difficulty in perfonninga "true"uniaxiel compression.So it’s importantto performthe equi-biaxial testfor evaluating elastomerparts in compressioa

Fig. 1. lJnisxisl tension.

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Transd,ter

Measurementsweremadein uniaxialtension Fig. I, uniaxial compressionFig. 2, plsrs,nr tension Fig. 3, equi-biaxial Fig. 4 and volumetric compression Fig. 5.

The uniaxiel tension and planersheer tests were performed using aMonsanto T-2000 screw type mechinewith a MonsantoE5042 laserextensometer.Theuse of a laser extensometertomeasurestrain, rather than crossheaddisplacement,eliminates measurement

The authors

JersyJ. LeydenservesaspresidentofAkron Rubber Development Laboratory

Abraham Pannikottu serves asARDL’s managerof predictivetesting.

.1 ois’ph Seiler uvenrkts isnicijinin Altlljs l’re-slicl,iv,’ ‘l’n’sl.rig Department.

Flg. 4. Equi-blaxlaltension.

Inc.

* Measursnsst TeapsrsairecRnerrr TerapetstersSpecimenSize: i.e irL 55.0 in. xO.Oiia. ibick

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Fig. 5. Schematicillustrstionsof deformation modes.

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* Executive summaryComputer.aidedengineering refers to the useof computersto perform de

sign calculations for determining an optimum shapeand size for a variety ofengineering applications.This modem conceptof engineeringmanagementhas led to importent advancesin the design and productionof componentsusadis’ aerospace,automotive,electronicsandother industriesthroughouttheworld.

* CAE enablesan engineerto test designideas by simulatingthe finction of* the part on the computer. Finite element analysisis one of these computer

simulation techniqueswhich is the most accurate,versatileand comprehensive techniquefor solving complex design problems.FEA permits the analysisof these complexstructureswithout the necessityof developingand applyingcomplexequations.

FEA programfor non4inearstressanalysisof elastomersis performed byutilizing two materialmodels:

* Mooney-Rlvlin model* OgdenmodalThe Moooey.Rivlinmodel is the most widely usedmodel for elastomeranal

ysis. The basicproblem feting the design engineeris how to obtainthe mote.rial coefficientsneededto use thesetwo modelsin FEA. At, expected,the effectivenessof design analysis is directly related to the quality of the materialinput materialcoefficients.* Akron RubberDevelopmentLaboratoryInc. hasdevelopeda reliablehistoryof standardproceduresfor determinationof thesecoefficientsfrom experimen’tal test d,sta.This paperwill discussvarioustestingtechniquesusedfor developing elnstomerniateri,si conelsente.Also, the Intent of this paper Is to showhow aging or serviceconditions can be incorporatedto obtain material coeflidentsfor elsatomerparts.

Finn,,,’ tensi,,n Plonr, ri’onnr,ren’tHou

The tensile end compressioncasesofthe uniaxial ar,dequi-biaxial modesareindependentfrom eachother. ThereFore, uniexinl tension sod uniaxial conspreasionprovide independentdata.

The following proceduresummarizesthe steps neededto calculstathe material coefficients:I. Run uninxinl tension, uniaxinl conspression, planar shear and biaxial tension tests for the testmateriel.Performthe testsin slow speedto achieve aquasi-staticcondition.2. Calculatethe stress-straindate.3. Fur Mooney-Rivlin two-point model,perform a linear regressionanalysisonthe experimentalstress’straindata. Todeterminecoefficients for five-pointmodel nod Ogdenmodel, perform anon-linear regressionanalysison theexperimentalstress-straindata. Thenumber of coefficientsneededto fit the

t,x1soriir,erit-s, I i’rrrvo. stipends on thesurioetnt ,,r ,,ccLir,rcy chaired Isy lii,’ riser.

ExperimentalThe elastomermaterials evaluated

were aili i,,:. I I’VMQ. fluoroeltisIFKM and hydrogenatednitrile rubberHN’BR. Theserubber formulationswere specifically compoundedfor gasketapplications.The formulationsarespecified in Tables1-3,

All three compoundswere aged inthree different fluids for 168 hoursat150’ C to seethe changein stress-strain datn. The three fluids includedIRM-903, 5W-In engine oil andautomatictransmissionfluid. All messurementewereconductedat room temperature.

Table I. Hydrogenated nltrlle rubberHNBR.

Fig. 5-Volumetric compressIon.

eiiss.,rnnr I

Fig. 3. Planar shear.IngredIent phr

ZetpoI2OlO’ 100.0N-774 45MPIaSlHaIl TOIM 5.0KsdoxOIlCZnO 5.0Naugard 445 15Vanes ZMTI 1.0DynamsrPPA-790 1.0SarelSR-517 5.0Vul-Cup4OKE 5.0* leonchemicals

* Ueuurms.atTerapsrsnsraBeenTemperature* SpsckuenSize. ASTM Diet’ Darnbbsll* Teeflate:ella perlsOanesa

Fig. 2. tlniaxial compression.

M,eneneniT,ep..nWC ses’rnewts,,sj kJI-..se* 5 ala 5Ca

- ns,thenC,,ered,,eh.Jerltdi,eni.,cfriSKli.5s.ll

c-Ea,t M5ilJl*; K* 515 M ipd.e,,’i 555Tess asspa 555’.

Table II. Fluoroelastomer FKM.

Ingredient phrFE56400 100.0MT flackN990 30.0MgOMaIlteD 3.0

CaOH5 6.03M Sped,ily Fleerepetymers Oaparlrssent

M,asermieasTerspersturcBoonTssiprrshirsSpecimenShe:ASIM CompressionSeeBoomTia Bass:0.2 its, perMisut

Table Ill, SIlicone PVMQ.

* MmaursnseotTemperature:Room Tenpesarure* SpecinseShe:3.00 In. x 0.5 Li. x 0.06 is. dick* TessRate0.2 sr. per sfinuea

IngredIentsDow Corning

24092-V5Third generationSiliconeCatayzed with STI V

ow, CoringSTt

Rubher & PlasticsNews * July 29, 1996 1 7

TECHNICAL

error from slippageat thegrips.The uniaxial compressionteet was

performedon an MTS 831.20ElastomerTest System.The compressiontest waspertbrmed on cylindrical testspecimens

Fig. 7. SchematIc illustrations of equivalent deformation modes through superposition of hydrostatic stress.

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Fig. 10. Equi-blaxialtension.Silicone.

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lubricatedwitts silicone ii I, ‘VIse cqui-hiaxial tension was perfoncied on a Iwemote Biaxial Stretcher.All tests wereperformed at room temperatureat astrain rateof 0.2inchesper minute.

Results and discussionA comparisonof the relativefit of lin

ear model, Mooney-Rivlin models andOgdenmodel for tensilebehaviorof silicone rubber is shownin Fig. SIt isclear that the linear equation followsthe elestomericbehavior up to 1O-per-centstrain level, TheMooney-Rivlinequationsarea good fit up to a 12S-percent strain level. The Ogdenmodelshowedthe best fit with the measuredtensile data over the full exteusioasrange.

The pure shearbehavior of a planarspecimenis comparedin Fig. 9. The linearequation showedgood fit at low

I stniisss.Muonoy-Rivlin end Ogdon models showedbettor lit witis the measuredengineering shearstressvaluesoverthe full strain range.

The compressionbehaviorof aged silicone rubber is compareduaing enequi.biaxisl test shown in Fig. 10. Thelinear equationshowsan aeceptablefitonly for very low strain values. TheMooney-liivlin equation yields a verygood fit up to 40-percentstrain. But theOgden model showed the best fit overthe full strainrange.

The compressionbehavior of imaged

and aged silicone rubber is shown inFig. 1. This plot illustrates the importance of aging studies for modelingelaatomer components used in oil any1-ronnients. Fig. 12 shows the compression behavior of FICM lo 5W-3O engineoil, and Fig: 13 shows the compressiondeflectioa behavior of HNI3R inautomatic transmission fluid.

ConclusionThetestmethodologyfor developing

the material constantsfor Mooney-Thy-SeeFEAt,page 18

Fig. 8. tiniaxial tension. SilIcone.

Fig. ii. Equl-biaxial tension. Silicone. Aged in M 903 for 168 hours.

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‘18 Rubber&PlaslicsNews* July29, 1996

a TECHNICaL

FEAContinoedIrenepage17un and Ogden material models issheewo from the viewpoint of a design!test engineer. Aisro domonstnek’dis how

Inn uoS ‘gill5 te,cl,oeie1eio,oscss list Ice,, sEe-chilly ,epplie’d licr olstoeie,ing,ie,ste,-i,, I dicta which can be usedfor modelingelasbmerpartsin service.

The Ogdenmodel shows the best experimentaldata strain level up to 100

percent. Broth the linoor end non-linnarequations showedreossonablecnrrelostion at low straiua up to 10 percent.Standardizing test parametersend testspeed is very important for obtainingreproducible data.

Before sloing a cocoa,plete I"lA on theSort, it, 5ens’ lost elste-e’ssoerylao verify the

oiools,s,e.,.sl lessee1,1 iii Se iii 0110 geeoeiOe°teic:eSl001pe’ sooe:l, Sep. Ieee l.e’iesg eel’

thnough tl,e preproceidsssr.lncssrpsorsstiesgfluid-aging studies in the FEA supporttesting is important for obtainingmeaningful material coefficients.

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References

L7. A. 0. isaac.A. 2. save.AppI. Pelyoa. Sd. 19,2:119 01975.15. I.. Mullies. .2. AppI. Pelye. Si. 2.217 19501.‘a, op. lieleesni,,. Ralel,erehs-m. ‘leebasel. 48. 24e

115121.250, NIl tiler ‘I’ Slicesli-is. A Nosie_ei, I’os’oossi,, lootMoe-ho,s..i SI,.’ OOooi,ie-e Ilisisissee. A ee,.’e,i,000e e’Ie..ee,n.eSeeLy,Cloieeoe,o. eelSSI. 1 C 15,1cc lace.15 8,,,. l.oo,ool,eo,Pi’ei,’,, A12$. ri,?, 050720.22. 00.8. Itirliro. ‘Forty Veils ,,rN,,e-lAeeoer5,,,,cue Mpchaairo- rn’s. ix iooe.l. Coego’ees en Itiseolsgy, Mexico 11954.23. M. Maaney..1. AppI. Icily,. Is,58259401

24. sw, hole,,. l"ssr. It, Sue, I ,eisose‘eoN ‘‘ci s’s A125, 5117 100iflS,25. S.T.J. l’ceg, °Nen-liecor Mulliaxial Fisite I,,roreesuenlevsetigatios or Soslido lerepellaeto,"APREL TR-S5-Ose 1955.58. ftT.sJ. Peng ned 00. W Leatel. 2. AppI. Phy,. 45.30404 119721.27. 057.1 O’o’e05eio,erl II. 10. 0 a,seoie-i, .0. AIsleS. ‘ito. ‘Ii.1r,110s I 01*750.15. KS’ Vol sos,,, iii. lee. V. 0,,,,,, 1,1.-I A,,5l. lesso,‘‘.5, 0!11571l’.1517

Is,. I’,-,’ lo,oor’l’eseoe 0’’ epistle, S s.,’ .115Ill-i’ll.30. N. flasher "0,1 Ii, Senill,. "Appli,’ol it,’gr,-o,si toeAe,oolyais." Juice Wits2& So,,.. Ni-asYolk Ills.31. Abaquo Ijaer’s Manual. }iiIthitt, Karlasea andSoreeeee,Inc., 5989.

Fig. 13. Equi-biaxiai tension. HNBR. Aged in automatic transmission fluid for 166hours.

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