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

Authors



Dr Mark C Thompson
Faculty of Dentistry
The University of Sydney
Sydney NSW 2006
Email: mthompson@pacific.net.au

Abstract

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

Abbreviations and acronyms:
CAD/CAM

computer-aided design/computer-aided milling

CR

composite resin

FEA

finite element analysis

FPD

fixed partial denture

PDL

periodontal ligament

Y-TZP

yttria stabilized tetragonal zirconia

Introduction

A comprehensive literature review into the ideal tooth preparation design for a ceramic inlay has previously been conducted by the authors;1 critical aspects such as cavity depth, isthmus width and total occlusal convergence were analysed and optimized cavity geometry formulated. A subsequent paper utilized the optimized inlay preparation design on abutments supporting an all-ceramic, three-unit fixed partial denture (FPD) with the lower first molar as the pontic. The prosthesis form design was improved to better distribute tensile forces particularly in the gingival embrasure area which displays peak tensile forces; this highly developed inlay supported prosthesis was compared against the conventional full crown supported FPD via a finite element analysis (FEA).2

The results from this numerical study predicted that peak stresses in the inlay bridge are around 20% higher than 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; in practice this is somewhat lower) when subjected to theoretical average maximum bite force in the molar region of 700 N. Maximum von Mises stresses occurred at the loading sites; the embrasure areas and the axio-pulpal line angle with maximum principal stresses of 693 MPa being confined to the gingival aspect of the embrasures. With careful and proper design, it was concluded that the use of inlays as support for an all-ceramic FPD could be successful.

Validation of the FEA is crucial if confidence in the results is to be accepted. Development and manufacture of the physical prototype, the preparation and mounting for testing and the testing procedure are all crucial if the validation is to be accurate and truthful in determining the genuineness of the FEA. There appears to be little work comparing the FEA of ceramic FPDs against robust experiments. Earlier validation studies have been quite rudimentary in their methodology, with little regard given to matching elastic moduli or realistic geometry; later studies are increasingly adopting realistic experimental designs with greater consideration given to matching material properties. However, there appears to still be absent accurate geometry, scale materials and loading conditions.3–9

Realistic experiments are required in order to confirm the validity of the FEA. Experiments relying upon simple beam loading designs and flexural tests as an approximation of the complex 3-D pattern of stresses and strains acting upon ceramics in the FEA must be considered highly misleading and not reflective of the overall simulation6 or clinical situation. Additionally, too little regard has been given to the need for matching the modulus of elasticity of all components within the experimental boundaries as seen in models utilizing metal abutments;10–12 this is especially relevant to the elastic modulus of the supporting structures which are primarily responsible in the distribution of occlusal stresses.1,13–16 Results from experiments failing to adequately deal with clinical reality must therefore be guarded in their applicability and not be interpreted as being absolute in their validity.

Unlike metallic alloys and other elastic–inelastic deforming solids, the strength of ceramics structures is dependent upon the testing method, specimen size and geometry, state of the surface, internal stresses and preparation method; any and all of which can significantly influence the results.13 This is particularly true where notching occurs (as in the gingival embrasure area of a FPD) due to development of a complex stress–strain state resulting from the constraint of the notch.14 Hence, if the data are to be reliable and validation true, the simulation must be realistic and as accurate a replication to the FEA as possible.

A particularly important issue concerns the close matching of the elastic moduli of the systems being commensurate with that of the relative strengths of the systems being tested and outcomes desired. The anticipated strength of the fully sintered yttria stabilized tetragonal zirconia (Y-TZP) is so high (700–1200 MPa) that if utilized would either necessitate the use of even stronger abutment material, thus introducing a fundamental mismatch of the critical elastic moduli of the abutments, or maintaining the use of CR abutments and risk testing the strength and bonding of the teeth/acrylic base as opposed to the bridge material. Choosing to use partially sintered zirconia is an important and novel distinguishing feature of the experimental methodology in this paper. Its use allows the precise and easy replication of numerous prototypes, each behaving in an elastic brittle manner identical to the fully sintered material whilst having a flexural strength low enough to enable three-point loading to test the stresses and strains upon the bridge design and not the adhesion and deformation of the supports. The physical properties of the partially sintered material are available neither from the manufacturer nor in the literature so the process of measuring flexural strength, toughness and elastic modulus has been described.

The aim of this study was to outline the methods used to produce and test exact bridge prototypes derived from the FEA virtual model, the testing of the ceramic structure, the determination of the mechanical properties of the material which hitherto has not been examined in detail and observations of the fracture tests. In addition, the procedure used for developing the FEA model for the test system is outlined.

Materials and Methods

Numerical model construction – the 3-D FEA

The construction of the FEA has been detailed in a previous study.2Table 1 details the material properties used in the FEA, in particular the Young’s modulus of the partially sintered zirconia which was determined via the use of the UMIS 2000 nano-indentation instrument developed at the CSIRO.

Table 1.   Material properties required within the FEA models.17 Young’s modulus for ceramic determined by indentation testing
MaterialYoung’s modulus (MPa)Poisson’s Ratio
  1. Partially sintered Y-TZP

Enamel84 1000.20
Dentine18 6000.31
PDL70.30.45
FPD ceramic15 6500.28

Experimental model construction – the prototype

Model teeth made from Filtek P60 composite resin (CR) due to its class leading compressive strength (395 MPa) and similarity of Young’s modulus to dentine (12.5 GPa)18 were fabricated by use of a sectioned silicone impression of a typical human lower right second molar and second premolar which closely matched the FEA abutment teeth. The mould was incrementally packed with P60, producing anatomical crown and root segments which were then bonded to form intact teeth (Fig. 1).

Figure 1.

 Completed CR teeth to be used for inlay abutments.

The inlay supported bridge STL file from the FEA was sent to a specialized ceramics laboratory which was able to mill via a computer-aided design/computer-aided milled (CAD/CAM) system dimensionally and geometrically precise bridge replicas in ‘green’ or partially sintered Y-TZP (Fig. 2a–2c). Partially sintered zirconia was preferred over the fully sintered material due to its lower strength, thus allowing the supporting replica teeth to be fabricated from composite resin as opposed to a metal die. The load-to-failure testing of a fully sintered Y-TZP bridge on composite resin teeth would likely lead to their failure long before the bridge. Additionally, the use of metal dies or replica teeth would drastically alter the Young’s modulus of the primary supporting structure, resulting in errors. Greatest accuracy in comparing the FEA to the prototype can only be achieved by utilizing a material with an elastic modulus very similar to dentine.

Figure 2.

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

The ability of the milling process to produce a precise replica of the inlay bridge developed in the FEM was demonstrated 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 around the entire periphery of the inlays.

A self-curing acrylic (PMMA) base was constructed prior with the alveolus of the abutment teeth moulded in place by repeated insertion and removal of the individual roots until the acrylic was almost set; this resulted in two half bases, one for each abutment. After the acrylic base had fully cured, a layer of poly vinyl siloxane (3M Imprint II) simulating the natural resilience of the periodontal ligament (PDL) was coated onto the roots and the teeth seated individually into their respective sockets. Excess poly vinyl siloxane was removed.

Oversized inlay preparations were treated with phosphoric acid. The cavity preparation and inlay component of the bridge was treated with an adhesive (3M Single Bond 2) which was applied so as to saturate the porous ceramic structure, leaving a bondable surface film. A bed of CR was placed in the preparations and the bridge placed under pressure so as to allow ‘squeeze out’ of material and subsequent re-adaptation of all margins. This was fully cured on the ramp cycle of an Optilux 501 curing light to minimize stresses.

Three inlay-tooth models were tested to failure on a Shimadzu AG-50 kNE with incremental and peak loads being recorded together with displacement. The CR teeth and base survived all testing and was reused, thus guaranteeing identical abutments and testing conditions. A 5 mm hardened stainless steel ball was placed (Fig. 3) so as to achieve stable three-point contact in the central fossa of the pontic. Loading was at a rate of 0.5 m per minute and continued until fracture.

Figure 3.

 The inlay-tooth complex ready for testing.

Ceramic specimens testing

Strength tests are singularly the most important source of information regarding the performance of a ceramic during loading. The tests provide a source of data regarding how a material may perform in service with data compiled through simple loading conditions with careful measurements taken of stress and stain.

Mechanical testing of ceramic specimens was essential as no data are available in the literature; this was in order to determine the physical properties for the partially sintered zirconia and in particular it’s flexural or tensile strength and the Young’s modulus. The three-point loading technique has been suggested as the preferable technique for tensile strength testing of brittle materials such as ceramics.19–21

Two series of tests were conducted on different sized specimens to determine fracture or flexural strength; the first being 5 × 5 mm on 20 mm outer supports and the second 2.5 × 2.5 mm on 10 mm outer supports. The purpose of this was to account for the effect of specimen size or volume upon the strength. Failure statistics as predicted by the Weibull approach describes the strength distribution of brittle materials based on the ‘weakest link’ theory; failure at any flaw leads to total failure of each individual sample. The largest flaw present in each specimen becomes the weakest link and predicates its survivability; therefore increasing specimen size also statistically increases the chance that a large flaw is present and thus larger specimens are generally weaker. A further series of tests were conducted to determine the fracture toughness of the partially sintered zirconia by way of the SEVNB test (single-edge V notch beam test) (Fig. 4).

Figure 4.

 Single-edge V notch beam test.

Preparation of all the ceramic samples was by diamond separating disc; samples were then carefully lapped on 1000 grit silicone carbide paper, emphasizing a longitudinal scratch pattern, and attention paid to ensure all corners were rounded and free of any chipping which may act as crack initiation sites. Samples were measured with a Mitutoyo Micrometer prior to testing, and crack length measured after fracture in the case of the notched sample tests.

Determining the best way of obtaining notched samples has always been slightly problematic for material scientists; as notch width decreases so too does the fracture toughness value KIC. Values have been found to level off at when the crack tip radius is below 10 μm,22 but how to obtain such a fine and consistent notch has always been difficult. A razor blade was inserted into the prepared V notch and moved back and forth to obtain an immeasurably fine notch radius.

Fracture strength is defined as the maximum tensile stress in the surface of a specimen fractured in bending (it must be remembered that stresses acting across the height of a specimen will vary from maximum tension on 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:

image

where σu,b denotes the maximum strength in bending, F is the fracture load and inline image is the width of the outer supports.24

Wb is the sectional modulus of the specimen and is given by the equation:

image

where inline image and inline image the width and height of the rectangular specimen respectively.

Pre-cracked specimens were used on the same three-point bend apparatus with samples taken from the same milled lot as the 5 × 5 mm specimens. The critical stress intensity factor is given by the equation:

image

for ��/�� = �� < 0.6 is

image
image

where KIC is the fracture toughness of the material, F is the breaking load, inline image is the width of the outer supports, inline image and inline image the height and width of the rectangular specimen respectively, a the length of the crack/notch and Y the dependent variable factor of the crack.23 It should be noted that the height of the samples relative to their support viz. aspect ratio is considered important; we kept all sample testing within the 1:4 ratio for standardization.

Elastic modulus testing for brittle materials has historically been inaccurate via the traditional static or bench-top testing methods,24,25 largely due to the inability to measure the small degrees of strain involved. Traditional bend testing would underestimate the correct value due to the inherent degree of compliance present in all large scale equipment, masking the microdimensions of strain involved (≤200 μm for the 2.5 mm2 sample). However, current quasi-static testing techniques such as nanoindentation are able to easily and accurately determine such properties.

The Ultra Micro Indentation System, UMIS-2000 (CSIRO, Campbell, Australia) is a nanoindentation instrument for investigation of the properties of the near-surface region of materials. Nanoindentation is a procedure which is non-destructive, relatively quick to perform and uniquely capable of characterizing the physical properties of both thin films and small volume samples. Being easy and the penetration accuracy of the indenter being just a few nanometres, it is considered the ideal method for determining not only material hardness, but elastic modulus and may be used for the measure of strain hardening, creep, fracture and other properties of surface and near surface regions with unique accuracy following submicron depths of penetration.

The UMIS-2000 utilizes several indenters including a spherical diamond, the Vickers square pyramid indenter and the Berkovich triangular pyramidal diamond indenter. Principally, the Berkovich indenter is used for brittle materials with a tip radius typically 50–100 nm, increasing to 200 nm with use and face angle 65.03°, its shaper geometry and longer diagonals more readily lends its self to finer measurement where penetration depth is shallow.24

Results

Ceramic specimen mechanical properties

Three-point testing of the 5 × 5 mm samples (n = 8) averaged 46.6 MPa of fracture load with a standard deviation of nearly 6 MPa; the 2.5 × 2.5 mm samples (n = 14) averaged 50 MPa with a standard deviation of just over 1 MPa. Testing of the SEVNB samples (n = 8) demonstrated excellent consistency in the results with an average fracture toughness value of 0.456 MPa√m and standard deviation of 0.076 MPa√m. Note well that the strain values given must not be regarded too seriously as these micrometre dimensions are well within the ability of the Shimadzu to resolve accurately and hence unable to provide a precise Young’s modulus. The preferred option for the determination of the elastic modulus and Poisson’s ratio of the ceramic samples was via nanoindentation testing (Table 1).

Millability and verification of the inlay contours

Computer-aided milling of the zirconia bridge from the STL file was verified dimensionally by comparing measurements taken from the FEM against the prototype; to ascertain and demonstrate the exactness of the geometry produced, a high contrast photo of the prototype (Fig. 5a) was superimposed on the FEM image of the bridge (Fig. 5b) with the ‘merge’ function of Photoshop (Adobe CS2 version 9). The result is demonstrated by the excellent confluence in the outlines of the two images, particularly in the embrasure areas and axio-pulpal line angles.

Figure 5.

 (a) High contrast photo of the buccal aspect of the zirconia inlay. (b) FEM image of the buccal aspect of the zirconia inlay. (c) Superimposition of Fig. 5a and 5b displaying the excellent confluence of their outlines.

Experimental model fracture patterns

Visual inspection of all three failed three-unit bridge models show that there was at least a single fracture developing from the gingival aspect of the weakest connector, travelling obliquely through the body of the pontic (Fig. 6). In two of the models, a second fracture developed vertically through the opposing connector resulting in the complete fragmentation and separation of the pontic. The loading site had evidence of slight fragmentation from where the ball contacted the fine edge of the oblique fracture as a result of the compressive nature of the damage.

Figure 6.

 Three experimental models displaying fracture patterns.

Discussion

The use of partially sintered zirconia milled directly from the FEA STL file is a unique experimental procedure. Utilizing a ceramic much weaker than the supporting material has allowed the use of CR for the abutments which has the advantage of not only possessing a Young’s modulus close to that of dentine, but the reuse of the original models, thus maintaining consistency across all tests. Problems associated with the production of numerous identical prototypes or replicas are also overcome with milling directly from the STL file as opposed to the more common method of producing the FEM after the experimental model has been made. As no mechanical data are available, three- point bend tests were necessary in order to determine the 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, whilst sufficiently high to allow the routine handling and seating of the bridge and most importantly accurate milling without fear of chipping or crumbling of the finer details. Milling was performed with a 0.5 mm tungsten carbide cutter to an accuracy of within 10 μm, leaving superb surface detail with no visible rippling or tooling marks in the critical embrasure areas. As an exercise to satisfy any doubts regarding the exactness of the overall geometric outline of the milled bridge compared to the numerical simulation, the superimposition of the two images demonstrates superb confluence in their overall shapes (Fig. 5c). Any perceivable differences can be accounted for by the parallax error and distortion from the cameras wide angle lens in macro mode.

The lower figure of 46.6 MPa for fracture strength tests on the three-point test with 20 mm outer support compared to 50 MPa with the 10 mm outer supports is as anticipated and in accordance with the Weibull prediction of larger samples being somewhat weaker than smaller volume samples.

Measurement of the strength of ceramics is known to produce significant scatter in the results, this phenomenon is due to the random positioning of flaws present throughout the structure, varying in size, location and orientation. This necessitates a statistical approach to describing quantitatively the data produced; hence Weibull analysis.

Qualitatively, the site of crack initiation, direction, pattern of growth are in excellent agreement with that produced by other authors via bench testing26 and state-of-the-art numerical crack simulation techniques.27 However, it must be emphasized that the testing in this study, as in the authors’ previous paper, differed crucially in that the anchorage of the pontic was via an inlay as opposed to full crown. Research articles concerning inlay supported fixed bridges are very few, especially where the material is all-ceramic. Of significance is where authors have sought to study the fracture behaviour of ceramic bridges (all crown supported); the observable results have been very similar though the support of the pontic differs (inlay vs. crown). It may be concluded that if the bond is excellent and does not fail, then the fracture initiation and progression as predicted by the FEA is the same in both cases and not through the weak isthmus region of the inlay as is common with Class II restorations.1

A recent two-dimensional (2-D) FEA analysis on the stress distribution in inlay supported bridges28 concludes that regardless of material used for the inlay bridge, the stress patterns are remarkably similar with tensile 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 the high compressive forces evident in our current 3-D FEA at the occlusal aspect of the connectors (as would be expected from the Law of Beams) and the loading of the ball indenter, nor was it able to show the subtle transition in stresses within the body of the inlay and pontic. Fracture behaviour from the 2-D numerical analysis could be predicted as being through the connector or through the inlay; very little additional information is given to confidently make any other prediction as a result of the 2-D FEA nor were the results validated against bench-top tests.

Fracture paths as predicted by the locations of the highest maximum principal stresses from the FEA model in this study can be clearly seen in Fig. 7a and from the von Mises in Fig. 7b. This coincides with a ‘zone of failure’ extending between the peak tensile stresses developing at the mesial and/or distal gingival embrasures, and then extending to the occlusal loading site. Failure under Model 1 (Fig. 6) depicts the crack front propagating from the more intensely stressed of the two gingival embrasures, extending to the occlusal loading site. Contact damage on the occlusal of the pontic developed as the crack tip approached the loading site and encountered the Hertzian stresses resulting from the loading ball. Models 2 and 3 (Fig. 6) show the fracture path developing from both connector sites, resulting in an obliquely travelling fracture path through the pontic, together with a vertical crack extending through the opposite inlay-pontic connector. Contact damage was also evident on the occlusal surface of the pontic.

Figure 7.

 (a) Predicted zones of failure from the maximum principle stresses. (b) Predicted zones of failure from the peak von Mises contours.

The initial crack development on the experimental models occurred at the gingival aspect of the weakest connector when the critical stress level is reached; this accurately reflects the peak tensile stresses displayed by the FEA. The formation and progression of cracks within the ceramic takes place so as to maximize the rate of energy release and minimize the strain within the system; hence the direction of cracking necessarily follows a path towards the highly stressed loading site on the occlusal surface of the pontic. The development of new cracks at the central fossa of the pontic originates from the blunt contact damage of the loading ball which is also anticipated from the FEA by very high von Mises stresses on the pontic’s occlusal (see Fig. 1 in Thompson et al.2). Initiation of the second fracture of the adjacent connector as depicted in Cases 2 and 3 reflects the equally high peak stresses developing at this gingival surface. Cracking possibly follows closely after the first connector has partially fractured and due to the inferior rotation of the major pontic segment, leads to the development of a vertical rather than another oblique fracture. This process of crack initiation and progression is in an effort to release and redress the imbalance of energy in the stress field as suggested by Irwin.23

As a comparison of the current FEA of the partially sintered zirconia with the FEA the authors’ previous paper,2 it is interesting to note that with full sintering comes a 12 times increase in the stiffness of the material as measured by the Young’s modulus. Even so, the stress contours are remarkably similar, differing only slightly on the quantum of the stresses resulting from the 200 N load (209.9 MPa vs. 190 MPa for the von Mises stress and 198 MPa vs. 191 MPa for the maximum principle stress). Primarily, the largest discrepancy is observed on the degree to which the stresses permeate 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 only moderate stresses with the partially sintered bridge reflecting the materials increased flexibility.

An encouraging recent study validated the results of mechanical tests of milled ceramic bars against an FEM, a process reversed from this current study.5 This study demonstrates that under simplistic conditions, the results of FEAs cannot only be precise but indeed more reliable. In comparison, our current study was conducted on accurate models of genuine prosthesis and their supporting structures, significantly more complex in geometry and behaviour than simple ceramic bars. Thus, the resultant stresses developed in the system is affected by a wide range of variables, some of which are difficult to quantify at present.

Our next study will correlate the predicted strength values from the FEA against detailed stress and statistical analysis of the inlay ceramic bridge and ceramic samples in what is essentially the quantitative validation. To date we have not been able to find any stress figures derived from FEA of dental bridges that have been successfully validated against experimental models. There exist validation of simple bars with numerical models but none relating to the complexity of geometry existing with real FPDs.

Conclusions

This study outlines the methodology used to produce and test the bridge prototypes and qualitatively validates the results of the FEA detailed in an earlier paper.2 The basis for using partially sintered zirconia as a model material is justified. The mechanical properties including flexural strength and fracture toughness of the partially sintered zirconia blocks has been measured. It is shown that using resin based composite as a model for the abutment teeth and partially sintered zirconia ceramic for the bridge enabled us to evaluate the fracture response of ball loading such a structure. The results demonstrate excellent congruence between the fracture behaviour predicted by the peak principal stresses from the FEA. Initiation sites and propagation path of the cracks established in the physical models are in agreement with the results obtained from the FEA. The preliminary results reported will be extended to explore additional aspects of the role of the boundary conditions, especially the bonding between composite and ceramic and an analysis and rationalization of the results.

Acknowledgements

The authors would like to thank and acknowledge the funding received from the Australian Dental Research Foundation for their financial assistance given towards the laboratory cost, the time and tireless energies of Ken Tyler (University of Sydney) and Georges Sara (Stone Glass Industries) for his help in fabricating the unique inlay bridges required.

Ancillary