the all-ceramic, inlay supported ﬁxed partial denture. part 3. experimental approach for...

8/12/2019 The all-ceramic, inlay supported fixed partial denture. Part 3. Experimental approach for validating the finite elem

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A D R F R E S E A R C H R E P O R T Australian Dental Journal2012; 57: 2330

doi: 10.1111/j.1834-7819.2011.01638.x

The all-ceramic, inlay supported fixed partial denture. Part 3.Experimental approach for validating the finite elementanalysis

MC Thompson,* CJ Field, MV Swain*

*Biomaterials, Faculty of Dentistry, The University of Sydney, New South Wales.Aeromechanical Engineering, Faculty of Engineering, The University of Sydney, New South Wales.

ABSTRACTIn a previous study, the authors used a finite element analysis (FEA) to evaluate the stresses developed during the loading ofan all-ceramic, inlay supported fixed partial denture and compared it with the more traditional full crown supportedprosthesis. To date there has been little research into correlating the responses of the numerical model against physicalmechanical tests; such validation analysis is crucial if the results from the FEA are to be confidently relied upon. This studyreports on the experimental methods used to compare with the FEA and thereby to validate the predictive fracture behaviourof the numerical model. This study also outlines the methods for manufacture and testing of the ceramic structure alongwith observations of the fracture tests. In addition the procedure used for developing the FEA model for the test system isoutlined.

Keywords:All-ceramic bridge, inlay fixed partial denture, experimental design, finite element analysis.

Abbreviations and acronyms:CADCAM = computer-aided designcomputer-aided milling; CR = composite resin; FEA = finite elementanalysis; FPD = fixed partial denture; PDL = periodontal ligament; Y-TZP = yttria stabilized tetragonal zirconia.

(Accepted for publication 1 August 2011.)

INTRODUCTION

A comprehensive literature review into the ideal toothpreparation design for a ceramic inlay has previouslybeen conducted by the authors;1 critical aspects such ascavity depth, isthmus width and total occlusal conver-gence were analysed and optimized cavity geometryformulated. A subsequent paper utilized the optimized

inlay preparation design on abutments supporting anall-ceramic, three-unit fixed partial denture (FPD) withthe lower first molar as the pontic. The prosthesis formdesign was improved to better distribute tensile forcesparticularly in the gingival embrasure area whichdisplays peak tensile forces; this highly developed inlaysupported prosthesis was compared against the con-ventional full crown supported FPD via a finite elementanalysis (FEA).2

The results from this numerical study predicted thatpeak stresses in the inlay bridge are around 20% higherthan in the full crown supported bridge with von Mises

stresses peaking at about 730 MPa (the theoretical

maximum strength of Y-ZTP is 900 to 1200 MPa; inpractice this is somewhat lower) when subjected totheoretical average maximum bite force in the molarregion of 700 N. Maximum von Mises stressesoccurred at the loading sites; the embrasure areas andthe axio-pulpal line angle with maximum principalstresses of 693 MPa being confined to the gingivalaspect of the embrasures. With careful and proper

design, it was concluded that the use of inlays assupport for an all-ceramic FPD could be successful.

Validation of the FEA is crucial if confidence in theresults is to be accepted. Development and manufac-ture of the physical prototype, the preparation andmounting for testing and the testing procedure are allcrucial if the validation is to be accurate and truthfulin determining the genuineness of the FEA. Thereappears to be little work comparing the FEA ofceramic FPDs against robust experiments. Earliervalidation studies have been quite rudimentary in theirmethodology, with little regard given to matchingelastic moduli or realistic geometry; later studies are

2012 Australian Dental Association 23

Australian Dental JournalThe official journal of the Australian Dental Association


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opposed to a metal die. The load-to-failure testing of afully sintered Y-TZP bridge on composite resin teethwould likely lead to their failure long before the bridge.Additionally, the use of metal dies or replica teethwould drastically alter the Youngs modulus of the

primary supporting structure, resulting in errors.

Greatest accuracy in comparing the FEA to theprototype can only be achieved by utilizing a materialwith an elastic modulus very similar to dentine.

The ability of the milling process to produce a precisereplica of the inlay bridge developed in the FEM wasdemonstrated by superimposing a high contrast image

of the inlay over the computer model.Oversized inlay preparations were made in the CR

abutments ready to accept their respective restorations.This resulted in a gap of approximately 1 mm aroundthe entire periphery of the inlays.

A self-curing acrylic (PMMA) base was constructedprior with the alveolus of the abutment teeth mouldedin place by repeated insertion and removal of theindividual roots until the acrylic was almost set; thisresulted in two half bases, one for each abutment. Afterthe acrylic base had fully cured, a layer of poly vinylsiloxane (3M Imprint II) simulating the natural resil-

ience of the periodontal ligament (PDL) was coatedonto the roots and the teeth seated individually intotheir respective sockets. Excess poly vinyl siloxane wasremoved.

Oversized inlay preparations were treated with phos-phoric acid. The cavity preparation and inlay compo-nent of the bridge was treated with an adhesive (3MSingle Bond 2) which was applied so as to saturate theporous ceramic structure, leaving a bondable surfacefilm. A bed of CR was placed in the preparations and thebridge placed under pressure so as to allow squeeze outof material and subsequent re-adaptation of all margins.This was fully cured on the ramp cycle of an Optilux501 curing light to minimize stresses.

Three inlay-tooth models were tested to failure on aShimadzu AG-50 kNE with incremental and peak loadsbeing recorded together with displacement. The CRteeth and base survived all testing and was reused, thusguaranteeing identical abutments and testing condi-tions. A 5 mm hardened stainless steel ball was placed(Fig. 3) so as to achieve stable three-point contact in thecentral fossa of the pontic. Loading was at a rate of0.5 m per minute and continued until fracture.

Ceramic specimens testing

Strength tests are singularly the most important sourceof information regarding the performance of a ceramicduring loading. The tests provide a source of dataregarding how a material may perform in service withdata compiled through simple loading conditions withcareful measurements taken of stress and stain.

Mechanical testing of ceramic specimens was essentialas no data are available in the literature; this was in orderto determine the physical properties for the partiallysintered zirconia and in particular its flexural or tensilestrength and the Youngs modulus. The three-pointloading technique has been suggested as the preferable

(a)

(b)

(c)

Fig 2. (a) Buccal view of inlay supported FPD. (b) Inferior view ofFPD. (c) Occlusal view of FPD.

Fig 1. Completed CR teeth to be used for inlay abutments.


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technique for tensile strength testing of brittle materialssuch as ceramics.1921

Two series of tests were conducted on different sizedspecimens to determine fracture or flexural strength; thefirst being 5 5 mm on 20 mm outer supports andthe second 2.5 2.5 mm on 10 mm outer supports.The purpose of this was to account for the effect ofspecimen size or volume upon the strength. Failurestatistics as predicted by the Weibull approachdescribes the strength distribution of brittle materialsbased on the weakest link theory; failure at any flawleads to total failure of each individual sample. Thelargest flaw present in each specimen becomes theweakest link and predicates its survivability; thereforeincreasing specimen size also statistically increases thechance that a large flaw is present and thus largerspecimens are generally weaker. A further series of testswere conducted to determine the fracture toughness ofthe partially sintered zirconia by way of the SEVNB test(single-edge V notch beam test) (Fig. 4).

Preparation of all the ceramic samples was bydiamond separating disc; samples were then carefullylapped on 1000 grit silicone carbide paper, emphasizinga longitudinal scratch pattern, and attention paid toensure all corners were rounded and free of anychipping which may act as crack initiation sites.

Samples were measured with a Mitutoyo Micrometerprior to testing, and crack length measured afterfracture in the case of the notched sample tests.

Determining the best way of obtaining notchedsamples has always been slightly problematic formaterial scientists; as notch width decreases so toodoes the fracture toughness valueKIC. Values have beenfound to level off at when the crack tip radius is below10 lm,22 but how to obtain such a fine and consistentnotch has always been difficult. A razor blade wasinserted into the prepared V notch and moved back andforth to obtain an immeasurably fine notch radius.

Fracture strength is defined as the maximum tensilestress in the surface of a specimen fractured in bending(it must be remembered that stresses acting across theheight of a specimen will vary from maximum tensionon one side to maximum compression on the other).For a rectangular cross section specimen on the three-point bend apparatus, tensile or yield strength is:

ru;b Fl

4Wb

where ru,bdenotes the maximum strength in bending,Fis the fracture load and l is the width of the outersupports.24 Wb is the sectional modulus of the spec-imen and is given by the equation:

Wb dh2=6

whered and h the width and height of the rectangularspecimen respectively. Pre-cracked specimens wereused on the same three-point bend apparatus withsamples taken from the same milled lot as the 5 5 mmspecimens. The critical stress intensity factor is given bythe equation:

KIC 3Fl

2h2dYa1=2

for ah = q < 0.6 isY 1:93 3:07q 14:53q2 25:11q3

25:80q4 for l=h 4

Y 1:96 2:75q 13:66q2 23:98q3

25:22q4 for l=h 8

whereKICis the fracture toughness of the material, F isthe breaking load,lis the width of the outer supports,handdthe height and width of the rectangular specimenrespectively, a the length of the cracknotch and Y thedependent variable factor of the crack.23 It should beFig 4. Single-edge V notch beam test.

Fig 3. The inlay-tooth complex ready for testing.

26 2012 Australian Dental Association

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fragmentation from where the ball contacted the fineedge of the oblique fracture as a result of thecompressive nature of the damage.

DISCUSSION

The use of partially sintered zirconia milled directlyfrom the FEA STL file is a unique experimentalprocedure. Utilizing a ceramic much weaker than thesupporting material has allowed the use of CR for the

abutments which has the advantage of not onlypossessing a Youngs modulus close to that of dentine,but the reuse of the original models, thus maintainingconsistency across all tests. Problems associated withthe production of numerous identical prototypes orreplicas are also overcome with milling directly fromthe STL file as opposed to the more common method ofproducing the FEM after the experimental model hasbeen made. As no mechanical data are available, three-point bend tests were necessary in order to determinethe fracture strength of the partially sintered zirconia.

The fracture strength range was determined to be

46.6 to 50 MPa which is low enough to not risk

damage to the CR models during testing, whilstsufficiently high to allow the routine handling andseating of the bridge and most importantly accuratemilling without fear of chipping or crumbling of thefiner details. Milling was performed with a 0.5 mmtungsten carbide cutter to an accuracy of within 10 lm,

leaving superb surface detail with no visible rippling ortooling marks in the critical embrasure areas. As anexercise to satisfy any doubts regarding the exactness ofthe overall geometric outline of the milled bridgecompared to the numerical simulation, the superimpo-sition of the two images demonstrates superb conflu-ence in their overall shapes (Fig. 5c). Any perceivabledifferences can be accounted for by the parallax errorand distortion from the cameras wide angle lens inmacro mode.

The lower figure of 46.6 MPa for fracture strengthtests on the three-point test with 20 mm outer support

compared to 50 MPa with the 10 mm outer supports isas anticipated and in accordance with the Weibullprediction of larger samples being somewhat weakerthan smaller volume samples.

Measurement of the strength of ceramics is known toproduce significant scatter in the results, this phenom-enon is due to the random positioning of flaws presentthroughout the structure, varying in size, location andorientation. This necessitates a statistical approach todescribing quantitatively the data produced; henceWeibull analysis.

Qualitatively, the site of crack initiation, direction,pattern of growth are in excellent agreement with thatproduced by other authors via bench testing26 andstate-of-the-art numerical crack simulation tech-niques.27 However, it must be emphasized that thetesting in this study, as in the authors previous paper,differed crucially in that the anchorage of the ponticwas via an inlay as opposed to full crown. Researcharticles concerning inlay supported fixed bridges arevery few, especially where the material is all-ceramic.Of significance is where authors have sought to studythe fracture behaviour of ceramic bridges (all crownsupported); the observable results have been verysimilar though the support of the pontic differs (inlay

vs. crown). It may be concluded that if the bond isexcellent and does not fail, then the fracture initiationand progression as predicted by the FEA is the same inboth cases and not through the weak isthmus region ofthe inlay as is common with Class II restorations.1

A recent two-dimensional (2-D) FEA analysis on thestress distribution in inlay supported bridges28 con-cludes that regardless of material used for the inlaybridge, the stress patterns are remarkably similar withtensile peaks at the gingival aspect of the connectors,and a compressive zone within the body of the pontic.However, the 2-D FEA in the study did not display thehigh compressive forces evident in our current 3-D FEA

Fig 6. Three experimental models displaying fracture patterns.


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at the occlusal aspect of the connectors (as would beexpected from the Law of Beams) and the loading of theball indenter, nor was it able to show the subtletransition in stresses within the body of the inlay andpontic. Fracture behaviour from the 2-D numericalanalysis could be predicted as being through the

connector or through the inlay; very little additionalinformation is given to confidently make any otherprediction as a result of the 2-D FEA nor were theresults validated against bench-top tests.

Fracture paths as predicted by the locations of thehighest maximum principal stresses from the FEAmodel in this study can be clearly seen in Fig. 7a andfrom the von Mises in Fig. 7b. This coincides with azone of failure extending between the peak tensilestresses developing at the mesial andor distal gingivalembrasures, and then extending to the occlusal loadingsite. Failure under Model 1 (Fig. 6) depicts the crack

front propagating from the more intensely stressed ofthe two gingival embrasures, extending to the occlusalloading site. Contact damage on the occlusal of thepontic developed as the crack tip approached theloading site and encountered the Hertzian stressesresulting from the loading ball. Models 2 and 3(Fig. 6) show the fracture path developing from bothconnector sites, resulting in an obliquely travellingfracture path through the pontic, together with avertical crack extending through the opposite inlay-pontic connector. Contact damage was also evident onthe occlusal surface of the pontic.

The initial crack development on the experimentalmodels occurred at the gingival aspect of the weakestconnector when the critical stress level is reached; thisaccurately reflects the peak tensile stresses displayed by

the FEA. The formation and progression of crackswithin the ceramic takes place so as to maximize the rateof energy release and minimize the strain within thesystem; hence the direction of cracking necessarilyfollows a path towards the highly stressed loading siteon the occlusal surface of the pontic. The development

of new cracks at the central fossa of the pontic originatesfrom the blunt contact damage of the loading ball whichis also anticipated from the FEA by very high von Misesstresses on the pontics occlusal (see Fig. 1 in Thompsonet al.2). Initiation of the second fracture of the adjacentconnector as depicted in Cases 2 and 3 reflects theequally high peak stresses developing at this gingivalsurface. Cracking possibly follows closely after the firstconnector has partially fractured and due to the inferiorrotation of the major pontic segment, leads to thedevelopment of a vertical rather than another obliquefracture. This process of crack initiation and progres-

sion is in an effort to release and redress the imbalanceof energy in the stress field as suggested by Irwin.23

As a comparison of the current FEA of the partiallysintered zirconia with the FEA the authors previouspaper,2 it is interesting to note that with full sinteringcomes a 12 times increase in the stiffness of the materialas measured by the Youngs modulus. Even so, thestress contours are remarkably similar, differing onlyslightly on the quantum of the stresses resulting fromthe 200 N load (209.9 MPa vs. 190 MPa for the vonMises stress and 198 MPa vs. 191 MPa for themaximum principle stress). Primarily, the largest dis-crepancy is observed on the degree to which the stressespermeate or are transferred to the supporting inlays,with critically high stress peaks occurring at the axio-pulpal line angle of the fully sintered bridges but onlymoderate stresses with the partially sintered bridgereflecting the materials increased flexibility.

An encouraging recent study validated the results ofmechanical tests of milled ceramic bars against anFEM, a process reversed from this current study.5 Thisstudy demonstrates that under simplistic conditions, theresults of FEAs cannot only be precise but indeed morereliable. In comparison, our current study was con-ducted on accurate models of genuine prosthesis and

their supporting structures, significantly more complexin geometry and behaviour than simple ceramic bars.Thus, the resultant stresses developed in the system isaffected by a wide range of variables, some of which aredifficult to quantify at present.

Our next study will correlate the predicted strengthvalues from the FEA against detailed stress andstatistical analysis of the inlay ceramic bridge andceramic samples in what is essentially the quantitativevalidation. To date we have not been able to find anystress figures derived from FEA of dental bridges thathave been successfully validated against experimentalmodels. There exist validation of simple bars with

(a)

(b)

Fig 7. (a) Predicted zones of failure from the maximum principlestresses. (b) Predicted zones of failure from the peak von Mises

contours.


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numerical models but none relating to the complexityof geometry existing with real FPDs.

CONCLUSIONS

This study outlines the methodology used to produce

and test the bridge prototypes and qualitatively validatesthe results of the FEA detailed in an earlier paper.2 Thebasis for using partially sintered zirconia as a modelmaterial is justified. The mechanical properties includingflexural strength and fracture toughness of the partiallysintered zirconia blocks has been measured. It is shownthat using resin based composite as a model for theabutment teeth and partially sintered zirconia ceramicfor the bridge enabled us to evaluate the fractureresponse of ball loading such a structure. The resultsdemonstrate excellent congruence between the fracturebehaviour predicted by the peak principal stresses from

the FEA. Initiation sites and propagation path of thecracks established in the physical models are in agree-ment with the results obtained from the FEA. Thepreliminary results reported will be extended to exploreadditional aspects of the role of the boundary conditions,especially the bonding between composite and ceramicand an analysis and rationalization of the results.

ACKNOWLEDGEMENTS

The authors would like to thank and acknowledge thefunding received from the Australian Dental ResearchFoundation for their financial assistance given towards

the laboratory cost, the time and tireless energies of KenTyler (University of Sydney) and Georges Sara (StoneGlass Industries) for his help in fabricating the uniqueinlay bridges required.

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2. Thompson MC, Field CJ, Swain MV. The all-ceramic, inlaysupported, fixed partial denture: Part 2. Fixed partial denturedesign: a finite element analysis. Aust Dent J 2011;56:302311.

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19. White SN, Caputo AA, Li ZC, Zhao XY. Modulus of ruptureof the Procera all-ceramic system. J Esthet Dent 1996;8:120126.

20. Augereau D, Pierrisnard L, Barquin M. Relevance of the finiteelement method to optimize fixed partial denture design. Part 1.Influence of the size of the connector on the magnitude of strain.

Clin Oral Investig 1998;2:3639.21. Ban S, Anusavice KJ. Influence of the test method on failure stress

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22. Nishida T, Hanaki Y, Oezzotti G. Effect of notch-root radius onthe fracture toughness of a fine-grained aluminas. J Am CeramSoc 2006;77:606608.

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27. Li Q, Ichim I, Loughran J, Li W, Swain M, Kieser J. Numericalsimulation of crack formation in all ceramic dental bridge.Key Eng Mat 2006;312:293298.

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Address for correspondence:Dr Mark C Thompson

Faculty of DentistryThe University of Sydney

Sydney NSW 2006Email: [email protected]


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