Weibull9,10 developed the following formula to handle the statistics of fracture strength in recognition of the huge variability in strength and reliability of brittle materials
where P is the failure probability, σ1 the samples inert strength, σ0 the samples Weibull scaling stress and m the Weibull modulus which is a measure of the variability in strength of the material, corresponding to the shape of the distribution curve.5 A larger m relates to a more homogenous material and thus higher survival rates. Engineering ceramics typically have a Weibull variability of between 10 and 15 compared to 5 for window glass, hence demonstrating the greater reliability of these ceramics over domestic glass.7 Thus, complex materials such as ceramics require the use of FEA because of the difficulty in determining long-term survivability through bench-top testing alone.
Literature review of the relationship between the gingival embrasure of an FPD and its long-term survival and methods used for testing
An extensive body of evidence has demonstrated or discussed that broadening the curvature of the gingival connector of FPDs results in better distribution of stresses.12–27 However, the relationship between radius of curvature and fracture resistance has not been examined in sufficient detail.13 The use of traditional load-to-failure bench-top testing is unable to recreate the failure mechanisms seen clinically,28 hence the use of FEA is gaining popularity because of its ability to accurately assess the complex biomechanical behaviour of irregular prosthetic structures and heterogeneous materials in a non-destructive, repeatable manner.
Kelly et al.18 conducted a fractographic analysis of 29 all-ceramic, crown supported FPDs which had failed; 20 after bench-top testing and 9 failing clinically. The coincidence of bench-top and clinical observations for the structural behaviour of these prostheses was examined. Detailed investigations into the in vitro prostheses proved that the failures had originated from the connector sites and in 70% of cases initiation was from the core-veneer interface. Most significantly, the cracks developed at the apex of the gingival embrasure and extended to the contact site. All 9 clinically failed FPDs shared this same mode of failure with the cracks originating from the gingival embrasure and extending to the site of loading.
A two-dimensional FEA conducted on the laboratory samples was consistent with the fractographic analysis, with peak tensile stresses localized around the connector area but only if there was a significant difference in the Young’s modulus between the core and veneering ceramics and, most interestingly, if a small amount of abutment rotation was allowed. The rigid fixation of the abutments displayed an FEA solution markedly different than one where the abutment was allowed to rotate or simply move due to the presence of the periodontal membrane, with the former FEA displaying a result akin to a classic four-point bend test, and the latter closely mimicking the fractographic analysis. Weibull calculations of fracture probability in both the FEA and fractographic analysis were very closely matched.
The major limitations of the above study were that the abutments were cast in Ni-Cr-Be, a material significantly stiffer than dentine and the absence of a simulated periodontal ligament, both of which led to the sample fracturing in a rather different manner than a dynamic biological structure. The elastic modulus of the supporting structure is very important in the distribution of stresses29–32 as demonstrated by the fracture resistance of all-ceramic crowns fixed on Co-Cr-Mo (E = 180–240 GPa) models being significantly higher than those cemented to natural teeth (E = 15–20 GPa for dentine and 50–85 GPA for enamel) – 1838 N vs. 888 N, respectively. Additionally, the connector dimensions and geometry were not carefully controlled. Nevertheless, the in vitro samples were able to closely mimic the results of the failed clinical models.
Fisher et al.14 utilized FEA to predict if computational methods could help FPD design improve in reliability. Their all-ceramic, crown supported FPD designs utilized three models, each differing in connector dimensions and connector length, roughly corresponding to embrasure radius, connector height and bucco-lingual depth as follows:
The results indicated that the Weibull curve moved significantly towards lower failure probability when the connector length increased as in the third design and cross-section increased from 8.75 mm2 to 14 mm2. Additionally, the FEA demonstrated that maximum stress decreased in the third group from 106 to 85 MPa. The authors reported that the effects of the periodontal ligament and cement film are negligible on the mechanics of fracture. However, other studies have been careful to account for these factors.
Kou et al.12 utilized a newly developed FEA model code to assess the fracture mechanism of yttria stabilized tetragonal zirconia (Y-TZP), crown supported FPDs. The study examined heterogenous Y-TZP under static loading and on stainless steel abutments, comparing it to a previous study by Sundh et al.27 which involved bench-top testing. Fracture patterns were very similar in both cases with all fractures initiating at the gingival embrasure, propagating diagonally under one single loading level (a property of brittle materials) and extending to the loading point. Additional analysis involving photo-elastic fringe patterns and acoustic emissions agreed with the results of the study by Sundh et al.27 and the current FEA.
The authors stated that a major limitation of their study was the simplified two-dimensional testing and like so many other studies, failed to account for the effects of a natural tooth’s modulus of elasticity, the influence of the cement film and the visco-elastic nature of the periodontal ligament. Ignoring the modulus of elasticity of the abutment and the luting cement has been shown to influence the fracture resistance of crowns33 and hence FPDs. The poor marginal fit of ceramic inlays and their lack of primary mechanical retention places greater importance on the role of the luting cement as compared to cast-metal inlays.34
Hojjatie et al.16 and Fischer et al.14 believed that the effects of the cement film and periodontal ligament could be ignored. However, Kelly et al.18 showed that ignoring the mobility provided for by the periodontal ligament restricts the rotational movement of the abutments, thus requiring greater fracture forces because the FPD functions more as a static beam rather than a dynamic anatomical structure. Likewise, Kappert et al.35 reported a mean fracture strength of 703 N for all-ceramic, three-unit FPDs cemented on abutments with simulated periodontal mobility compared to mean fracture strengths of 2225 N when fixed to ridged abutments.
Wolfart et al.36 bench-top tested a total of 64 all-ceramic, inlay retained FPDs made from heat pressed lithium disilicate glass ceramic (LDGC) (n = 32) and Y-TZP (n = 32) with half from each group made with different connector dimensions of 3 × 3 mm or 4 × 4 mm. A comparison of their quasi-static fracture resistance and fatigue strengths when changes were made to their connector dimensions in the two material groups was conducted. The abutments were Co-Cr-Mo, supported in an alloy base with simulated periodontal ligament made from silicone material and the FPDs were cemented with a composite luting agent.
The results for the median fracture strengths were as follows:
Statistically, the quasi-static loading and cyclic loading showed significant differences between both groups of LDGC (p ≤ 0.03) but not between the two groups of Y-TZP. The difference between LDGC and Y-TZP was significant for both connector sizes (p ≤ 0.001).
However, by using Co-Cr-Mo as the abutment material, this study failed to take into account the ability of dentine to redistribute stresses due to its significantly lower modulus of elasticity and, as demonstrated by Kappert et al.,35 can lead to fracture forces markedly different to that displayed by natural teeth. Moreover, the use of a Co-Cr-Mo may also not adequately bond to the composite resin luting cement, thus impeding the adhesion of the frameworks.
Oh and Anusavice13 tested the effect of various all-ceramic FPD connector designs based on the hypothesis that increasing the radius of curvature of the gingival embrasure leads to a decrease in fracture probability. The results concluded that variations in the occlusal embrasure radii was of no significance, with variations in gingival embrasure radii of between 0.25 mm and 0.90 mm increasing the mean fracture strength by more than 140% (p ≤ 0.0001).
Oh, Götzen and Anusavice22 further tested the hypothesis that increasing gingival radii curvature would lead to increasing fracture resistance of FPDs via 2 three-dimensional FEA models based on the original study by Oh and Anusavice.13 A change in the gingival radius from 0.9 to 0.45 mm was carried out in order to maintain a constant connector height of 4 mm. Fractographic analyses of the 40 failed FPDs from the Oh and Anusavice13 study were assessed and compared to the FEA, revealing that the failure origin was at the gingival embrasure in all 40 specimens. The results of the FEA correlated well with the fractographic findings, with peak compressive stresses occurring at the occlusal embrasure and peak tensile stresses at the gingival embrasure. Weibull moduli were 6.3 for the group with the narrow gingival embrasure and 8.6 for the group with the lager embrasure.
Plengsombut et al.37 studied the effects of a sharp (0.06 mm radius) vs. a round (0.6 mm radius) gingival embrasure shape on the fracture resistance of all-ceramic core materials, namely a pressed and milled LDGC and Y-TZP ceramic blocks. The results showed a significant difference in the fracture strength of the material due to, not only the gingival geometry, but also the fabrication technique. Specifically, if the material was machined, i.e. computer-aided design/computer-aided milled (CAD/CAM), then the connector design affected the fracture resistance. If on the other hand the material was pressed, then the connector shape had no significance on the material’s strength.
Lithium disilicate based materials possess larger flaws, a coarser surface finish compared to Y-TZP materials and hence were structurally weaker regardless of fabrication technique or connector shape. Y-TZP is inherently tougher and possesses a smoother surface finish; therefore is structurally strong and less influenced by connector shape, but still benefits from the effects of stress distribution afforded by the rounded gingival embrasure.
Magne et al.20 performed a two-dimensional FEA (the authors accepted that a three-dimensional FEA would more realistically model stresses and strains but at the cost of greater processing requirements) investigating: (1) the stresses at the surface and interface of 3-unit posterior adhesive FPDs made with composite resin, fibre-reinforced CR, gold alloy, LDGC, high alumina glass ceramic or Y-TZP; and (2) the influence of slot vs. 2-surface vs. 3-surface abutment preparations. The different materials and abutment preparations were constructed upon a digitized cross section of a 3-unit FPD. Included in the numerical analysis was the periodontal ligament (PDL) and supporting bone. A 50 N simulated vertical load was applied to the pontic and the stresses within the restorative materials. Tooth/restorative junction and surface stresses were calculated and compared.
The results concluded that for all materials, the stress patterns were remarkably similar to that displayed in a typical three-point bending test, with highest tensile stresses at the gingival surface (peaking at the gingival embrasure), compressive at the occlusal, and the abutments were subject to mainly compressive forces. Overall, the distribution of stresses was most favourable for the composite material due to its lower modulus of elasticity (12.3 GPa). However, this material was deemed to be clinically unsuccessful for FPD use because of its relatively low fracture toughness. With improving material toughness comes increasingly high stiffness and brittleness, culminating in the alumina ceramics and Y-TPZ with moduli of elasticity as high as 402 and 205 GPa, resulting in the placement of proportionately higher stresses on the interfacial surfaces and cement layers.
Kiliçarslan et al.38 tested the fracture resistance of 32 posterior, metal-ceramic crown supported (n = 8) and inlay-retained (n = 8) FPDs, and all-ceramic inlay retained FPDs (LDGC-n = 8, Y-TZP-n = 8) utilizing load-to-failure bench-top testing.
The results were that all metal-ceramic FPDs failed via adhesive failure of the ceramic-to-metal with 7 of 8 in the retainer area and 1 in the pontic. All-ceramic inlay supported FPDs failed via cohesive failure of the ceramic structure with 4 fracturing in the connector and 4 in the inlay retainer. The metal ceramic FPDs had the highest mean failure load at 1318 N for the crown supported group and 858 N for the inlay supported group. LDGC showed the lowest failure load at 303 N whilst the Y-TZP displayed static fracture strength of 1247 N, very close to that of the metal ceramic, crown supported group.
The use of metal models and the absence of a simulated PDL were accepted by the authors as a limitation. Further commentary must be made regarding the use of Sinogol (a provisional cement), thus lacking the proper adhesive qualities of a composite resin so needed in the bonding of the inlays, for the adhesive is paramount in the overall success of a bonded restoration.39 Brittle materials, such as ceramics, are weakest when exposed to tensile stresses.40 Hence, subjecting a material or design to such tensile stresses is considered to be an excellent test of its properties. Proper designs for the critical connector and pontic must relate favourably to elementary beam theory. Unlike beams, however, the dimensions and shape of FPDs is never uniform but heavily dependent upon the tooth preparation, which in turn is heavily influenced by the morphology of the remaining sound tooth structure after caries removal, the individual anatomical and geometric alignments of the abutment teeth, the length of the edentulous span and the luting agent used.
Summary of the literature conclusions
Based on our analysis of the literature, the following were concluded: (1) tensile stresses are concentrated at the gingival aspect of the connector and the vast majority of ceramic failures are initiated at this site; (2) increasing the gingival embrasure radii results in better distribution of stresses and higher fracture loads; (3) increasing the dimensions of the connector also results in higher fracture loads; (4) rigid abutment fixation results in fracture strengths and stresses different to abutments that are allowed to rotate via a PDL; (5) the elastic modulus of the abutment material is significant in accurately reproducing clinical performance; (6) the effects of a luting agent is important; and (7) three-dimensional FEAs are more accurate than two-dimensional.
Traditional load-to-failure testing methods have proved irrelevant in predicting the clinical performance of ceramics, largely because they cannot recreate the failure mechanisms seen in clinical specimens. Numerical analysis proves to be a more accurate predictor.41 With reference to the conclusions of the literature review above, it should be possible to construct an optimized all-ceramic, inlay supported FPD with stresses reduced to a minimum and test the design via an accurate numerical simulation viz. FEA.
This paper aims to test the design hypothesis that the use of an idealized inlay preparation geometry on the abutments and increasing the gingival embrasure radii and broadening the connector of the bridge, will minimize stresses within the all-ceramic inlay supported FPD to the degree where it will be clinically acceptable compared to the all-ceramic full crown supported FPD. Two three-dimensional finite element models were constructed for the biomechanical analysis and comparison. The connector designs were as follows: (1) inlay supported FPD – mesial connector height 3.5 mm, width 4.8 mm and gingival embrasure radius of 0.9 to 1.0 mm, distal connector height 3.5 mm, width 5.4 mm and gingival embrasure radius 1.4 mm average. These dimensions reflect the results of the above studies in minimizing the effects of stress and strain; and (2) full crown supported FPD – mesial connector height 4.0 mm, width 5.8 mm and gingival embrasure radius 0.8 to 0.9 mm, distal connector height 4.0 mm, width 6.0 mm and gingival embrasure radius 0.8 to 0.9 mm.
All material properties were kept standardized. However, in the interest of replicating clinical norms, the connector area of the crown supported prosthesis was deliberately enlarged and the embrasure radii reduced, thus taking into account clinical and laboratory norms in making use of as much connector height and width as possible. This bolsters the connector strength but reduces the gingival embrasure radii in order to improve interproximal aesthetics. Likewise the connector area on the inlay supported prosthesis was enlarged but due to the constraints of the inlay widths, the contact was necessarily smaller both in height and width.