The Relationship BetweenAbutment Taper and

Resistance of CementedCrowns to Dynamic

Loading

H. W. Anseim Wiskott, DMD, MS, MSD'University of GenevaGeneva. Switzerland

lack I. Nicholls, PhD"University of WashingtonSeattle. Washington

Urs C. Beher, DMD, Prof Dr Med Dent"University of GenevaGeneva, Switzerland

This siudy investigated Ihe relationship between abutment total occlusalconvergence angle (laper} and the resistance of cemented crowns subjectedto dynamic loading. Crown and abutment analogs were placed using zinc-oxide-eugenol, ïinc-phosphate, glass-ionomer, or resin composite cement.Total occlurai convergence angles of 2,5, 5, 10, 15, 20, 30, and 40 degreeswere tested. Dynamic stresses were applied to the luted components until thebond failed or the components reached 10^ load cycles. The data wereanalyzed using the staircase technique. The relationship betweenconvergence and resistance was approximately linear for ali the cementstested. Crowns luted with resin composite cemenf were more resistant todynamic lateral loading (han those placed using glass-ionomer or zinc-phosphate cements. Crowns luted with zinc-oxide-eugenol cement presentedthe least resistance to cyclic lateral stresses, ir^t ! Prosthodont1996:9:117-130.

Cemented crowns may be dislodged by mastica-tory or parafuncfional forces. The stabilizing

properties of a given abutment have been ascribedto its retention and resistance features. Retention isdefined as the poíeníial to oppose the removal ofthe restoration along its path of placement, and re-sistance is defined as tbe capacity to prevent dis-lodgment of the crown by forces directed in lateralor oblique directions,^ However, such a distinctionfrequently remains purely theoretical, since bothfactors are closely interrelated.

'Lecturer. Division of Fixed Prostbodontics. Schooi ofDentistry.

"Professor, Department of Restorative Dentistry. Schooi olDentistry.

•"Professor and Ctiairman. Division of Fixed Prosthodontics.School a( Dentistry.

Reprint requests: Or H. W. Anieim Wisitott. Division of FixedProsthodontics. University of Geneva, 19. rue Barthélemy-Menn. 1205 Geneva. Switzeriand

This investigation was supponed by grants from the SwissProstbodontic Society and the Academic Society of Geneva.

The relationship between total occlusal conver-gence (taper) and retention of cemented cones wasestablished by Isrgensen- and confirmed byKaufman et al,^ The Jorgensen hyperbola was laterformulated mathematically by Rosenstiel"* as:

Retention fg/rr 380Taper fdegri

The 45-dcgrt'C' axis of symmetry of tbe curve waslocated at about 15 degrees of total convergence.To maximize retention, many educators thus advo-cated a convergence angle of 5 to 7 degrees wbenpreparing teeth for cemented crowns. According toTyiman and Malone,^ "axial reduction should notexceed 2 to 5 degrees occlusogingivally" andJobn5ton et al^ recommended "5 to 7 degrees ofparallel," Similar views were also expressed byShillingburg et al,^ This teaching principle, how-ever, is at odds with data published by Eames et al,^Ohm and Silness,^ Mack,'° and Nordlander et a l , "who demonstrated that clinicians tend to prepareabutments with convergence angles averaging 15 to25 degrees. Although according to the J0rgen5en^

Voiume?, Number 3, t996 1 1 7 The International lojmal of Prosthodontics

Abiitmeni Taper and Resisiance io Dynamic Loading

Fig 1 To reproduce tiie stresses appiied to iuted restora-tions under clinicai conditions, tine teeth must be subjected toback and torth stresses in the buccolinguai direction

diagram such convergence angles would providevastly inadequate retention, the angles still appearto provide adequate resistance in terms of thelongevity of the cemented restorations,

A number of authors have made attempts to de-termine resistance by subjecting restorations tooblique or lateral forces,'^"'" Because of the natureof the chosen experimental design, the results wereunsatisfactory, because in many instances the toothanalog(s) or the restoration either fractured or per-manently deformed under the applied stress.Clinically this mode of failure is seldom observed.Indeed, it has been the authors' observation thatcrowns usually loosen by failure of the cementbond alone without damage to the abutment or therestoration.

The purpose of this study was to reevaluate cur-rent assumptions about the relationship betweenabutment total occlusal convergence and the resis-tance of cemented crowns to dynamic lateralforces using an innovative experimental apparatus.

Materials and Methods

Testing Principie

The testing principle applied in this study wasbased on the following premises:

1, Resistance to laterally directed forces and notretention is the primary determining factor incrown stability, Intraoral force measurementson lateral arch segments during normal masti-catory fijnclion have demonstrated the pres-ence of force vectors in the verticai as well as

in the horizontal planes,'^'^ Tbese studies con-clusively showed that, during chewinji, theteeth were subjected to alternating coiTii,.iiia-tions of buccoiingual and occlusogiii.>;ivilforces,

2 In general, dislodgment of a crown occuii. àtiera substantial number of masticatory stress cy-cles. This process generally affects the integrityof the cement layer only. It will not harm eitherthe tooth or the restoration,

3, The cement bond does not fail because of asingle intense load application, but only after alarge number of repeated load cycles (¡e, fa-tigue]- The implications of fatigue in prostho-dontic failure have been previously de-scribed.'^

An experimental design that would duplicatebuccolingual force vectors should apply back andforth stresses to the components under Investiga-tion. Such a device could be built for cementedcrowns according to the principle shown in Fig 1.Although more elaborate designs are conceivable,in the situation pictured only two discrete stressvectors wil l be applied to the structures to betested. Consequently, the stress concentrationsleading to ultimate failure will always be located Inthe same zones of the cement interface.

However, intraoral stresses continuously altertheir direction during chewing and therefore sub-ject the restorations to a field of vectors of varyingdirections. This condition was approximated in thisstudy (Fig 2a), Crown and abutment analogs havingvarying convergence angles were fabricated asaxisymmetric structures that spun around their lon-gitudinal axes. After cementation, each specimen'scrown analog was clamped into a collet, and a ballbearing was affixed to the abutment analog. Whenthe abutment analog was loaded via its ball bear-ing, alternating tension-compression stresses devel-oped inside the rotating structures (Fig 2b). Forcesof different magnitudes were applied to each con-vergence angle investigated. The relationship be-tween convergence angle and resistance was estab-lished by determining the mean force level atwhich 50% of the sampies survived a predeter-mined number of load cycles.

Specimens

An overall view of the test specimens is shown inFig 3, The patrix (male portion) consisted of a cone(ie, the abutment analog) with a shaft 30 mm inlength. The matrix (ie, the crown analog, 8 mm indiameter X 7 mm in height) conformed to the

Tiie [nlernstional lournai of Prosihodonlii 118 ; 9 , Number 2, 1996

Crown/abulment analogs

— Bali beanng

Alwlment Taper jnd Resistance Lo Dynamic Loading

Fig 2a (Lett) Woriting principle of rotational faltgue tests.The specimen rotates around ils main axis.Fig Zb (Below) During rolation, the iuted components aresubjected to sinusoidai tension-compression cycies.

Cement escapechannel

Convergenceangie

Cement thici<ness:40 ± 5 Mm

Fig 3 Dimensional specifications of the test specimens.

patrix, and was extended with a shaft 30 mm in tapers of 2.5, 5, 10, 15, 20, 30, and 40 degrees,length X 6 mm in diameter. To decrease intracoro- Because of tbe large number of tests required, itnal hydrostatic pressure during cementation, an was essential that the specimens be reusable afterescape channel was provided. Seven of these each cementation and thus be of adequate bard-matrix-patrix combinations were fabricated with ness, rigidity, and resistance to corrosion.

Voiume 9, Mumbcr 2, 199& 1 1 9 The International lournal of Prosthodantics

Abutnienl T.iger mri Mpiislance to Dyramit LoadinK

Table 1 Product InventoryProdLCl name Description Specifications

600 Alioy

Ai u-oxyde

Cement Spacer

Duraiay

Extrude

New Fuji Rock

Rexiilium 3v

Micro 12 Ultra

MOC75U2

Digitmaster

MH 600E

Digitmatic Indicator

102

Collet

Capmix

Silamat

48350

Temp Bond

Phosphacap

Keiac-cem Maxicap

Variolink

Hay nes InternationalKokomo, Indiana

ColielBaliaigues, SwitzeriandBeile üe St CiaireChats worth, CaliforniaRelianceWorth, iilinoisKerrRomulus, MichiganGCTokyo, Japan

Jenenc/PentronWailinglord, ConnecticutUnidenlGeneva, SwitzerlandMotoroiaSchaumburg, liiinoisTesaRenens, SviiitzerlandMaho, Babel, & CoPlronten, GermanyMitutoyoTokyo, JapanSchaublinBevilard, SwitzerlandSuhnerBrugg, SwitzeriandEspeSeefeld, GermanyVivad entSchaan, LiechtensteinEskenaziGeneva, SwitieriandKerrRomulus, MichiganVivadentSchaan, LiechtensteinEspeSeeteid, GermanyVivadentSchaan, Liechtenstein

industriai Ni-Cr-Fe aiioy

Aiuminum oxide

Die spacer

Autopolymenzing resin

Impression materiai

Type IV slone

Ni-Cr-Be alloy

Chemical cement remover

Optical switch

Thickness-measuringinstrument

Numericaily controiiedmachine lool

z-axis-measuringinstrument

Engineering lathe

Cement mixer

Cement mixer

Solid carbide drill

Zn-0-eugencitemporary cementZinc-phosphate cemeni

Glass-ionomer cemeni

Composite cemeni

min 72% Ni, 15,5% Cr, 8% Fe, 0,5% Si,1.0% Mn, 0,08% C, 0.5% Cu, 0,35% At,0.3% TI50 pm at 2 kg/cm^

Grey

Methyl-methacryiate resin

Poiy(vinyi siiosane) elastomer

20 mL water/100 g powderSetting expansion 0,03%Compressive strength: 53 MPai SO 6873Í 77% Ni; < 15% Cr; < 10% Mo; < 10% W;Co;Ti; •:5% Al; < 1,8% Be25% phosphoric acid

GaAs LED

Reading accuracy: 0.002 mm

Machining acouracy; ± ,0025 mm

Reading accuracy 0,001 mm

Machining accuracy: ± 0,005 mm

0 6 mm

4,450 ± 5% Qsciilatians per minute

Diaroc, DIN ia97R

Mixing ratio 50:50

iSO R 1566; Mixing ratio 1 mg:0,6 mL

ISO 7489' 1986; Mixing ratio 0.7 mg:033 mL

Mixing ratio 50:50

The patrix was machined from an industrial Ni-Cr-Fe alloy (600 Alloy, Haynes Internalional,Kokomo, IN) with carbide cutting tools (No, 4ÍS350,Eskenazi, Geneva, Switzerland!, (Specifications anddescriptions for all products used are listed in Table1,) To provide adequate cement space, the matrixwas prepared as follows: Individual impressions(Extrude, Kerr, Romulus, Ml) were made of each ofthe machined cones and poured in type IV stone(New EujiRock, GC, Tokyo), After coating the diewith one layer of die spacer (Cemeni Spacer, Bellede St Claire, Chatsworth, CA), a new impression wasmade and also poured in die stone. After the stonehad set, a iayer of separating medium was applied,and a pattern that approximated the shape of the

future matrix was fabricated with autopolymerizingresin (Duraiay, Reliance, Worth, IL). The resin pat-tern was then repositioned on the patrix andmounted into the chuck of an engineering lathe(102, Schaublin, Bevilard, Switzerland) where it wasmachined to specifications, leaving a dimensionalexcess ol about 0,5 to 1 mm. The machined resinpatterns were cast in a Ni-Cr alloy (Rexillium 3vJeneric/Pentron, Wallingford, CT), Eventually thécastings were again turned on the engineering latheto the final dimensions shown in Fig 3- The insidesurface of each crown analog was standardi/:ed byairborne particle abrading using SO pm aluminurrioxide (Alu-oxyde, Collet, Ballaigues, Switzerland)The tapered surface of the abutment analog was

The International lournal of Prosrhodontics 1 2 0 Volume 9, Number 2,1996

ALiLlmeiit Taper and Resistance lo Dynamic Loading

Fig 4 Paralleling device. Themiddle bar is mounted on brassgliders and oan be moved alongthe steel bars. The protectionwater prevents the luting agentIrom running into the collet. - Weight

.— .Collet

•~^— " Abutment analog

Crown analog

— Protection water

Collet

refined using 1000-grit abrasive paper (Presi Well,Walter Ebner, Le Lode, Switzerland).

Cement and Cementation

Four cemenl types were tested: a provisional zinc-oxide-eugenol cemenl (Temp Bond, Kerr), a zinc-phosphate cement (Phosphacap, Vivadent, Schaan,Liechtenstein), a glass-ionomer cement (Ketac-cemMaxicap, ESPE, Seefeld, Germany), and a resincomposite cement (Varioiink, Vivadent).

To ensure congruent seating of the patrix andmatrix, a paralleling device was constructed (Fig 4)that consisted of a frame made of two cylindricalsteel rods seated in aluminum blocks- A third

aluminum block was fitted with brass guides andcould move freely inside the frame on tiie steelrods. Using a numerically controlled machine tool(MH 600E, Maho, Babel, & Co, Pfronten,Germany), collet supports (Collet, Suhner, Brugg,Switzerland) were centered and affixed inlo themovable and stationary pieces of aluminum. Thisdevice was mounted vertically on a stand. Thecongruence of both collet axles was checked witba Digimatic Indicator (Mituloyo, Tokyo) by mount-ing 6 X 50-mm steel rods into the collets and as-sessing the deviation after 10 cycles of mounting,dismounting, and translation of the movable bar.Deviations of ± 0.010 mm were registered, whichwas considered acceptable.

; 9, Number 2, 1996 121 The imernational loumsl of Prostliodonlics

Abu mien r TU pi lo Dyna

Using the paralleling device, trie space left be-tween the patrix and matrix components could bedetermined. Both parts were seated into each otberafter the matrix had been coated with a layer ofpoly(vinyl siloxane) impression material. Afterpolymerization, the impression material was care-fully removed using the tip of a scalpel,

A self-restraining micrometric dial gauge(Digitmaster, Tesa, Renens, Switzerland) was usedto measure the thickness of the impression inaterialat various locations. About 90% of those measure-ments fell into a 40 ± 5 pm range (full range = 25to 65 pm). After measurement, all samples werelightly airborne-particle abraded with Alu-oxyde toremove any remaining silicone,'®

The zinc-phosphaie and the glass-ionomer ce-ments were provided in premeasured capsules.These were triturated for 5 and 10 seconds, respec-tively, in the triturators supplied by the manufac-turers ICapmix, Espe and Silamat,Vivadent), For thezinc-oxide-eugenol and resin cements, efforts weremade to standardize the quantities of base and cat-alyst by using scoops of appropriate dimensions,Eor cementation, the crown analog was mountedinto the inferior collet, with the opening facing up.The patrix was mounted into the translating barand acted like a plunger. After mixing, the crownanalog was coated with cement and the abutmentanalog was gently seated. At completion of thisstep, a 5-kg steel block was placed on the force-shaft, resulting in a 55.42-N total force applied tothe specimens (steel block -i- weight of the parallel-ing frame components). The specimens were leftundisturbed for 30 minutes, after which they wereremoved from the paralleling device and placed intap water. Testing was begun after 24 ± 3 hours.

After each test, any zinc-oxide-eugenol, zinc-phosphate, or glass-ionomer cement that remainedon the test components was completely removedwith a cleaning solution for dental instruments(Micro 12 Ultra, Unident, Geneva, Switzerland)and ultrasonic vibration. The composite cemenlwas first burned off over a bunsen burner and thecombustion residues removed with curettes. Thenthe specimens were placed in the cleaning solution,Einally, the crown-analogs were gently airborneparticle abraded with aluminum oxide to removeany remaining residues, and the patrices parts werelightly sanded using lOOO-grit sandpaper.

Testing

The fatigue machine is shown in Eig 5a and dia-grammatically explained in Fig 5b, The test speci-mens were clamped into a collet. Rotation from an

Fig Sa Overali view ol one unit of the fatigue macliine, A =the bertii with the opticai switch, B - the weigint; C = theobiique dram; D = the baii bearing and the specimen; E - thecounter (number of cycles and rotationai speed); and F = theirrigation hose.

electric motor was transmitted to tbe test specimenvia two pulleys and a belt. The force on the outerend of the specimen was applied by Pb-Znweights. The rotations of the specimen werecounted by a slotted disk that rotated inside an op-tical switch (MOC75U2 Motorola, SchaumburgIL), the output of which was fed into an arithmeticunit that dLspiayed the number of cycles and tberotating speed. At failure of the cement interfacethe weights dropped onto their berth which acti-vated an electronic relay. The electrical supply tothe motor was disconnected, and counting on thearithmetic unit stopped. The rotational speed w:.=setto 1000 rpm, " ^ ^

The cement interfaces were kept moist by continuous irrigation with tap water.

I of Proslliodontics 122 ï9 . Number 2, 1996

Atiulmenl Taper and Reíiílance lo Dynamic Loading

Irrigation hose

Bail bearing

Spring , __

Drain

Slotted disk/optical switch

Fig 5b Diagrammatic representation of one unit of the fatigue machine.

Experimental Procedure and Analysis

The procedure consisted of spinning the specimensunder load (Figs 6a and 6b). The specimens werethus subjected to repeated tension-compressionstress cycles. The upper limit of the test was set at10^ cycles. Spinning was started after the Pb-Znweights had been suspended to the outer end ofthe specimen. For each applied load the specimenwas registered either as having failed or havingreached lO*" cycles without breakage la runout).The goal of the procedure was to determine theload ievei (L^) (m - mean) that caused 50% of thesamples to survive lO*" stress cycles. The spreadaround this value was also calculated.

An analytical technique that applies to quantal(fail or not-fail) data is the "staircase analysis"'^-^"in which a series of samples is tested in sequence.At the onset, the procedure requires two educatedguesses in that an entry load level (L ,) that corre-sponds to the estimated value of L^ and a load in-crement (L¡^ ,) are determined. An initial specimenis run at L , ,. Depending on the outcome of thetest, the second specimen is cycled at L , - L¡^^, ifthe first specimen failed, and at L .,, -t- L¡ ^ if it ranout. In the third run, the applied load is again in-creased or decreased by L¡^^,, depending on thesurvival of the second specimen. One such seriesis shown in Fig 7 with L , = 26 N and L¡ ^ = 2 N,

Fig 6a Specimen under load.

After the data were collected, they were tabulatedas shown in Table 2, When L^ (the lowest level atwhich failure occurred) is set to 22 N, then L^ iscalculated as:

If the computation had been based on runouts, L^(the lowest level at which a runout was observed)would have been set to 20 N and L^ calculated as:

•'oiuírie9. Number 3, 1996 1 23 The International lournal of Pro5(liodontics

AbuLnienL Taper and Resislance lo Dyii.imic- Loading Wiikoll cl i

Bail bearing Test specimen

irrigation iiose

VaselineCoating

Fig 6b Diagrammatic representation ot the specimen, auxiliary parts, and coliet. The petrolatumcoating prevents water trom running either inte the coilet or into the bali-bearing.

There may be situations where runouts and fail-ures are not observed in equal numbers, as in tbepresent example. Tbe first equation is applicable ifthe number of runouts exceeds tbe number of fail-ures, the second when faiiures are more frequentthan runouts.

The standard deviation is computed as follows:

SD = 1.62O\L,„„- + 0.029

/here L = mean load ievel at which 50% of speci-

mens runout and 50% fail; L^ = lowest load levelat which failure occurred; L ^ ^ = chosen load in-crement; n = 2;n¡ (n. = number of failures for eachload level) (see Table 2|; A = Sin- (i = load level];andB=I i2n¡ .

The equation defining SD is valid wben

In tbe present example, L^ = 26.3 and SD =4,70,

Thirty runs were performed for each cement typeTo compensate for possible procr^rJui-aJerrors, the cements were tested in sequenci s of (enTbat is, after ten runs of zinc-oxide-eugenol, ¿-¡^^'

The lnlemalK,nal loürníl oi Pruithodontic^ 1 2 4 Volume 9, Number 2, 1996

Abulmeni Tjper and Resistance lo Dynamic Loading

Table 2 Data Arrangement for Statistical Analysis (15-Degree Taper SpecimenCemented With Glass-ionomer Cement)Applied force{N)

30

262422

Force level(')

43210

No, of failuresi")46221

n^15

1618

20

A = 40

64

0B = 128

V A = 2 i n ; B = I,^n,

Fig 7 Example of staircaseanaiysis for the specimen with a15-degree convergence anglecemented with glass-ionomer ce-ment. Square = specimens thattailed priof to 10^ cycles; ring =runouts; L , = 26 N;L.,,. = 2N,

30 .—r

28 •—

26 \-m—-

24

22

2010 15 20

Specimen number

phosphate, or glass-ionomer cements, the cementtype wa5 changed. The resin cement was tested lastbecause each new run required a light sandblastingof the specimens. It was hypothesized that thiswould inevitably alter their initial dimensions, theconsequences of which were difficult to assess.

For each convergence angle, the outcome of thetest was expressed as L^ and its 95% confidenceinterval (CI), A custom-designed computer programwas used to obtain L^ ± 95% CI from the staircaseanalysis. Thus, a difference between the two valueswas considered significant at the 5% level if theconfidence intervals did not overlap. The regres-sion analysis was performed using the SYSTAT soft-ware package,^'

Results

The relationship between total occlusal conver-gence and the applied mean load for the four ce-

ments tested is depicted in Fig 8 and tabulated inTables 3 to 6, This relationship could be de-scribed by linear regression (applied force = Œ Xconvergence -i- ß) where o; = the slope of the line,and ß = the y-axis intercept at 0 degrees of con-vergence. These lines are also displayed. Forzinc-oxide-eugenol cement, the 0-degree inter-cept was 9.07 N and fhe slope was -0.105, Forthe zinc-phosphate cement, the (5-degree inter-cept was located at 20,5 N, and the slope was-0,339, For the glass-ionomer and the resin ce-ments the 0-degree intercepts were 35,7 N and43,9 N, respectively. The corresponding slopeswere-0,371 and -0,259,

With the exception of the 2,5- and 5-degreespecimens cemented with glass-ionomer and resincomposite cements, none of the computed confi-dence intervals overlapped. It follows that all theother experimental data are different at the 95%level of significance.

Voljiiie9, 125 Tile International iournal of Prosthûdontlcs

tnt Tape I Resistance to Dyna Loading

Table 3 Experimental Data and RegressionParameters ¡or the Zinc-Oxide-Eugenol Cement

Table 4 Experimental Data and RegressionParameters for the Zinc-Phosphate Cement

Taper(degrees)

2-55.0

10.015.020.030.040.0

i-,„±SD

8.71 ± 1.269.57 ±2.527.36 ± 0.946.86 ± t.1t6.86 Í 2.046.37 ±2 184.83 + 1.05

95% CI

8.23-9.208.58-10.66.99-7.736.43-7.296.06-7.665.52-7.214.42-5.24

Taper(degrees)

2.55.0

10.015.020.030.040 0

19.0 ±2.4120.6 ± 2.3417.2 ±2.1914-2 ±2.1713.8 ±2.479.8 ± 2.0777*2 .11

95% CI

18.1-19.919.7-21.516.4-18.113.4-15.012.8-14.78.9-10.66.8- e.5

Linear regression: slope = -0.105, y-intercept - 9 07 N; correlation be-tween taper and resisiance < 0 924: slope sO, F = 29.18, P< 003.

Composite

Glass-ionomer

Zinc-phosphate

Zinc-oxide-eugenol

0 2.5 5 10 15 20 30

Taper (degrees)

Fig 8 Relationship between taper and sustained mean ioad under dynamic loading for the four cements tested.

The Internalional lournal of Proithodonlic; 7 2 6 Volume 9, Number 2, 1996

Atiulment Tape 1 Resistance to Dynamic tending

Table 5 Experimental Data and RegressionParameters for the Glass-ionomer Cement

Taper(degrees) í-^^íSD

2.55.0

to.o15.020,030,040,0

39,6 ± 11,434.0 ± 20,328.2 ± 6,8426.3 ± 4,7029.5 ±6,3424.1 ± 8,7022.6 + 7,51

Linear regression: slope = -0,371; y-inlercept = 35,7 N; correlation De-tween laper and resistance: 0,857; slope s 0, F = 13,794, P< .014,

Table 6 Experimental Data and RegressionParameters for the Composite Cement

Taper(degrees) L^ ± SD 95% CI

25,9-43,125,5-30,924.5-28.527.1-32.020.7-27.419.7-25.6

2,55,0

10,015,020,030,0

48,0 I 17,536,8 ± 7.25«.O ±12 634 7 + 4,6942 0 ± 3,4338,3 • 19,632,2 + 2,85

41,1-54.933.9-39,638,9-49,032,8-36,640,2^3,830,6-46,031,1-33.4

Linea' regressicn: siope = -0 259; y-intercept: 43,9 N; correlationtmeeniaper and resistance: 0,638: slope *0 , F ^3.433, P>:,123.

Discussion

Relatiotiship Between Abutment Taper andResistance of Cemented Crowns to Lateral Forces

Figure 8 indicates that, within the limits of the pre-sent experimental model, the relationship betweentaper and resistance cannot be described as a hy-perbolic function of the form;

re,ijs!ai)ce = Ftaper

Clearly, the relationship is approximately linear forthe four types of cements tested. The slope of theregression lines varied somewhat depending on thetype of luting agent. The resistance of zinc-oxide-eugenoi cement was the least dependent on theconvergence angle, while the crown analogscemented witb zinc-phosphate, glass-ionomer, andresin composite cements were more dependent onthe convergence angle.

Some authors developed a mathematical modelwhich led to the concept of a "limiting taper," thatis, a definite convergence angle below which theabutment would present resistance and abovewhich all resistance would be lost,""^'' As de-scribed, resistance would thus be an all-or-nothingtype of phenomenon. The concept relies heavilyon the beight-to-base ratio of the preparation,wbich must be low if the abutment is to presentsuch a limiting taper, in the present experiment,the height-to-base ratio was 0.875 and thus eventhe 40-degree cones still "had resistance" (ie,therefore, 40 degrees was not above the limitingtaper!. From the slopes of Fig 8, it can be inferredthat tbe limiting taper approach cannot be ac-cepted as absolute, because the degree of occlusalconvergence has a bearing on resistance.However, a convergence angle above the limiting

Fig 9 Broiten specimen. The internai angle between the shani<and the crown anaiog was too sharp. This configuration ied tostress concentrations and caused fatigue tailure of the metai.

taper might cause a sharp drop in the resistanceslopes. Thus, a definite appraisal of the conceptwould require a different set of specimens with alower height-to-base ratio.

Experimental Procedure

The experimental apparatus de^icribed here mightappear unusual in that its analogy to clinical struc-tures is not immediately obvious. Nevertheless,within the constraints of the specimen design wbichmust be rolation-symmetric, the experimental appa-ratus is well-suited to the application of alternatingstresses as they take place on prosthodontic struc-tures clinically,^^ Whichever design is chosen forthe sample, there must be no sharp internal angles,or the stress concentration that is generated in thoselocations might cause breakage of the specimen it-self rather than cleavage of the interface beingtested. In fact, seven crown analogs fractured dur-ing testing of the composite cement (Fig 91 and hadto be refabricated. Therefore il is important (1) thatthe internal angle between the shaft and the crown

127 The International Journal of Prosthodontics

Ahiilnienl Tiipcr and Resiilance lo Dyn.imic Loiidinn WiskotI et ,i

13

12

109

m

íO

— 6"O

ppl

3

2

1

h-

-

• ^ .

HI

3

: i

—

•t1 o •

-H

••

-4

•

5 10 15 20 25 30 35 40 45

Test number

Fig 10 Hypothetical staircaserun. In zone 1 (prerun], ttie samesample is cycled unlii taiiure.This stress ieuei is laken asstarling point tor ttie staircaseanalysis. Zone 3 is ihe actuai"cyciing range" thai can be usedfor analysis. Zone 2 is the ap-proach lo the cycling range, itcannot be applied for staircasecomputations. Square = speci-mens thai failed prior to 10^ cy-cies: soiid circle = same speci-men has been cycled up to to^times by increasing the appliedioad by L ^ , between eacli test;ring = runouts.

analog be rounded as much as possible, and (2)that the diameter of the cement escape channel in-side the axle be kept small and its opening beplaced at least 2 mm away from the crown analog.

For economic and practical reasons, the analogshad to be reusable after each test and thus neededto be refurbished between each trial; yet finding asuitable material for the specimens proved to be atedious procedure. Different alloys (nickel-platedsteel and several stainless steels) were tested butwere found not to respond to the requirementsplaced on the crown and abutment analogs. TheNi-Cr alloys that were eventually used were judgedadequate as to their hardness and resistance to thecleaning solution. However, they were difficult tomachine and required extremely hard but fragiletungsten carbide cutting tools.

The influence of the surface state on the type ofexperiments described herein is unknown, becausedata generated for retention tests cannot be directlytransferred to the present experimental procedure.Nevertheless, to ensure the maximum of consis-tency to the surfaces, the specimens were sandedeither with sandpaper or by airborne particle abra-sion (sandblasting). For the zinc-oxide, zinc-phos-phate, and glass-ionomer cements, none of theseprocedures was mean! to remove material from thesurface but merely to dull the shiny spots that ap-peared as a result ofthe compressive stresses on theload-bearing areas. For the composite cement, thecombustion residues that remained on the speri-

mens after burning the composite cement requiredremoval using gentle blasts of aluminum oxide.

Although every effort was made to avoid damag-ing the specimens, alterations of the geometry ofthe crown-abutment analogs could not be ex-cluded. Several observations, however, would indi-cate a lack of influence of the refurbishing proce-dures on the data obtained: (1) no alterations insurface shape or specimen geometry could be de-tected visually; ¡2) several reassessments of avail-able cement space made during the course ofthe study did not reveal differences relative to theinitial measurements; (3) there was no perceivablechange in the amount of freedom of the patrix in-side the matrix; and (4) for none of the tapers testedwas there a detectable trend in the recorded datasuggesting a systematic error due to an alteration ofthe premises of the experiment. Thus it could beconcluded that the results obtained (L^) were influ-enced only by the experimental parameter (taper)and random variations in the testing conditions.

The main drawback of the procedure lies in thetime required for testing. The preliminary estima-tion required to set the parameters of the staircaseanalysis (L^ ,, l.^^^^) may be vastly inappropriate.When this occurs, the initial approach to L ^ is te-dious. To avoid wasting an inordinate number ofsamples, the first specimen is usually cycled in in-cremental steps (ie, it is not replaced after eachrun) until failure occurs. This procedure is termed a"prerun," Staircase analysis is then started at a load

l of Prostliodontk 128 Volume?; Number 2, 1996

Abutment T.î|jiT and Reiiílanct lo Oynamif Loadine

level tbat approximates the one tbat caused failurein the prerun. The three pbases of a bypotbeticalsequence are presented in Fig 10. As shown, onlysamples that failed in tbe cycling range of loadscan be used in the final analysis.

At 1000 rpm, a specimen rotates for aboul 18bours, after wbicb a new sample can be spun. For30 samples, a testing sequence where only newspecimens are used will thus take approximately 1month. If the samples are refurbished and requiresome additional time for cement setting, tbe totaltime is usually doubled or tripled.

In the present study, the specimens were spun ata bigh-cycling frequency to reduce the time re-quired for testing. However, at a normal chewingrate (60 to 80 cycles per minute] tbe rate of crackpropagation inside the luting agent may differ fromits progression at 1000 cycles per minute. In otherwords, for dental cements tbe relationship betweenL^ and tbe cycling frequency is unknown. If astrain rate dependency exists, there should be asbift of the regression lines of Fig 8 along the verti-cal axis. Their shape, however, is unlikely to bemodified, and thus the conclusions of the presentstudy remain valid,

A comparable type of argument can be made asto the irrigation with tap water. Although effortswere made to mix hot and cold water, tbe temper-ature was always below 37°C, Yet it has beenshown that the compressive strength of a zinc-oxide cement decreased by a factor of two wbenthe temperature was raised from 23''C to 37°C,-^ Asimilar observation was made for zinc-phospbatecement where a decrease in strength of about 10%was noted when the temperature was raised (nodata is available on the effect of temperature onglass-ionomer and composite cements]. Again,such a temperature-dependent behavior mightcause vertical shifts in the lines of Fig 8, but is veryunlikely to affect their shape.

Cement as Mechanical Links

Threaded components and screws are well-suitedto connecting prefabricated components as theyare available in implant dentistry. Nevertheless,cementation is likely to remain the main mode offixation in restorative dentistry. Yet the fracturemechanics of cemented cones is still poorly un-derstood. From Fig 8 it appears tbat the four ce-ments tested differed in their resistance proper-ties, Zinc-oxide-eugenol presented the lowestresistance and resin composite cement presentedthe highest resistance under cyclic loading.Furthermore, while the zinc-oxide-eugenol and

the zinc-phospbate cements were fairly consistentin Ihe experimental data obtained, the glass-ionomer and the resin cemenf in particularyielded data wi th a much greater spread.However, after multiple checking of tbe samples,no definite cause could be ascertained, Furtberstudies will be required to determine tbe origin ofthe variation observed.

The majority of the data on cements has beengenerated by crown pull-out tests^^-^" andposts^^"^' or standard materials science analyses(compressive strength, tensile strength, elastic be-havior, adhesive properties!, indeed, an elementarymaterial parameter such as compressive strengthbears some relationship to tbe resistance valuesdisplayed in Fig 8,^- A number of authors baveproposed semiempirical models in order to explaintbe relationsbips tbat exist between cements, taper,retention, and resistance,^^'^•' Altbough some ofthese approaches appear more promising''' tbanotbers,^'^'-'' in all likelibood tbe criteria that deter-mine the resistance properties of cemented crownsare more intricate than previously thought. Ourpresent hypothesis is that these parameters couldbe subdivided into three groups. The first relates totbe geometric configuration of tbe abutment;height, diameter, and taper. The second groupcomprises material constants sucb as tbe cementStrength in compression and shear as a function offilm thickness, Tbe tbird group relates to tbe adhe-sive properties of the cement-abutment and ce-ment-restoration interface. All this informationsbould be gatbered under dynamic loading condi-tions.^^ Investigations are presently under way toassess the relative importance of these parameters.

Conclusions

Within the limits of the experimental model pre-sented, it was concluded tbat:

1, The relationship between abutment taper andresistance to dynamic lateral loading Is approx-imately linear,

2, Crowns luted using resin composite cementwere more resistant than crowns luted usingglass-ionomer cement, wblcb in turn weremore resistant tban crowns luted using zinc-phosphate cement. Crowns luted using zinc-oxide-eugenol cement presented tbe least resis-tance to cyclic lateral stresses.

Furthermore, this study has shown that rotationalfatigue tests can be applied to the strength quantifi-cation of cemented interfaces.

' o l jme l . Number 2, 199b 129 Intemalional iournai of Prosthodontics

Abutment Taper and lieiistsnce to Dyii

Acknowledgments

The help of the fol iowing personç i; gratefully acknowledged:M, Barros, D, Held, C. Lopez, and C, Pécora for Iheir machin-ing skills; R. Renevey for casting of the matrices; L, Ming ofESPE, P, Oehri of Vivadent, and K, Loelliger of Kerr for the ce-ments supplied.

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Tiie Interniitionai Journal of Prosthodontics 130 rre9. Number 2, 1996