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Biomaterids 18 (1997) 1659-1663@ 1998 Published by Elsevier Science Limited

Printed in Great Britain. All rights reservedPII : SO142-9612 (97) 00124-5 014%9612/98/519.00

Validation of a small punch testingtechnique to characterize themechanical behaviour of ultra-high-molecular-weight polyethyleneSteven M. Kurtz, Jude R. Foulds, Charles W. Jewett, Sanjeev Srivastavand Avram A. Edidin*Failure Analysis Associates, Inc., 2300 Chestnut Street, Suite 150, Philadelphia, PA 19103, USA; Osteonics, R&DCorporate, Allendale, NJ, USA

The small punch or miniaturized disc bend test has been used successfully to characterize the ductilityand fracture resistance of metals and ceramics with specimens measuring 0.5 mm in thickness. Thisstudy was performed to demonstrate the feasibility of performing small punch tests on implant gradeultra-high-molecular-weight polyethylene (UHMWPE). Large-deformation finite element simulationswere developed and validated to explore the hypothesis that the macroscopic constitutive behaviour ofUHMWPE may be inferred from a miniature specimen testing technique which can be used to charac-terize the ductility and work to failure for UHMWPE. The load-displacement curve was insensitive tocyclic preconditioning of the test specimen and only mildly sensitive to the loading rate. Furthermore,the initial slope of the small punch load-displacement curve was used to determine the elasticmodulus of the UHMWPE with the help of the inverse finite element method. The ultimate goal of thisresearch is to develop the capability to perform local measurements of material tensile and staticfracture properties in as-manufactured, as-sterilized and as-retrieved UHMWPE components. 0 1998Published by Elsevier Science Limited. All rights reservedKeywords: Ultra-high-molecular-weight polyethylene, mechanical properties, small punch test, finiteelement analysisReceived 12 May 1997; accepted 30 June

For the past decade, the small punch or miniaturizeddisc bend test has been used successfully tocharacterize the duct.ility and fracture resistance ofmetals and ceramics with specimens measuring only0.5 mm in thickness-3. Development of the smallpunch test for metall:ic materials has been driven bythe need to measure in-service degradation ofmechanical properties with a limited volume ofavailable material. By virtue of its small specimen size,the test also provides a convenient means of character-izing material at spec:ific locations in a component orstructure. By concurrently performing small punchtests and static fmcture tests, researchers haveempirically correlated small punch mechanicalbehaviour with fracture toughness in metal andceramic specimens (Xi, for brittle materials or /IC orductile materials23). The primary disadvantage of thisempirical approach is that a large volume of bulktensile and fracture data is required for a given materialin order to make reliable engineering predictions fromsmall punch test resu1t.s.Correspondence to Dr S. .Kurtz.Tel: 001 215 751 1661; fax: 001 215 7510660; e-mail: [email protected]

1997

An alternate interpretation of the small punch test,developed by Foulds et a1.l uses the inverse finiteelement method to infer conventional tensile stress-strain properties based upon optimal matching of theexperimental and simulated small punch load-displacement curve. The as-determined tensile stress-strain behaviour is then used to compute, by the finiteelement method, the local strain energy densityaccumulated to initiate cracking in the small punchspecimen. This critical strain energy density,considered a material fracture initiation criterion, isanalytically (by simulation) applied to the standardplane strain compact tension specimen crack tip toobtain the conventional fracture toughness, JrC (andI&). Tensile and fracture properties measured usingthis approach have been shown to be reasonablyaccurate for a wide range of metals, but have yet to beexplored for polymers, such as ultra-high-molecular-weight polyethylene (UHMWPE).Although UHMWPE has been used successfully intotal joint replacements during the last three decades,there is increasing concern in the orthopaediccommunity that gamma radiation sterilization malimit the long-term wear performance of the polymer4 -!I.As gamma-irradiated UHMWPE components age on1659 Biomaterials 1997, Vol. 18 No. 24


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1660 Small punch testing of UHMWPE: S. M. Kurtz et al.

the shelf or in the body, the physical properties of thepolymer (such as density and crystallinity) degradeinhomogenously with depth6-a. The density ofUHMWPE has been related to mechanical properties(such as elastic modulus or yield stress)g and to theshape of the true stress-strain curve in uniaxialtension by empirical relationships that were obtainedfrom bulk mechanical tests. Therefore, it has beenpossible to infer that retrieved components, for whichone can measure inhomogeneous density distributionsthrough the thickness, also have inhomogeneousmechanical properties through the thickness.Miniature specimen testing provides an opportunityto directly measure properties in inhomogeneousUHMWPE components. For example, Collier et al5measured the ultimate elongation and ultimate tensilestrength of UHMWPE using miniature tensilespecimens (0.2 mm thick) manufactured parallel to thesurface of shelf-aged tibia1 trays and bar stock material.An order of magnitude reduction in ductility wasobserved between specimens prepared from a degradedsubsurface region (characterized by a white band upontransverse microtoming) and specimens prepared fromundegraded stock material. However, it remainsunclear how properties measured from smallspecimens of UHMWPE may be effectively comparedwith macroscopic or bulk material properties.Consequently, the primary goal of the present studywas to demonstrate the feasibility of performing smallpunch tests on specimens manufactured from implantgrade UHMWPE. The secondary objective was toquantify the sensitivity of the small punch mechanicalbehaviour to changes in test conditions, such asloading rate. Large-deformation finite elementsimulations were developed and validated to explorethe hypothesis that the macroscopic constitutivebehaviour of UHMWPE may be inferred frommicromechanical tests, Ultimately, the small punchtesting technique in conjunction with the inverse finiteelement method may provide local, accurate estimatesof both conventionally measured tensile and staticfracture properties for UHMWPE components,

MATERIALS AND METHODSExperimentalDisc-shaped small punch specimens of 6.4mmdiameter and 0.5mm thickness were machined from a64-mm-thick sheet of compression-mouldedGUR4120HP resin (PolyHi Solidur, Fort Wayne, IN,USA), having a reported molecular weight of 2.0 to 2.5million g mol-I. Small punch specimens were carefullymachined from the stock material to avoid phasechanges near the surface. Characterization of theUHMWPE physical properties using the densitygradient column technique (DGC) and differentialscanning calorimetry (DSC) revealed that the densityof the virgin material was 0.934gcme3 and that thecrystallinity was 51%. No traces of oxidation wereobserved at the centre of the machined specimen, asdetermined by Fourier transform infrared spectroscopy(FTIR). Since gamma sterilization and degradationwere expected to substantially reduce the ductility,virgin material was chosen for this study to provide

Alignment AlignmentAsseebly Pin 3.8 mm Pin Assembly

Tdia.

tBolt

t -_)I It t

Guide

2.5 mm --)dia. I/-L

t Specimen:6.4 mm dia. x 0.5 mm thick

Figure 1 Schematic of the disc-shaped small punchspecimen, the testing guide and die, and the hemisphericalhead punch.

the most-ductile small punch testing scenario forimplant grade UHMWPE.The disc-shaped specimens were tested in bendingby indentation with a custom-built, hemisphericalhead punch, as described previously (Figure ~)l.Specimens were tested at constant punch displacementrates of 0.25 mm min-l (number of specimens, R = l),0.5 mm min-l (n = 5), 2.5mmmiri (n = 4) and5.0 mm min-l (n = 4). During the testing, the punchload and displacement were digitally recorded, whilethe back (bulged) surface of the specimen wasvideotaped via a borescope. Selected specimens weregold-coated (2OOA thickness) and examined at x18and higher magnifications using a scanning electronmicroscope at 10 kV to characterize the specimenbefore and after testing.Initial tests showed that the linear (elastic) portion ofthe load-displacement curve occurred at displacementsof less than 0.064mm and at loads of less than 3N.Consequently, four additional tests were performed at arate of 0.5 mmmin- using a low range (4.5N) on an89 N capacity load cell. An extensometer was attached tothe device for measurement of displacement (rather thanmachine actuator displacement, i.e. stroke, used earlier)to more accurately characterize the initial, linear portionof the load-displacement curve. During these tests, thesamples were cyclically loaded 10 times in a range fromapproximately 0.2 to 2.7 N to demonstrate the stabiliza-tion (saturation) of the slope of the initial linear portionof the curve. After cyclic preconditioning, the range ofthe load cell was increased to 89 N and the samples weretested to failure at a rate of 0.5 mm min-I. The surface ofthe specimen during these low-amplitude cyclic loadingtests was not videotaped.The effect of changing test conditions (e.g. loadingrate, cyclic preconditioning) on features of the load-displacement curve, such as mean peak load, wasdetermined by two-sample t-tests assuming unequalvariance. A P-value of 0.05 was used for statisticalsignificance.AnalyticalTwo-dimensional (axisymmetric) finite element modelswere developed to aid in interpreting the experimental

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Small punch testing of UHMWPE: S. M . Kurtz et a/. 1661small punch tests results. The large-deformationstructural problem was solved with NIKE2D (LawrenceLivermore National Laboratory, Livermore, CA, USA)using isotropic elasticity and rate-independentisotropic plasticity to model the mechanical responseof UHMWPE to failure, based on previous bulkmechanical testing*, The plasticity model in NIKEBDwas validated for UHMWPE by simulating a tensiontest to failure, which for bulk GUR4120 specimenswere previously shown to occur at nominal(engineering) strains of 421%11.The axisymmetric: finite element model of thesmall punch test consisted of 1602 four-nodedquadrilateral elements. Sliding contact between thespecimen, punch head, punch guide and receivingdie was modelled with slidelines using the penaltystiffness method12 and a coefficient of friction of 0.1was used between the UHMWPE and the polishedcontacting steel surfaces13. The polyethylenespecimen was modelled with 12 elements throughthe thickness, and zoning studies were performed toverify spatial and temporal convergence of thecontact solutions.The resultant load1 acting on the punch head, inconjunction with the prescribed displacement, wasused to compile a load-displacement curve for thesmall punch simulation. The elastic modulus for thesimulated UHMWPE specimen was then parametricallyvaried between 255 and 102lMPa. For each of theparametric simulations, the initial slope of the load-displacement curve, 1:, was computed up to O.O64mm,which during preliminary experiments was observedto correspond with linear elastic behaviour. A linearleast-squares correlation was then sought between theinitial stifmess of the simulated load-displacementcurve and elastic modlulus:k=AE (1)

where k is the initial stiffness, A is a constantcoefficient, and E is the elastic modulus.Equation 1 was inverted to predict elastic modulusfor GUR4120 based on the initial stiffness measuredduring the small punch test. During previous bulkmechanical testing of GUR412014, the elastic moduluswas found to be 85l f 33 MPa (six specimens weretested in compression). A two-sample t-test assumingunequal variance wals used to compare the elastic

modulus from the bulk mechanical test with the elasticmodulus predicted by Equation 1.

RESULTSExperimentalThe load-displacement behaviour of the small punchtest specimen displayed distinctive features (Figure z),such as a peak load early during the test, followed by acomparatively long, plastic membrane stretchingphase, analogous to the stretching of a bulk tensilespecimen. The load and displacement at failure, aswell as the energy or work to failure, providedadditional quantitative measures of the specimenductility and fracture resistance (Figure 2). Synchroni-zation of the videotape and load-displacement curvesdemonstrated that the small punch test specimen

90 I,,,,,,,,,,,,,,,,.80 _ UHMWPE

Ultimate Load 81Displacement -60

z 50u$ 40a 30

0 1 2 3 4 5Punch Displacement (mm)Figure 2 Features of a typical load-displacement curve forthe small punch test performed to failure on a UHMWPEspecimen.failed catastrophically at an easily distinguishable,abrupt load-drop point on the load-displacementcurve.Videotapes of the small punch tests further showedthat the specimens underwent easily discerniblechanges in opacity during the test, consistent withphase changes in the crystalline structure of thepolymer during large plastic deformations. Thescanning electron micrographs of tested specimensprovided additional evidence that the specimens weresubjected to reproducible, large-scale plasticdeformations (Figure 3). Micromachining lines wereevident in the flat, as-manufactured specimens andwere homogeneously stretched as the test progressed.However, the machining lines were obliterated duringthe large deformations culminating in specimen failureand probably did not affect the outcome of the smallpunch test.

Figure 3 Scanning electron micrographs of a UHMWPEsmall punch specimen tested to failure (x18). Note theobliteration of machining lines near the summit of thespecimen.Biomatetials 1997, Vol. 18 No. 24


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1662 Small punch testing of UHMWPE: S. M. Kurt z et al.90807060

5 50i 40A 30

2010

00

Rate = 0.5 mm/min

1 2 3 4 5Punch Displacement (mm)Figure 4 Repeatability of the small punch test load-displa-cement curve for UHMWPE. The four repeat tests wereconducted at a rate of 0.5 mm min- on the same day.

Relatively little variation in load-displacementbehaviour was observed during repeated tests of thespecimens at the same punch displacement rate(Figure 4). Mean test results (&one standard deviation)for three testing rates are provided in Table I.Increasing the punch rate significantly increased thepeak and ultimate loads, and decreased the ultimatedisplacement during the tests (P < 0.05). However, theeffects of increasing the loading rate, while statisticallysignificant, were not substantial. A fivefold increase inthe loading rate (from 0.5 to ~.5mmmin-), increasedthe peak load by ll%, increased the ultimate load by9%, and decreased the ultimate displacement by 6%.The work to failure for the small punch specimens wasnot significantly affected by increasing the loading rate(P > 0.05).Approximately 0.04mm of creep deformation wasobserved during the cyclic preconditioning, althoughthe slope of the load-displacement curve remainedrelatively unchanged (Figure 5). After 10 loadingcycles, the average initial slope of the load-displace-ment curve was 61.2 f 4.1 Nmm-. The creep inducedby cyclic preconditioning was approximately 1% ofthe total deformation to failure. Cyclic preconditioningdid not significantly affect the peak load, ultimatedisplacement, ultimate load, or the work to failure(P > 0.05).AnalyticalThe initial linear slope of the simulated load-displace-ment curve up to 0.064mm was linearly correlatedwith the elastic modulus of the material (r2 > 0.99,Figure 6):

k = 0.0742 E (2)

Table 1 Effect of testing rate on small punch test results

UHMWPE2.5 - Rate = 0.5 mmlmin

2.0 -sa 1.5-gJ l.O-

0.5 -

O.OK0 0.02 0.04 0.06 0.08 0.1Punch Displacement (mm)

Figure 5 Load-displacement behaviour of a small punchtest specimen during cyclic preconditioning.

Bulk Testing Results (E=851+33 MPa)

tn 0 200 400 600 800 1000 1200Elastic Modulus (MPa)Figure 6 Elastic modulus versus analytically predictedinitial stiffness (up to displacements of 0.064mm) in thesmall punch load-displacement curve.

where the initial stiffness, k , is in Nmm- when theelastic modulus, E, is in MPa. Equation 2 was invertedto provide elastic modulus as a function of initialstiffness:E = 13.5 k (3)

Based on Equation 3 and the experimentallydetermined initial stiffness of the small punch loaddisplacement curve (i.e. 61.2 f 4.1 Nmm-l), the elasticmodulus for the four tested CUR4120 specimens waspredicted to be 826 f 56MPa. The difference betweenthe elastic modulus predicted by Equation 3 for thesmall punch test and the elastic modulus measuredduring previous bulk mechanical tests was not statisti-cally significant (P > 0.05).

Rate Number of Peak load Ultimate disp. Ultimate load Work to failure(mm min-) tests (NJ (mm) (NJ WJ)0.5 5 60.9 f 1 O 4.63 f 0.06 51.9 f 2.8 207 f 82.5 4 67.4 f 3.0 4.35 f 0.14 56.3 * 2.1 217 + 145.0 4 69.0 f 1.5 4.30 & 0.18 55.6 f 2.7 217 i 10



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Small punch testing of UHMWPE: S. M. Kurtz et a/. 1663

DISCUSSIONThe small punch test is a reproducible miniaturespecimen testing technique which can be used tocharacterize the work to failure and ductility forUHMWPE used in total joint replacements. Theresults of this study demonstrate that the load-displacement curve is insensitive to cyclic precondi-tioning of the test sample and only mildly sensitiveto the loading rate. In addition, the initial slope ofthe small punch load-displacement curve ismeasurable and ma:y be used to predict the elasticmodulus of UHMWPE in conjunction with theinverse finite element method.The mild sensitivity of the small punch test resultsto loading rate was, consistent with previous bulkmechanical testing results. Stojek and Li15 recentlyinvestigated the effect of strain rate on the bulktensile properties of UHMWPE. Researchers observedno statistically significant changes in elastic modulusand yield stress when the strain rate was increasedby an order of magnitude. Although the mechanicalresponse of polymers is well known to be strain ratedependent, it appears that UHMWPE does notexhibit marked strain rate sensitivity at roomtemperature.Small punch test specimens, despite their miniaturesize, deformed consistently and homogeneously up tothe point of catastrophic failure. The 0.5-mm-thicksmall punch specimen was nearly on the same lengthscale as the consolildated UHMWPE resin particles,which typically range in size from 50 to 250mm.However, localized deformation or necking of thespecimen was not observed in video tapes or scanningelectron micrographs, suggesting that the miniaturespecimen deformed homogeneously as a continuumduring testing.The small punch test is a promising tool by which todirectly evaluate UHMWPE mechanical properties inas-sterilized and as-retrieved components. Furtherresearch is needed to demonstrate the reliability andreproducibility of the small punch test followingsterilization and accelerated ageing. The long-termgoal of this research is to develop a miniature specimentesting technique capable of characterizing mechanicalproperties at the ar-ticulating surface of UHMWPEcomponents for direc:t comparison with in vitro andi n v ivo wear performance.

ACKNOWLEDGEMENTSSpecial thanks to J. Moalli, R. Windmiller, D. Crane,L. Pruitt, and S. Valenty for their contributions.Supported by a Research Grant from OsteonicsCorp.

REFERENCES1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

Foulds, J. R., Woytowitz, P. J., Parnell, T. K. and Jewett,C. W., Fracture toughness by small punch testing.J. Testing Eval., 1995, 23, -10.Mao, X., Saito, M. and Takahashi, H., Small punch testto predict ductile fracture toughness JIc and brittlefracture toughness KIc. Scripta Metal Mater., 1987, 25,2481-2485.Mao, X., Shoji, T. and Takahashi, H., Characterizationof fracture behaviour in small punch test by combinedrecrystallization-etch method and rigid plasticanalysis. J. Testing Eva]., 1987, 15, 0-37.Sutula, L.C., Collier, J.P. Saum, K.A. et al ., Impact ofgamma sterilization on clinical performance of polyethy-lene in the hip. Cli n. Or t hop., 1995,319,28+0.Collier, J. P., Sperling, D. K., Currier, J. H. et al ., Impact ofgamma sterilization on clinical performance of polyethy-lene in the knee. J. Arthroplasty 1996,11,377-89.Kurtz, S. M., Rimnac, C. M. and Bartel, D. L., Degrada-tion rate of ultra-high molecular weight polyethylene.J. Or t hop. R es., 1997, 15, 7-61.Bostrom, M.P., Bennett, A. P., Rimnac, C.M. and Wright,T. M., The natural history of ultra-high molecular weightpolyethylene. Clin . Orthop., 1994,309,20-28.Rimnac, C. M., Klein, R. W., Betts, F. and Wright, T. M.,Post-irradiation aging of ultra-high molecular weightpolyethylene. J. Bone Joint Surg., 1994, 76-A, 1052-1056.Kurtz, S. M., Rimnac, C. M., Li, S. and Bartel, D. L., Abilinear material model for ultra-high molecular weightpolyethylene total joint replacements. Trans. 40thORS, 1994, 19, . 289.Kurtz, S. M., Rimnac, C. M., Santner, T. J. and Bartel,D. L., An exponential model for the tensile true stress-strain behavior of as-irradiated and oxidativelydegraded ultra-high molecular weight polyethylene.J. Ort hop. Res., 1996,X4, 755-761.Kurtz, S. M., Jewett, C. W., Moalli, J. E., Vogt, R. M. andEdidin, A.A., The true ultimate stresses and fracturemorphology of ultra-high molecular weight polyethy-lene upon tensile failure. Trans. ASME Bioengineering(Summer), 1997, pp. 57-58.Engelmann, B., NKE2D. a Nonl inear, I mpl ici t , Tw o-Di mensional Fini te Element Code for Soli d Mechanics.Lawrence Livermore National Laboratory ReportUCRL-MA-105413, Livermore, CA 1991.McKellop, H. A. and Clark, I. C., Evolution and evalua-tion of materials-screening machines and joint simula-tors in predicting i n v iva wear phenomena. InFundamental Behavior of Ort hopedic Bi omaterials,ed. P. Ducheyne and G. W. Hastings, 1984, pp. 51-85.Kurtz, S. M., Jewett, C. W., Moalli, J.E. and Edidin,A. A., An elastic-plastic material model for the truestress-strain behavior of ultra-high molecular weightpolyethylene in tension and compression. Trans.ASME Bio engineeri ng (W int er), 1997 36, 311-312.Stojek, M.D. and Li, S., The effect of strain rate on thetensile properties of ultra-high molecular weightpolyethylene. Trans. 21st Sot. Bi omat er., 1995, p. 385.Lykins, M.D. and Evans, M. A., A comparison ofextruded and molded UHMWPE. Trans. 2lst Sot.Biomater, 1995, p. 112.


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