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J Dent Res 82(3): 238-242, 2003
© 2003 International and American Associations for Dental Research

RESEARCH REPORT
Biomaterials & Bioengineering

Lifetime Prediction of All-ceramic Bridges by Computational Methods

H Fischer*, M Weber, and R Marx

Department of Dental Prosthetics, Section of Dental Materials, University of Technology Aachen, Pauwelsstrasse 30, D-52074 Aachen, Germany;

*corresponding author, h.fischer{at}rwth-aachen.de


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
There has been limited use of ceramic materials for all-ceramic posterior bridges. Major reasons are the low strength, the strength scatter, and the time-dependent strength decrease of ceramics due to slow crack growth. The objective of this study was to predict the long-term failure probability and loading capability of all-ceramic bridges (Empress 1, Empress 2, In-Ceram Alumina, and ZrO2) by computational techniques. The lifetimes of different bridge model designs were predicted by means of the NASA post-processor CARES. Bridges made of zirconia showed a very high mechanical long-term reliability. Empress I and InCeram Alumina seem to be insufficient as posterior bridge materials based on this prediction. The lifetime of the all-ceramic bridges can be significantly increased by improving the design in the connector area. We conclude that computational techniques can help to judge a ceramic material and a specific ceramic bridge design with respect to mechanical reliability before clinical use.

KEY WORDS: all-ceramic bridges • long-term failure probability • lifetime prediction • finite element method


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
All-ceramic bridges exhibit outstanding esthetics and excellent biocompatibility. However, a problematic aspect is their strongly limited loading capability. This is critical for wide-span bridges and especially in the case of a posterior bridge, because mastication forces are much higher in the molar region than in the front (Körber and Ludwig, 1983). The limited loading capability is caused by the limited strength and the low fracture toughness of ceramic materials (Green, 1998). The mechanical long-term behavior is even more critical, since ceramics exhibit a time-dependent strength decrease (Munz and Fett, 1999). This phenomenon is caused by the so-called subcritical crack growth. Microscopic flaws that are statistically distributed in ceramic components can extend as cracks even with a low stress level. The more the microscopic cracks grow, the lower the strength of the ceramic material, i.e., the lower the loading capacity of the ceramic bridge.

The strength, and thereby the loading capability, of ceramic components exhibits a characteristic large scatter because of the natural microscopic flaws that are statistically distributed in brittle materials (Ritter, 1995). Therefore, fracture statistics methods are used to examine the loading capability of ceramic components. Using the two-parameter Weibull distribution (Weibull, 1939), one can give a probability of failure at a certain stress level that occurs in a ceramic material. To evaluate the failure probability of a complex ceramic component like a dental bridge, one must analyze the stress distribution at a given load, typically done using the finite element method (Gallagher, 1976). With the help of a post-processor that uses the information of the three-dimensional stress distribution in the ceramic component, the long-term failure probability can be predicted (Nemeth et al., 1989; Brückner-Foit et al., 1993).

This gives the clinician the opportunity to compare the long-term failure probabilities of dental bridges made of different ceramic materials before clinical trials. Furthermore, it is possible to modify the design of the bridge with respect to a minimized failure probability. The hypothesis of the present study is that, on the basis of these computational techniques, it becomes possible for clinicians to judge different ceramics for their potential use as posterior bridge materials. The results will be discussed in terms of a recommendation for a suitable bridge design and a reliable ceramic material based on mechanical aspects. Moreover, possibilities and limitations of the presented computational technique itself for the dental field will be discussed.


   MATERIALS & METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Finite Element Analysis
A three-dimensional model of a three-unit posterior bridge was created on a HP-UX computer platform by means of the solid modeling progam of the finite element software I-DEAS (version ms6, Electronic Data Systems, Plano, TX, USA). The dimensions of the two bridge abutments were 7.0 x 9.0 x 10.0 mm, and those of the pontic component were 7.0 x 9.0 x 7.0 mm. Three different designs were chosen for the connector areas between the abutments and the pontic. In the first model, henceforth called ‘basis model’, the size of the cross-sections of the connecting areas was 14 mm2 (3.5 x 4.0 mm). The length of the connecting crosspieces above the interproximal embrasures was 0.1 mm. In a second model, this connecting crosspiece length was again 0.1 mm as in the basis model, but the size of the cross-sections of the connectors was decreased from 14 to 8.75 mm2 (2.5 x 3.5 mm). The connecting areas of a third model were of a size identical to that of the basis model (3.5 x 4.0 mm), but the length of the connecting crosspieces was increased from 0.1 to 0.5 mm. It was assumed that the enamel in the FE model was completely removed and replaced by the ceramic material. The underlaying structure in the model was dentin. The influence of the pulp, of the periodontal ligament, and of the adhesive or cement layer was negligible (Hojjatie and Anusavice, 1990). To limit the computer process time, we assumed the bridge to be symmetrical with respect to the abutments. Therefore, the calculations were performed on halves of the bridge models. The three-dimensional models were meshed with approximately 17,000 structural solid four-node tetrahedral elements. The connecting area between the abutment and the pontic was re-meshed with a finer mesh to increase the accuracy of the stress and reliability calculations. The models were exported into the program MARC/MENTAT (version 2001, MSC Software Corp., Palo Alto, CA, USA) in which the boundary conditions and the material data were defined. To simulate the physiological rotation movement of a natural tooth, we prescribed a rotation axis (rotation around the z-axis, no translation in x-, y-, and z-directions). The symmetrical requirements due to the ‘half-bridge calculations’ were considered. The bridges were loaded by 600 N (half-bridge model: 300 N) on the occlusal surface at 90° in the middle of the pontic component. The load was distributed onto three nodes of adjoining finite elements. The 600-N force is very large for a single occlusal contact (Körber and Ludwig, 1983). This load case was chosen so that we could analyze the stress distribution under extreme conditions (worst case). Four different all-ceramic bridge materials were chosen for the load simulations in the ‘basis’ bridge model: Empress 1 and Empress 2 (both Ivoclar, Schaan, Liechtenstein), In-Ceram Alumina (Vita, Bad Säckingen, Germany), and ZrO2 (3Y-PSZ zirconia, Metoxit, Thyangen, Switzerland). The elastic constants, Young‘s modulus E, and Poisson‘s ratio v, used for the evaluation of the FE-stress distributions, were E = 67 GPa and v = 0.19 for Empress 1, E = 96 GPa and v = 0.22 for Empress 2, E = 251 GPa and v = 0.22 for In-Ceram Alumina, E = 205 GPa and v = 0.31 for ZrO2, and E = 18 GPa and v = 0.27 for the dentin (‘root’) in the model (Fischer et al., 2001).

Post-processing with CARES/LIFE
The files containing the three-dimensional stress distribution data were exported to the post-processor CARES/LIFE (NASA Lewis Research Center, Cleveland, OH, USA) (Nemeth et al., 1989, 1993). CARES/LIFE (Ceramic Analysis and Reliability Evaluation of Structure Life Prediction) calculates the time-dependent reliability of ceramic components subjected to mechanical loading. The program accounts for the phenomenon of subcritical crack growth by utilizing the power law (Munz and Fett, 1999). The two-parameter Weibull cumulative distribution function is used in the software to characterize the variation in component strength (Weibull, 1939). The multi-axial stress model developed by Batdorf was used for the calculations (Batdorf and Crose, 1974). Griffith cracks were assumed to occur, i.e., were chosen for the crack geometry in the model (Griffith, 1924).Volume flaws were assumed to be responsible for failure, i.e., a volume flaw reliability analysis was performed. A value of 1.0 was chosen for the constant for the semi-empirical mixed-mode fracture criteria (Shetty, 1987). Theoretical long-term failure probabilities were predicted after a continuous, static load of 100 N for 1, 5, and 10 yrs, respectively. The characteristic material values, characteristic strength {sigma}{Theta}, Weibull modulus m, and the parameters of the subcritical crack growth, i.e., the fatigue parameter n, and the power law constant B used for the longterm failure probability predictions were: {sigma}{Theta} = 89 MPa, m = 8.6, n = 25, and B = 5.8•101 MPa2sec for Empress 1, {sigma}{Theta} = 289 MPa, m = 8.8, n = 20, and B = 2.3•103 MPa2sec for Empress 2, {sigma}{Theta} = 290 MPa, m = 4.6, n = 18, and B = 6.0•103 MPa2sec for In-Ceram Alumina, and {sigma}{Theta} = 937 MPa, m = 18.4, n = 35, and B = 2.2•105 MPa2sec for ZrO2 (Marx et al., 2001).


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
The detailed views of the the finite element model show the different designs that were chosen for the connector areas between the abutments and the pontic: the basis model (Fig. 1aGo), the model with the smaller cross-section area (Fig. 1bGo), and the model with the longer crosspiece (Fig. 1cGo), respectively.



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  		Figure 1. Finite element model with all-ceramic bridge design used for this study. To limit the computer process time, we assumed the bridge to be symmetrical with respect to the bridge abutments. Therefore, the calculations were performed on a half of the bridge model. Three different designs were chosen for the connector areas between the abutments and the pontic. The dimensions (x-, y-, z-directions) were: (a) 0.1 x 3.5 x 4.0 mm (basis model), (b) 0.1 x 2.5 x 3.5 mm, and (c) 0.5 x 3.5 x 4.0 mm.

 
The FE stress distribution (Fig. 2Go) appeared very simular for all 4 ceramics used as bridge materials in the simulations. The maximum principal stress {sigma}1 that occurred for all 4 ceramic bridges on the lower side of the area connecting the bridge abutment and the pontic component was 85 MPa for Empress 2 (see arrows), 72 MPa for Empress 1, 130 MPa for In-Ceram Alumina, and 125 MPa for ZrO2.



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  		Figure 2. Stress distribution in a posterior bridge (basis model) made of Empress 2 at a load of 600 N. (a) View from the bottom onto the half-bridge model. The ‘root’ FE elements are removed for clarity. (b) View is oblique from the front onto the connector area of the pontic component. The ‘root’ FE elements and the bridge abutment are removed for clarity. The maximum principal stress ({sigma}sx73;1 = 85 MPa, see arrows) occurs on the lower side of the area connecting the bridge abutment and the pontic (white).

 
Theoretical long-term failure probabilities after a continuous, static load of 100 N for 1, 5, and 10 yrs, respectively, between 2.6 and 6.0% were predicted for Empress 1, between 0.25 and 1.0% for In-Ceram Alumina, and between 0.00083 and 0.0026% for Empress 2 (Fig. 3Go). The failure probability of ZrO2 was nearly 0, even after 10 yrs.



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  		Figure 3. Failure probabilities F after 1, 5, and 10 yrs of the modeled Empress 1, Empress 2, In-Ceram, and ZrO2 all-ceramic bridges after a continuous, static load of 100 N.

 
The position of the Weibull curve in the lifetime diagram, indicating the respective long-term failure probability of the bridge (material: Empress 2), was influenced by the bridge design in the connector area (Fig. 4Go). The middle curve (1 = 0.1 mm, a = 14 mm2) represents the basis bridge model. The left curve was evaluated for a bridge model with a smaller size of the cross-section of the connector area (a = 8.75 mm2), and the right curve was evaluated for a bridge model with a longer connecting crosspiece above the interproximal embrasure (1 = 0.5 mm). The maximum principal stress {sigma}1 that occurred again on the lower side of the area connecting the bridge abutment and the pontic was 85 MPa for the basis model, 115 MPa for the bridge design with the smaller cross-section area, and 106 MPa for the design with the longer crosspiece.



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  		Figure 4. Weibull plot with long-term failure probability F of Empress 2 bridge with different designs. Influence of the size of the cross-section area (a = 14 vs. 8.75 mm2) between the bridge abutment and the pontic component and influence of the length (1 = 0.1 vs. 0.5 mm) of the connecting crosspiece above the interproximal embrasure.

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
The analysis of the stress distribution in the loaded ceramic bridges showed that the connector area between the bridge abutment and the pontic component is the critical part of the dental restoration (Fig. 2Go). This finding correlates to experimental results (Tinschert et al., 1999). As shown in Fig. 2Go, the maximum principal stress in the connector area of the Empress 2 bridge is only about 85 MPa, at a very high load of 600 N. This indicates that short-term loadings cannot be responsible for failure. All 4 ceramic materials have greater characteristic strength values {sigma}{Theta} (Marx et al., 2001) than the maximum principal stresses {sigma}1,max evaluated at 600 N loading in the simulation ({sigma}1,max = 72 MPa vs. {sigma}{Theta} = 89 MPa for Empress 1, {sigma}1,max = 85 MPa vs. {sigma}{Theta} = 289 MPa for Empress 2, {sigma}1,max =130 MPa vs. {sigma}{Theta} = 290 MPa for In-Ceram Alumina, and {sigma}1,max =125 MPa vs. {sigma}{Theta} = 937 MPa for ZrO2). The analysis of the stress distributions by means of the CARES/LIFE post-processor revealed that long-term aspects as well as statistical effects influence the risk for failure of all-ceramic bridges.

The long-term failure probability values at a constant load on a mean load level (F = 100 N) were calculated (Fig. 3Go). The application of a continuous load of 100 N was chosen, again, to simulate a kind of ‘worst case’ situation. Note that even a bruxer averages only about 1-2 hrs of tooth contact a day. Nevertheless, the predictions help us to compare and judge the mechanical reliability of the 4 all-ceramic systems as bridge materials under well-defined, equal, and constant boundary conditions. The analysis revealed that Empress 1 exhibited very high failure probabilities of 2.6% after 1 yr, 4.6 % after 5 hrs, and 6.0 % after 10 yrs, respectively. Assuming that a decreased contact time will decrease the failure probability about one order of magnitude, the material still seems to be insufficient as a reliable posterior bridge material.

The simulations were performed with parameters of the subcritical crack growth that were evaluated in a normal laboratory atmosphere (22°C, 60% rel. humidity) (Marx et al., 2001). It is known that the crack growth parameters n and B may decrease with increasing humidity (oral environment: 100% rel. humidity) (Munz and Fett, 1999). Lower crack growth parameters increase subcritical crack growth, and thereby accelerate the time-dependent strength decrease. Based on this argument, the long-term failure probability values for In-Ceram Alumina (0.25% after 1 yr, 0.83% after 5 yrs, and 1.0% after 10 yrs) may indicate insufficient loading capacity as a posterior bridge material as well. Empress 2 seems to be much more suitable as a bridge material for the molar region. The predicted failure probability values are about three magnitudes smaller compared with the respective F-values of In-Ceram Alumina (10-4 vs. 10-1%). The study confirmed the excellent mechanical behavior of the ceramic material zirconia, as documented in technical publications (Hannink et al., 2000). No failure probability value could be evaluated even after 10 yrs of static loading.

Fig. 4Go revealed that the detail design of the connecting area between the bridge abutment and the pontic component has a great effect on the long-term failure probability of the ceramic bridge. The Weibull curve is moved to shorter lifetimes and to higher failure probabilities when the size of the area of the cross-section is decreased from a = 14 mm2 (middle curve) to 8.75 mm2 (left curve). Moreover, the Weibull curve is significantly moved to longer lifetimes and to lower failure probabilities when the length of the connecting crosspiece above the interproximal embrasure is increased from 1 = 0.1 to 0.5 mm (right Weibull curve). In contrast, the maximum principal stress of the modified model with the longer crosspiece (1 = 0.5 mm), evaluated by the (short-term) FE-analysis was higher than the maximum stress in the basis model (106 vs. 85 MPa). This reveals that the stress peaks may furnish preliminary information but are not a reliable criterion for a prediction of long-term failure probability.

The materials used in the FE model were assumed to be isotropic and homogeneous. No adhesive or cement layer, pulp, and periodontal ligament were included in the FE model as described in MATERIALS & METHODS. These simplifications may have an effect on the stress distribution. Nevertheless, the major findings of this study will not be questioned by these simplifications.

The results indicate that the computational method used in this study—the finite element method in combination with the post-processor CARES/LIFE—is a suitable tool for predicting different life expectancies for different ceramic bridge materials and different connector designs. It should be stressed that the calculated life expectancies will not be identical with the respective clinical lifetimes because of the mentioned limitations used for the numerical simulations. In a further study, the predicted life expectancies should be correlated with experimental clinical data. Such correlations could reveal in vivo influences that additionally affect the long-term failure probability of all-ceramic bridges.


   ACKNOWLEDGMENTS
 
The authors are grateful to Noel N. Nemeth, NASA, Glenn Research Center, Cleveland, OH, for providing the software CARES/LIFE and for helpful discussions. This work was funded by the LuFG Zahnärztliche Werkstoffkunde, RWTH Aachen, Germany (internal funds).

Received February 21, 2002; Last revision November 15, 2002; Accepted November 26, 2002


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Batdorf SB, Crose JG (1974). A statistical theory for the fracture of brittle structures subjected to nonuniform polyaxial stresses. J Appl Mech 41:459–464.

Brückner-Foit A, Heger A, Munz D (1993). Festigkeitsund Lebensdauerverteilung keramischer Komponenten unter mehrachsiger Belastung. In: Mechanische Eigenschaften keramischer Konstruktionswerkstoffe. Grathwohl G, editor. Oberursel: DGM Informationsgesellschaft mbH, pp. 43-54.

Fischer H, Dautzenberg G, Marx R (2001). Nondestructive estimation of the strength of dental ceramic materials. Dent Mater 17:289–295.[Medline]

Gallagher RH (1976). Finite element analysis. Berlin: Springer.

Green DJ (1998). An introduction to the mechanical properties of ceramics. Cambridge: Cambridge University Press.

Griffith AA (1924). The phenomena of rupture and flaw in solids. Philos Trans R Soc 221:163–189.

Hannink RHJ, Kelly PM, Muddle BC (2000). Transformation toughening in zirconia-containing ceramics. J Am Ceram Soc 83:461–487.

Hojjatie B, Anusavice KJ (1990). Three-dimensional finite element analysis of glass-ceramic dental crowns. J Biomech 23:1157–1166.[ISI][Medline]

Körber KH, Ludwig K (1983). Maximale Kaukraft als Berechnungsfaktor zahntechnischer Konstruktionen. Dent Lab 31:55–60.

Marx R, Fischer H, Weber M, Jungwirth F (2001). Crack parameters and Weibull moduli: subcritical crack growth and long-term durability of all-ceramic materials. Dtsch Zahnärztl Z 56:90–98.

Munz D, Fett T (1999). Ceramics: mechanical properties, failure behaviour, materials selection. 1st ed. Berlin: Springer.

Nemeth NN, Manderscheid JM, Gyekenyesi JP (1989). Ceramics analysis and reliability evaluations of structures (CARES). NASA Technical Paper 2916; Cleveland, OH: Glenn Research Center.

Nemeth NN, Powers LM, Janosik LA, Gyekenyesi JP (1993). CARES/LIFE. Users and programmers manual. Cleveland, OH: NASA, Glenn Research Center.

Ritter JE (1995). Predicting lifetimes of materials and material structures. Dent Mater 11:142146.

Shetty DK (1987). Mixed-mode fracture criteria for reliability analysis and design with structural ceramics. J Eng Gas Turbines Power 109:282–289.

Tinschert J, Natt G, Doose B, Fischer H, Marx R (1999). High performance ceramic posterior bridges. Dtsch Zahnärztl Z 54:545–550.

Weibull W (1939). A statistical theory of the strength of materials. Handlingar 151: Ingeniörs Vetenskaps Akademien.





This Article
Right arrow Abstract Freely available
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Citing Articles
Right arrow Citing Articles via ISI Web of Science (21)
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Right arrow Articles by Fischer, H
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