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Influence of Connector Design on Fracture Probability of Ceramic Fixed-partial Dentures
1 Department of Prosthodontics, College of Dentistry, Health Science Tower, PO Box 100435, University of Florida, Gainesville, FL 32610-0435, USA; Correspondence: * corresponding author, woh{at}dental.ufl.edu
Fracture of ceramic fixed-partial dentures (FPDs) tends to occur in the connector area because of stress concentrations. The objective of this study was to test the hypothesis that the radius of curvature at the gingival embrasure of the FPD connector significantly affects the fracture resistance of three-unit FPDs. Two three-dimensional finite element models (FEMs), representing two FPD connector designs, were created in a manner corresponding to that described in a previous experimental study (Oh, 2002). We performed fractographic analysis and FEM analyses based on CARES (NASA) post-processing software to determine the crack initiation site as well as to predict the characteristic strength, the location of peak stress concentrations, and the risk-of-rupture intensities. A good correlation was found between the experimentally measured failure loads and those predicted by FEM simulation analyses. Fractography revealed fracture initiation at the gingival embrasure, which confirms the numerically predicted fracture initiation site. For the designs tested, the radius of curvature at the gingival embrasure strongly affects the fracture resistance of FPDs.
Key Words: ceramic FPD • finite element analysis • fractography • Weibull analysis • risk-of-rupture intensity
Stress distributions in a clinical prosthesis can be quite complex. They can consist of compressive, tensile, shear, or mixed stress patterns under typical conditions (Anusavice, 1996; Abu-Hassan et al., 1998). Brittle materials, such as dental ceramics, are weak when exposed to tensile stresses (Peterson et al., 1998). Therefore, tensile stress is generally considered as a meaningful variable for the assessment of ceramic materials relative to their service life, especially in the presence of flaws. In three-unit ceramic fixed-partial dentures (FPDs), the connector area can be considered as a fracture risk factor, which can increase the tensile stress concentration under flexural compressive loading (Inglis, 1913). The failure rate of three-unit ceramic FPDs around connector areas between retainers and pontics has been reported to be relatively high, especially with the sharper connectors (Kelly et al., 1995; Sorensen et al., 1999). If the connector design is altered in regions where maximum tension occurs, the characteristic stress pattern can be optimized to improve the survival time of three-unit FPDs. The results of other studies suggest that stresses are better distributed with broadly curved connectors than through the use of more sharply curved connector geometries (Hojjatie and Anusavice, 1990; Kamposiora et al., 1996; Pospiech et al., 1996). However, specific dimensional limits and sensitivity analyses were not performed. A prediction of the survival times for ceramic prostheses can be obtained by well-designed prospective clinical trials; however, prosthesis designs are variable, and it is difficult to standardize the designs to ensure realistic estimates of survival times as a function of shape parameters. Model tests with actual ceramic specimens fabricated to the anatomic configuration of teeth may be a useful tool for the identification of their behavior (Kern et al., 1993; Koutayas et al., 2000). Once the mean loads to failure of prostheses are determined, these data can be applied in mathematical equations to analyze the characteristic strength of the restorations. These invaluable data may reduce the failure probability of ceramic restorations that are controlled by multiple flaws, which cause ceramic structures to fail at stress levels far below their expected strength (Griffith, 1920).
In a previous study, Oh and Anusavice (2002) tested 10 ceramic FPDs for each of 4 connector designs of three-unit ceramic FPDs made of an experimental lithia-disilicate-based core ceramic (VP, batch #1989, Universal shade, Ivoclar AG, Schaan, Liechtenstein), 4 mm in height and 5 mm in width. The core ceramic frameworks were pressed at a temperature of 910°C for 20 min under a pressure of 5 bars. The connector designs were based on the following radii of curvature at the occlusal embrasure (OE) and gingival embrasure (GE): Design I, OE, 0.90 mm and GE, 0.90 mm; Design II, OE, 0.90 mm and GE, 0.25 mm; Design III, GE, 0.25 mm and GE, 0.90 mm; and Design IV, OE, 0.25 mm and GE, 0.25 mm. The FPD specimens were cemented with a resin-based composite on epoxy dies, and compressively loaded axially with a 14.3-mm-diameter steel bearing at the center of the pontic at a crosshead speed of 0.5 mm/min until failure occurred (Fig. 1
Fractography is a well-established method for determining the sites of fracture origin that are the most likely areas for clinical failure (Kelly et al., 1990, 1995; Thompson et al., 1994; Mecholsky, 1995). The stress distribution, failure strength, failure probability, and survival probability of FPD designs can also be estimated by finite element analyses (FEA) based on CARES/ Life post-processing software (Nemeth et al., 1990). The fracture-initiating flaw sites may or may not be coincident with the highest stress concentration areas in a geometric morphology. The objectives of the present in vitro study were: (1) to determine the magnitude and sensitivity of connector design on the fracture resistance of three-unit all-ceramic FPDs; (2) to identify the flaw origins and crack propagation modes; (3) to compare the experimental failure stresses as a function of design with those obtained from finite element stress analysis models; and (4) to estimate the structural reliability of two FPD designs.
Fractography The 40 failed pairs of three-unit FPDs specimens from our previous study (Oh and Anusavice, 2002) were collected and stored in a clean environment for fractography for the identification of crack origin, the direction of crack propagation, and the mode of failure. All of the fracture surfaces were cleaned in an ultrasonic bath, palladium-coated, and examined at low magnification (30X), then at higher magnification (70X) under an optical microscope with the aid of a fiber-optic light. Some of the representative specimens were further analyzed by scanning electron microscopy (SEM) (JSM 6400, Jeol, Peabody, MA, USA).
Finite Element Analyses
All connectors were 4 mm in height and 5 mm in width. Two radii of curvature at the gingival embrasure were designed: Model I, 0.45 mm, and Model II, 0.25 mm. Since the previous experimental study found no statistically significant effect of occlusal embrasure radius on the fracture resistance of the ceramic FPD, the occlusal embrasures for Models I and II were prepared with an identical sharp-notch design. A radius of 0.45 mm was selected rather than a radius of 0.90 mm at the gingival embrasure for Model I to maintain connector height constant at 4 mm without altering the curvature at the gingival embrasure. Thus, simulation Model I and Model II were matched with the designs of experimental Groups A (Designs I and III: radius of the GE, 0.90 mm) and B (Designs II and IV: radius of the GE, 0.25 mm), respectively. A simulated load of 100 N was applied at the central fossa of the pontic. This loading configuration induced maximum bending stress in the prostheses. The load was distributed uniformly over the plane of symmetry (central cross-section of the pontic) through the use of coupling equations. This option was chosen to minimize any Hertzian contact stresses, which would increase the localized stress and may cause local chipping of a ceramic, and that would yield erroneous results in the simulation analysis. Horizontal displacement of all nodes belonging to the plane of symmetry was constrained to create symmetrical boundary conditions. Linear elastic stress analyses were performed with the ANSYS FEA software to determine the stress distribution within the ceramic and to identify the regions where peak stresses occur.
Reliability Estimation
Statistical Analyses
Fractography The fracture origin was detected at the gingival embrasure in all samples (Fig. 1B  ). On the lustrous fracture surface, velocity hackle patterns consistently converged toward the semilunar area. Pores were more concentrated at the gingival embrasure areas, and some of the flaws related to multiple pores, ranging from 10 to 60 µm in diameter (Fig. 1C). The greatest probabilities for crack origin sites within the gingival embrasure were as follows: (1) 67.5% in the buccolingual plane at the center, and (2) 53% in the mesiodistal plane at abutment crowns (Table 1 ).
Finite Element Model Analysis Two sites of severe stress concentrations were identified. Peak compressive stresses occurred at the occlusal embrasure, and peak tensile stresses developed at the gingival embrasure, either at the center or at a position shifted slightly buccally. The peak tensile stress, under a unit load of 100 N, was higher, with the smaller radius of curvature at the gingival embrasure: Model II revealed a higher peak tensile stress (21.0 MPa) than Model 1 (16.1 MPa) (Table 2 ).
Reliability Estimation The Weibull moduli (m) were 6.3 for Group A and 8.6 for Group B. The characteristic strength values for experimental Groups A and B were 987 N and 735 N, respectively. These values were comparable with the values of 1031 N and 740 N for simulation Models I and II, respectively (Table 2 ). The maximum tensile stress values under loads associated with values of characteristic strength values are also summarized in Table 2. The distribution of typical risk-of-rupture intensity values computed for each design under its failure load is shown in Fig. 1D. Peak intensity sites were found close to the apex of the gingival embrasure curvature, and were shifted slightly toward the pontic. This result may be predictive of the most probable site of fracture initiation leading to failure of these FPD designs.
The morphology of the connector design at the gingival embrasure is critical in reducing the fracture probability in the experimental test specimens, and these results are consistent with those yielded from the mathematical (FEA) analyses. Model I, having a larger radius of curvature at the gingival embrasure, exhibited a lower tensile stress concentration at the gingival embrasure, compared with Model II. This is in agreement with a previous finding of greater stress concentration within the connector, and the stress concentration was greater for a reduced height and a broader connector width for FPDs (Kelly et al., 1995; Kamposiora et al., 1996; Pospiech et al., 1996). In the present study, an axial force applied at the center of pontic in a three-unit FPD produced a compressive stress distribution pattern within the prosthesis at the occlusal embrasure and a tensile stress distribution at the gingival embrasure, supporting the theoretical concept proposed by Anusavice (1996). Considering the fracture susceptibility of ceramic prosthesis to tensile stress, this finding is useful for designing three-unit ceramic FPDs (Peterson et al., 1998). The fracture resistance can be improved by increasing the radius of curvature at the gingival embrasure of the FPD without affecting esthetics by keeping the occlusal embrasure as sharp as possible.
Present fractographic analyses revealed that the failure origin of the three-unit ceramic prosthesis occurred at the gingival embrasure in all specimens, supporting the FEA model prediction of the highest tensile stress concentration at the gingival embrasure. This finding is consistent with a previous study of retrieved clinical ceramic three-unit FPDs in which all cracks initiated in the connector region (Kelly et al., 1995). In our study, cracks propagated from the gingival embrasure toward the occlusal loading on pontic. The fracture origin was most common at the center of the gingival embrasure in a buccolingual dimension, and it was shifted slightly toward the margin area of the abutment crown in a mesiodistal direction. In some of the samples, adjacent margins were chipped or fractured, breaking the cement seal. This finding supports a suggestion that the ceramic be reinforced at the proximal margin area. Interestingly, the stress distribution pattern in simulation models was not consistent with the failure patterns found in the experimental study: The peak intensity shifted slightly to the pontic side (Fig. 2D
Different sizes (from 10 to 60 µm) of pores were concentrated around the flaw site, indicating a strong relationship with the reduced fracture resistance of the FPDs (Koseyan and Biswas, 1976; Thompson et al., 1994; Abu-Hassan et al., 1998) (Fig. 2C The Weibull failure probability can be used to predict the service lifetime of intrinsically brittle materials, such as ceramic ceramics, by calculating the risk of failure as a function of time (Kelly et al., 1995; Tinschert, 2000). Weibull moduli for the ceramic restorations ranged from 6.3 to 8.6, which was consistent with the value reported for In-ceram core ceramic (m = 6.7) (Kelly et al., 1995). The probability of failure based on FEA corresponds well with the experimental values. The numerically calculated characteristic strength values were slightly higher than the experimental values by a factor of only ± 5%. This finding supports the case of the mathematical model and the experimental in vitro model, and also indicates that NASA CARES software is potentially useful for estimating the strength characteristics and survival probabilities of three-unit ceramic FPDs. Based on the conditions of this study, the following conclusions are proposed: (1) The radius of curvature at the gingival embrasure strongly affects the fracture resistance of all-ceramic FPDs, (2) fracture mechanics principles can provide critically important information for the identification of sensitive design factors and probable fracture sites in clinical prostheses, and (3) NASA CARES software used as an adjunct to FEA is useful for the optimization of prosthesis designs.
This paper was presented at the IADR General Session, Chiba, Japan, June, 2001. Dr. Oh was the recipient of the 2001 Frechette Award. This study was supported by NIH-NIDCR Grant No. DE06672. Received for publication August 3, 2001. Revision received April 17, 2002. Accepted for publication June 17, 2002.
Journal of Dental Research, Vol. 81, No. 9,
623-627 (2002)
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