The influence of different core material on the FEA-determined stress distribution in dental crowns

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1 Dental Materials (2006) 22, The influence of different core material on the FEA-determined stress distribution in dental crowns Niek De Jager*, Marcel de Kler, Jef M. van der Zel Department of Dental Material Science, Academisch Centrum Tandheelkunde Amsterdam, Universiteit van Amsterdam and Vrije Universiteit, Louwesweg 1, Amsterdam, 1066 EA, The Netherlands Received 6 January 2005; accepted 13 April 2005 KEYWORDS Core material; Stress distribution; Finite element analysis; Dental crowns Summary Objectives. All ceramic restorations without metal have great advantages in their biocompatibility and aesthetic aspects. With the introduction of new core materials, the cores are sufficiently strong to produce long lasting all-ceramic restorations; however, the stresses in the veneering porcelain could still determine the longevity. The objective of this study was to evaluate, by finite element analysis (FEA), the influence of different core materials on the stress distribution in dental crowns. Methods. The model of a multi-layer all-ceramic crown for posterior tooth 46 produced with CAD CAM-technology was translated into a three-dimensional FEA program. This crown model was made with gold, zirconia, and alumina-based porcelain core and their matching veneering porcelains. The stress distribution due to the combined influences of bite forces, residual stresses caused by the difference in expansion coefficient of the core material and the veneering porcelain, and the influence of shrinkage of the cement was investigated. Results. Stiffer core material does not always for various reasons result in lower stresses in the veneering porcelain. Significance. This study indicates that the actual distribution of the tensile stresses and the design of restorations must be taken into account; otherwise, the significant contribution of stronger and tougher core materials to the performance of allceramic restorations may be offset by the weaker veneering porcelain. Q 2005 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. Introduction * Corresponding author. Tel.: C ; fax: C address: n.de.jager@acta.nl (N. De Jager). Despite the increased effort to prevent dental decay, there is still a need for prosthetic reconstructions. All ceramic restorations without metal have great advantages in its biocompatibility /$ - see front matter Q 2005 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi: /j.dental

2 The influence of different core material on stress distribution 235 and aesthetic aspects. However, all-ceramic restorations, particularly when placed in the posterior region, have a history of being prone to brittle fracture. To overcome brittle fracture, strong ceramic core materials have been developed to support the weaker veneering ceramic materials. The bending strength of Yttria stabilized tetragonal Zirconia (Y-TPZ) ceramics [1,2] is close to the actually used gold alloys [3]. With the introduction of these new core materials the cores are sufficiently strong to produce long lasting all-ceramic restorations; however, the stresses in the veneering porcelain could still determine the longevity. The stiffer ceramic core material might not result in lower stresses in the veneering porcelain than in crowns produced with gold alloy cores. All-ceramic restorations that are produced from these new materials are still more brittle and less ductile than metal ceramic restorations. As a consequence, the preparation and cementation procedures are more critical for all-ceramic restorations, than for metal ceramic restorations. [4]. For manually produced restorations, the stress distribution is difficult to predict, as the core and veneering porcelain layer shapes and sizes are operator dependent properties. However, for computer designed and manufactured restorations, these parameters, as well as those of the preparation, are digitally available and thus more amenable to stress analysis and failure prediction. Finite element stress analysis (FEA) seems to be a proper tool for such an evaluation. FEA was originally developed in the aircraft industry [5] and has become widespread in the engineering field. In dentistry, FEA has been used to determine stress distributions in teeth by authors like Farah et al. [6]. Many authors have been making finite element analysis of dental restorations since then. DeHoff et al. [7] studied the influence of the residual stresses due to thermal contraction mismatch between two layers forming the crown. Hojjatie et al. [8] and Palamara et al. [9] studied the influence of occlusal loads on the dentin and the restoration with a three dimensional finite element analysis, where Kamposiora et al. [10] and Shinohara et al. [11] studied specifically the effect of the cement layer on the restoration, taking into account the occlusal loads. Proos et al. did extensive work applied to margin design, different cement materials, and cement layer design [12,13] and different core materials and thicknesses [14,15]. Based on these experiences it was hypothesized that FEA is a proper tool for the multi causal evaluation of mechanical failure of dental restorations. The objective of this study was to evaluate, by finite element analysis (FEA), the influence of different core materials on the stress distribution in dental crowns and the risks for failure. Materials and methods The CAD model of the crown for posterior tooth 46 of a patient produced with CAD CAM by Cicero, Elephant Dental B.V. (Hoorn, the Netherlands) was selected to be translated into a three dimensional FEA program. The crown model was made with gold (Crown 1), zirconia (Crown 2), and alumina-based porcelain (Crown 3) core and their matching veneering porcelains. The materials used are listed in Table 1. The crown had a chamfer with collar preparation and a uniform cement layer thickness of mm except on the outline where the thickness was mm. Conversion CAD to FEA models The conversion of the CAD to the FEA model was realized in the way as described by De Jager et al. [4]. The final model consisted of two ceramic layers (veneer and core), a cement layer, and the prepared tooth (Fig. 1) and consisted of 52,000 parabolic wedge and parabolic tetrahedron solid elements all together. The finite element modeling and post processing was carried out with FEMAP software (FEMAP 8.10, ESP, Maryland Height, MO, USA), while the analysis was done with CAEFEM software (CAEFEM 7.3, CAC, West Hills, CA, USA). The material data used in this model are shown in Table 1. The material properties for the crown materials are data supplied by the supplier. The data for the dentine [16] and the cement [17,18] are from literature. The following assumptions were made in order to simplify the calculations: 1. The material of the cores and the veneering porcelain layers, the tooth dentine, and the luting cement after setting were assumed to be homogeneous, linearly elastic, and isotropic. The anisotropy of the crown and the dentine was not taken into account, although due to the structure the mechanical properties of dentine do vary with orientation and location as shown by Konishi et al. [19];

3 236 N. De Jager et al. Table 1 Relevant physical properties of the materials used. Group Property Gold alloy Veneer Zirconia core Veneer Alumina core Veneer Sintagon plus Procera all-ceramic Sakura interaction Cercon smart ceramics Carrara PdF Carrara interaction Elephant Elephant DeguDent Elephant Nobil Biocare Elephant Elastic Module (GPa) Poisson ratio NA Linear thermal expansion coefficient, mm/m K, C Three point bending strength (MPa) Source Elephant MSDS, Elephant MSDS, DeguDent MSDS, Elephant MSDS, NobilBiocare MSDS, Elephant alloy chart Figure 1 The layers composing the FEA model. 2. The time dependent setting process of the luting cement was mimicked by a time independent elastic plastic material property [18], although this model has defined properties for uniform cement layer thickness only and the cement layer thickness for the model varied from on the outline to mm; 3. The influence of the periodontal ligament on the stresses in the crown is negligible, although Reese [20] found that the ligament and alveolar bone is of importance for the stress distribution; 4. The influence of the pulp chamber in the preparation on the stresses in the crown is negligible as found by Hojjatie et al. [8]; 5. The distribution of the temperature during processing of the crown is uniform; 6. The visco-elastic behavior above the glass transition temperature (T g ) creates a stress free state in the ceramics. DeHoff et al. [21] showed that the stress above this temperature decrease quite rapidly, and the influence of the visco-elastic behavior of the porcelain near the softening temperature is negligible; 7. The modulus of elasticity and the Poisson ratio are constant during the processing of the crown, although as has been shown by Käse et al. [22] that these properties are temperature dependent, especially near the softening temperature. All nodes in the x y plane, which corresponds to the root portion of the prepared tooth (Fig. 1), were assumed to be fixed; no translation or rotation was allowed in any direction.

4 The influence of different core material on stress distribution 237 There were three stress outputs: stresses due to bite forces, residual stresses due to the difference in expansion coefficient of the two layers forming the crown and the influence of shrinkage of the cement. The stresses caused by the influences were calculated separately, then the three outputs were combined using the linear combination facility of FEMAP, which recalculates the combined stresses based on the output vectors of the linearly combined components. In post processing, the contour options average elemental without use of the corner data were used for visualizing the results of the Max Prin Stress and the Max Shear Stress. Stresses due to bite forces A calculation was done with bite forces as load. This study assumed a bite force on these molars of 665 N, which is about the maximum normal bite force [16], although it was reported by Nishigawa [23] that the maximum bite force during, sleep associated, bruxism can exceed 800 N for individuals. The bite force was distributed uniformly on the points of the crown in contact in occlusion perpendicular to the surface. The resulting vertical (z) component was made 665 N. Residual stresses To determine the residual stresses after the production process of the crown, caused by the differences in expansion coefficient of the two materials forming the crown, the temperature expansion diagrams of the core materials and the veneering porcelains according to the suppliers (Elephant Dental, Hoorn, the Netherlands, Degudent GmbH, Hanau, Germany and Nobel Biocare, Gothenburg, Sweden) were used to calculate the expansion. The difference in thermal expansion coefficients, not those of both layers separately, was used to avoid as much as possible allocating stresses due to this calculation on the non-ceramic layers. For the all-ceramic crowns the temperature at the glass-transition point of the veneering porcelains is lower than that of the ceramic cores, as is for the metal ceramic crown the glass-transition point of the veneering porcelain lower than the weakening point of the metal core; only the difference in linear expansion of the two materials from the temperature at the glass-transition point of the veneering porcelain to room temperature was used in calculating the stresses. Stresses due to shrinkage of the cement The setting of resin composites is a complex time dependant process, throughout which material properties undergo a dramatic change in a relatively short period. To determine the stresses due to shrinkage of the cement during hardening of the resin composite a time independent non-linear elastic plastic material model was used according to the findings of De Jager et al. [18] for RelyX ARC of mm layer thickness. Figure 2 The stresses (in MPa) in the veneering porcelain at the occlusal surface.

5 238 Results Stresses in the veneering porcelain at the occlusal surface Fig. 2 shows the maximum principal stress of the combined stresses due to bite forces, difference in N. De Jager et al. expansion coefficient of the veneering porcelain and the core material, and shrinkage of the cement at the occlusal surface. The stresses decrease with increasing Young s modulus of the core materials, with the exception of the tensile stress in Crown 3. The bite forces are the main component of the principal tensile and compressive stresses of the combined stresses (Table 2). Table 2 The maximum principal tensile and compressive stresses in the crown and the maximum shear stresses in the cement. Maximum Stress of the combined stresses and their components in: Max Prin Stress (Mpa) Crown 1 Crown 2 Crown 3 Veneering porcelain occlusal surface Tensile stress due to: Bite forces Different ceramics Shrinkage cement K1 3 5 Combined stresses Compressive stress due to Bite forces K159 K134 K119 Different ceramics Shrinkage cement Combined stresses K164 K133 K116 Core veneer interface Tensile stress due to: Bite forces Different ceramics Shrinkage cement 0 0 K1 Combined stresses Core Cement core interface Tensile stress due to: Bite forces Different ceramics K1 K1 1 Shrinkage cement K2 K4 49 Combined stresses Crown Cervical surface Tensile stress due to: Bite forces Different ceramics Shrinkage cement K12 K11 K11 Combined stresses Maximum stress of the combined stresses and Max Shear Stress (MPa) their components in: Crown 1 Crown 2 Crown 3 Cement Layer Shear stresses due to Bite forces Different ceramics Shrinkage cement Combined stresses Crown 1, metal ceramic crown; Crown 2, all-ceramic crown with Y-TPZ core; Crown 3, all-ceramic crown with alumina based core. Note: positive values are tensile stresses, where negative values are compressive stresses.

6 The influence of different core material on stress distribution 239 Figure 3 The stresses (in MPa) at the interface of the veneering porcelain and the core. Stresses at the core veneer interface Fig. 3 shows the maximum principal stress of the combined stresses at the core veneer interface. The stresses increase slightly with increasing Young s modulus of the core (Table 2). The bite forces are an important component of the maximum principal tensile stress at the core veneer interface. Stresses in the core at the cement core interface At the core surface (cement core interface) the bite forces are an important component of the maximum principle tensile stress of the combined stresses; this stress is increased in Crown 3 by the thermal contraction mismatch of the veneering porcelain and the core material (Table 2). Stresses at the cervical surface Fig. 4 shows the crowns in lingual-bucal view, showing that the highest stress at the cervical surface is located at the distal-lingual side. With increasing Young s modulus of the core the stresses in the cervical surface increase. The relatively high principal tensile stress at the cervical surface of the core in the all-ceramic Figure 4 The stresses (in MPa) at the cervical surface in lingual-bucal view.

7 240 N. De Jager et al. Figure 5 The stresses (in MPa) in the cement layer. crowns is mainly caused by the bite forces (Table 2). Stresses in the cement layer Fig. 5 shows the maximum shear stress in the cement layer of the combined stresses, which is caused by the combination of the bite forces and the shrinkage of the cement (Table 2). The influence of the thermal mismatch of the core materials and the veneering porcelain is negligible. There is no significant difference in the stresses in the cement layer of the three crowns. Discussion For the interpretation of the results of this study one has to take into account that clinically placed crowns might differ significantly from the FEA models. Possible errors are introduced by the translation from the CAD into the FEA model and are introduced during the production of the crowns; for instance, glazing of crowns will round off sharp edges. Other possible errors arise from the assumptions listed in Section 2 and the way the load was applied in the FEA model. The maximum tensile and compressive stresses at the occlusal surfaces of the three crowns (Fig. 2) in this study are the result of an applied bite force of 665 N on one element. The stresses are lower than the material strength of the applied materials (Table 1). A bite force of 665 N is of clinical relevance [16], however, such a point load, applied on only one element will hardly occur clinically. We applied such a point load for reason of simplicity. Clinically during loading restorations develop features that have come to be called wear facets. Clinicians recognize that wear facets are usually not point contacts, as supposed in this study, but have dimensions of up to approximately 3 mm in diameter. This effect will result in a distribution of the bite forces on a greater area what will lower the stresses found. Also in this study the number of occlusion points influences the stresses developing in the occlusal surface layer [4]. On the other hand produced crowns might differ from the FEA model, as contact damage flaws and the surface roughness of the porcelain will affect the materials strength [24]. The compressive stresses diminish with stiffer core material (Table 2). Stiffer core material will result in smaller displacements and smaller displacements will result in the veneering porcelain in lower stresses. The highest tensile stress is lower in Crown 2 than in Crown 1, but increases in Crown 3. The latest might be explained by the fact that with stiffer core materials bite forces will also result in smaller impressions with sharper deformations at the edge of the impression, resulting in higher tensile stresses (Fig. 2). At the core veneer interface the maximum tensile stress is higher for the crowns with ceramic cores (Fig. 3). Reviewing the literature and the failure rate of core veneer all-ceramic crowns revealed that delamination of the veneering porcelain from the core structure is a common failure mode [25,26]. Thompson et al. [27] found that Cerestore crowns mainly failed from sites

8 The influence of different core material on stress distribution 241 located at or near the core veneer interface, and estimated failure stresses from the initial flaw size for two crowns at 15 and 68 MPa. The stresses in this study are of the same magnitude, indicating that stiffer core material is not improving the stresses at the core veneer interface. The principal tensile stresses in the core at the cement core interface (Fig. 4) were considerably lower than the strength of the core material. In 1989 Kelly et al. [24] analyzed Dicor crowns that clinically failed at the cementation surface. The maximum strength of the materials studied in 1989 would have led to a high failure probability with the stresses found in this study, but the strength of the ceramic core materials has been improved considerably since then. The maximum tensile stresses due to the bite forces diminish with stiffer core material. In Crown 3 the shrinkage of the cement is the main cause of the highest tensile stress. The stiffer core material in Crown 3 results in higher resistance to the shrinkage resulting in higher stresses.. The tensile stress at the cervical surface (Fig. 4) is increasing with stiffer core material (Table 2). The principle tensile stress at this location is mainly tangential. Fracture could initiate at these locations in spite of the FEA calculated stress being lower than the strength of the material, because stress intensities can be high due to shape and size factors [28], as well as increased susceptibility to flaw formation at the crown margins. In our FEA models the veneering porcelain does not end exactly at the outline, which is often the case with the produced crowns; otherwise the shrinkage of the cement might have caused still higher stresses due to the more unfavorable load condition in those circumstances on the veneering porcelain. Although the crown has a chamfer with collar preparation due to imperfect preparation at the distal-lingual side, the shape of the preparation in this location is rather knife-edge. Clinicians will recognize the difficulty in fabricating a perfect preparation, especially in the lower jaw on the lingual side. This is recognized by Begazo et al. [29]; from the preparations they studied, nearly all showed to have one or more locations with imperfections, most in the lower jaw. The maximum shear stress in the cement layer (Fig. 5) is caused by the combination bite forces and shrinkage of the cement (Table 2). There is no significant difference in the shear stresses in the cement layer with the different core materials. The stresses are higher than the bond strength as published by Cobb et al. [30] and the bond strength and its development in time of RelyX ARC as published by Braga et al. [31] indicating that in the clinical situation there is a considerable risk of bonding failure. 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