d e n t a l m a t e r i a l s 3 0 ( 2 0 1 4 ) 321–326
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.intl.elsevierhealth.com/journals/dema
A cusp supporting framework design can decrease critical stresses in veneered molar crowns Armin Kirsten ∗ , Daniel Parkot, Stefan Raith, Horst Fischer Department of Dental Materials and Biomaterials Research, RWTH Aachen University Hospital, Germany
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objectives. Veneered zirconia restorations predominately fail due to veneering fractures. It
Received 25 January 2013
is hypothesized that a cusp-supporting framework design can prevent these catastrophic
Received in revised form
failures in all-ceramic restorations. Therefore, we investigated the influence of framework
14 October 2013
design and framework material on the stress distribution in a single tooth restoration using
Accepted 9 December 2013
the numerical finite element method. Methods. A three-dimensional model of a veneered lower molar (36) crown with constant outer shape was used. The framework design was either cusp supporting or with a constant
Keywords:
framework thickness. Zirconia, alumina, and a gold alloy were used as framework material.
Chipping
A glass ceramic material was used as veneering material for both cases. Two different load
Veneering failure
cases were simulated: terminal occlusion with load distributed over the occlusal surface of
Cusp supporting design
the tooth and a fairly extreme load case with all force concentrated on one cusp.
Framework design
Results. Maximum tensile stresses in the glass ceramic veneering material concentrated
Framework material
in the fissure region for all models. A cusp supporting framework design decreased the
Stress distribution
maximum tensile stresses significantly up to 30.5%. The distolingual load case resulted in
Finite element analysis
an approximately fourfold higher stress level compared to the terminal occlusion load case.
All-ceramic restorations
Significance. A cusp supporting framework design can significantly decrease the maximum tensile stresses in the veneering material of single crowns. Based on the numerical results of this study it can be expected that such a design could decrease the risk of veneering failure in vivo. © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Failure of all-ceramic dental restorations is predominately caused by cohesive fractures of the glass ceramic veneering material. Failure rates up to 13.6% were reported due to this “Chipping” called failure mode [1,2]. Chipping occurs more often for glass ceramic veneers on zirconia frameworks compared to alumina or metal supported restorations [3–15]. One reason for this fact could be the phase transformation mechanism from tetragonal to monoclinic that is present in
zirconia. Therefore, this mechanism was considered to have an impact on the chipping behavior [4,5,16,17]. Other investigations showed an influence of the firing process of the glass ceramic veneering [6–8]. Comparing metal alloys, alumina, and zirconia material properties as thermal conduction k and specific heat capacity C are highly different (gold alloy: k = 200 W m−1 K−1 , C = 130 J K−1 kg−1 ; alumina: k = 30 W m−1 K−1 , C = 775 J K−1 kg−1 , zirconia: k = 2 W m−1 K−1 , C = 450 J K−1 kg−1 ) [6]. Therefore, a slower cooling process was suggested to decrease the stress level within the veneering material [6–8]. Other approaches to reduce these residual
∗ Corresponding author at: Department of Dental Materials and Biomaterials Research, RWTH Aachen University Hospital, Pauwelsstrasse 30, 52074 Aachen, Germany. Tel.: +49 241 80 80931; fax: +49 241 80 82027. E-mail addresses: [email protected], [email protected] (A. Kirsten). 0109-5641/$ – see front matter © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.dental.2013.12.004
322
d e n t a l m a t e r i a l s 3 0 ( 2 0 1 4 ) 321–326
thermal stresses focused on the difference in the coefficients of thermal expansion (CTE) [9,10]. It is discussed that the mismatch between the CTE of veneering material and framework material should be adapted for veneered zirconia restorations [11]. Another important factor influencing the chipping behavior of veneered zirconia restorations is the framework design. An anatomical shape of the framework results in a low and nearly constant veneering thickness. This design is considered to prevent chipping in contrast to a thin framework with a thick and irregularly shaped veneering [12,13]. Two different stress types can be considered to explain this behavior: residual thermal stresses due to the firing process and mechanical loading stresses. Residual thermal stresses were shown to be affected by the framework and the veneering thickness. A thin veneering layer tends to a higher stress level using samples with constant zirconia thickness compared to a thicker veneering layer [17]. Compressive stresses occur in the framework due to the CTE mismatch [14]. For a simple bilayer model, stresses can be calculated using equations derived by Swain [6]. However, no clear advice can be given for an adequate thickness ratio because additional residual stresses can be affected by other influences e.g. the phase transformation in zirconia as well [14]. Zhang et al. investigated the residual stress distributions in an anatomical 2D-Model with constant outer shape of the veneering using the finite element method (FEM) [15]. They found decreasing maximum tensile stresses in the glass ceramic material with increasing framework thickness. A cusp supporting design of the framework may therefore be advantageous to prevent chipping. Mechanical stresses that occur during mastication can also be strongly affected by the framework design. In a previous FEM-study we investigated the influence of connector thickness in a dental bridge on the stress profile within the veneers [18]. A strong dependence of the framework design and material on the stress distribution was found for different connector sizes. We hypothesized in this study that a cusp supporting framework design can significantly decrease maximum tensile stresses in the veneering material of a single crown. Therefore, we studied different mastication scenarios using the finite element method. If this hypothesis can be confirmed a cusp supporting design could decrease the risk of veneering failure in vivo.
2.
Materials and methods
Geometrical data of the abutment 36 was generated by scanning a prepared gypsum model in vitro. A lower molar was designed to define the veneering surface. This outer contour of the crown was kept constant for all simulations. The 3D-model was imported in STL-format into a commercial CAD software (3matic 5.1, Materialise, Leuven, Belgium) to fix artifacts and holes in the mesh. Two different framework designs were constructed: a coping with an almost constant framework thickness of approx. 0.8 mm and an anatomically shaped cusp supporting
Fig. 1 – Investigated models. (A) Cross section of the molar crown framework design with almost constant framework thickness. (B) Cross section of the molar crown framework design with cusp supporting framework design, (C) terminal occlusion load case and (D) concentrated load on distolingual cusp.
Table 1 – Material properties of simulated structures. Young’s modulus (GPa) Dentin [19] Glass ceramic [20] Gold alloy [21] Zirconia [19] Alumina [22]
18 64 93 205 410
Poisson’s ratio 0.27 0.21 0.39 0.31 0.23
framework with an almost constant veneering thickness of approx. 0.5 mm (Fig. 1a and b). No cement gap was simulated. The geometric data was meshed using a curvature-based mesh software (ANSYS ICEM CFD, CFX Berlin Software, Berlin, Germany). Approximately 185,000 tetrahedral elements were generated for each model. Finite element calculations were carried out using a commercial software package (ANSYS 14.0, Ansys Inc., Canonsburg, PA, USA). In order to simulate the influence of different framework materials the Young’s moduli and Poisson’s ratios were varied. Zirconia, alumina, and a typical gold alloy were used as framework materials. The material properties of a dental glass ceramic were chosen to define the veneering material. The abutment material was defined as dentin. All material properties used are listed in Table 1 [19–22]. Two different loading cases were assumed. To simulate a physiological mastication behavior nine loading areas were defined on the occlusal surface. Additionally a fairly extreme loading situation was simulated by defining one loading area on the distolingual cusp of the crown. Each defined loading area had a radius of 1 mm (Fig. 1c and d). A force of 600 N in total was allocated to the respected areas as pressure load normal to the surfaces in each model. The bottom of the abutment teeth model was fully constrained for all simulations. The finite element analysis type was linear and quasi-static.
d e n t a l m a t e r i a l s 3 0 ( 2 0 1 4 ) 321–326
Stress concentration zones in the framework and in the veneering materials were investigated in post processing. Quasi-brittle materials as glass ceramics, zirconia, and alumina predominately fail because of tensile stresses [22]. Therefore, first principal stress was analyzed for those materials. For the ductile gold alloy von-Mises-Equivalent-Stresses were calculated and used as failure criterion.
3.
Results
Maximum principal stresses were located at the occlusal interface toward the abutment (Fig. 2a and b). The overall stress
323
level in the case of distolingual concentrated load was significantly higher compared to the terminal occlusion load case (Figs. 3 and 4). However, a significant influence of the framework design on the maximum stresses was not found in framework tensile stress distributions. Maximum von-MisesStresses in the gold alloy frameworks were about 20 MPa for terminal occlusion and about 145 MPa for the distolingual concentrated load case. Maximum first principal stresses in the zirconia frameworks were about 25 MPa for the terminal occlusion load case and about 160 MPa for distolingual concentrated load case. In the alumina framework even higher first principal stresses of about 39 MPa and 185 MPa could be investigated
Fig. 2 – Stress distributions of the investigated simulations. (A) Von-Mises-Stresses in the framework for terminal occlusion load case with gold alloy as framework material and constant framework thickness, coronal view. (B) First principal stress ( I ) in the framework for concentrated distolingual load case with zirconia as framework material and cusp supporting design, coronal view. (C) First principal stress ( I ) in the veneering material for terminal occlusion load case with gold alloy as framework material, constant framework thickness. (D) First principal stress ( I ) in the veneering material for terminal occlusion load case with gold alloy as framework material, cusp supporting design. (E) First principal stress ( I ) in the veneering material for concentrated distolingual load case with zirconia as framework material, constant framework thickness. (F) First principal stress ( I ) in the veneering material for concentrated distolingual load case with zirconia as framework material, cusp supporting design.
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Fig. 3 – Maximum von-Mises-Stress in gold alloy frameworks depending on load case and framework design.
for the terminal occlusion and the distolingual load, respectively. First principal stresses in the veneering material for terminal occlusion load are presented in Fig. 2c and d. Maximal tensile stresses were located in the fissures between mesiolingual and distobuccal cusps. This stress distribution was similar for the cusp supporting design and the model with constant framework thickness. The stress distributions in the veneering material for concentrated distolingual load case are presented in Fig. 2e and f. The maximal tensile stresses were located in the fissures between distolingual and distobuccal cusps. A comparison of maximal tensile stresses in the veneering material for different framework designs for terminal occlusion load case is presented in Fig. 5. Calculated stresses for this load case were in a range between 16 MPa and 38 MPa. Maximal stresses for the cusp supporting framework design were up to 30.5% lower than the stresses calculated for the constant framework thickness model with alumina as framework material. This dependence was found similar for zirconia and the gold alloy (27.3% and 15.3%, respectively). However, stresses in the veneering on the gold alloy framework were found to be up
Fig. 4 – Maximum first principal stress in zirconia and alumina framework depending on load case and framework design.
Fig. 5 – Maximum first principal stress in the veneering material depending on framework material and design for the terminal occlusion load case.
to 96.9% higher than tensile stresses in the veneering on alumina frameworks (in the case of cusp supporting framework design). Maximum first principal stresses in the veneering material were significantly increased for the distolingual located load case (Fig. 6). Maximum stresses between 87 MPa and 188 MPa were found. By a change in framework design a decrease in maximum tensile stresses of 24.4% (alumina), 18.0% (zirconia), and 11.4% (gold alloy) was observed. However, for this load case an increase in maximum tensile stresses up to 89.6% (cusp supporting framework design) was calculated due to different framework materials.
4.
Discussion
A clear decrease of resulting tensile stresses in the veneering was observed in the model with cusp supporting framework design in comparison to the designs with constant framework thickness. This was found to be true for zirconia, alumina, and
Fig. 6 – Maximum first principal stress in the veneering material depending on framework material and design for the distolingual concentrated load.
d e n t a l m a t e r i a l s 3 0 ( 2 0 1 4 ) 321–326
gold alloy framework, and for both the terminal occlusion load case and the fairly extreme distolingual concentrated load case. An explanation for this behavior can be given by the fact that a higher amount of stress is absorbed by the thicker framework material which has a higher stiffness compared to the glass ceramic. A similar result was found in another study on all-ceramic bridges [18]. Anatomically shaped and cusp supporting framework design is recommended by several authors to reduce the risk of chipping in all-ceramic restorations [12,13,23]. This statement can in principle be supported by the results of this study. Cusp supporting framework design can thereby significantly decrease the risk of catastrophic failure in the veneering material. A change of the loading case, however, has a significant influence on the absolute values of tensile stresses. If the overall load of 600 N is concentrated on the distolingual cusp, maximal tensile stresses in the veneering material will increase to the fourfold value compared to the same load uniformly distributed on several points on the occlusal surface. The location of maximum stresses is influenced by the loading case as well. Such an extreme loading situation can appear when an unexpected and stiff element is present in the bolus or a wrongly adjusted occlusion exists. Therefore, such a worst case scenario is suitable to investigate the chipping risk. FEM-simulations are always simplifications of reality. Thus a careful selection of the model is needed to ensure a valuable outcome. In the present study, root and periodontal ligament of the abutment tooth were not simulated. It was shown by several authors that the resilience of abutment teeth can have a big influence on stress level of all-ceramic bridges. For single tooth restorations, however, this influence is negligible [24,25]. The outer geometry of all-ceramic restorations is strongly defined by anatomical and physiological circumstances. However, a modification of the framework design does not affect the outer shape of the restoration which means that a thicker framework automatically results in a thinner veneering and vice versa. Therefore, we decided to create a model with constant outer shape where the framework thickness is either constant or anatomically optimized. In reality, two stress types (residual thermal and mechanical) interfere, which means that the negative effect of one stress type can decrease the positive effect of the other [10]. In the present study, we did not simulate residual thermal stresses that might be present due to a firing process on purpose. Thus we could focus on the stresses that occur during mastication. Stresses in the framework material were concentrated in the occlusal area toward the abutment in all cases (alumina, zirconia, and gold alloy) (Fig. 2a and b). A cusp supporting design had no significant influence on the maximum stresses in the framework material (Figs. 3 and 4). Moreover, these maximum stresses were below the critical stresses of the framework materials, respectively. A maximum vonMises equivalent stress of approx. 148 MPa occurred in the gold alloy framework (Fig. 3). A typical gold alloy exhibits 0.2% yield strength of 620 MPa [26]. Maximum tensile stresses up to 195 MPa were calculated for the alumina frameworks (Fig. 4). This material exhibits a characteristic strength of approx. 350 MPa [22]. In the zirconia framework material a
325
maximum tensile stress of 165 MPa was calculated (Fig. 4). Zirconia exhibits a characteristic strength of approx. 1.300 MPa [27]. These results are in accordance with the reported low rate of framework fractures in veneered restorations in vivo [28]. The incidence of chipping on veneered zirconia frameworks is significantly higher compared to veneered metal alloy and alumina frameworks in vivo [1,3]. Therefore the influence of framework material on tensile stress distribution was investigated as well. A remarkable increase in tensile stresses occurred when the gold alloy was chosen as framework material. For the same model and the same loading case the maximum tensile stresses increased up to 96.9% due to the variation of framework material. In our model the framework material affected the stress distribution more than the geometrically optimized design did. Tensile stresses within the veneering material on the gold alloy with a cusp supporting framework design were even higher than the maximum tensile stresses that occurred in the veneering material on the zirconia coping without any cusp support (Figs. 5 and 6). Those unexpected results stand in contrast to the higher chipping incidence of veneered zirconia copings in vivo [1]. Stresses in the veneering material on alumina frameworks were the lowest in our simulations. An explanation of this behavior can be found in the Young’s modulus of the gold alloy (93 GPa) that is much lower than the Young’s modulus of zirconia (205 GPa) and alumina (410 GPa), respectively [19,20]. A stiffer material can absorb more stress with a low deformation. Therefore, higher stresses occur in the veneering material on gold alloy frameworks. As a result, the high stiffness of both zirconia and alumina has a positive effect on the tensile stress distribution in the veneering material. Highest stresses in the veneering material were located in the fissures for all cases. However, cracks were also reported to start at the cusps of a veneering during chipping [29]. This could additionally indicate that chipping cannot only be reasoned in mechanical stresses that result from chewing. Moreover, it should be noted that residual thermal stresses interfere with the simulated loading stresses. Additionally the contact area between antagonist and restoration could be influenced by wear particles, an increased surface roughness, and shear stresses that result from friction. Other influences should be investigated additionally to minimize the risk of cohesive failure in all-ceramic zirconia supported restorations. The thermal conduction coefficient of zirconia is hundredfold lower than that of the gold alloy and still even tenfold lower than that of alumina [6]. This may have a significant influence on the distribution of residual thermal stresses in the veneering material due to the firing process. It was shown already that a lower cooling rate can improve the chipping resistance of veneered zirconia restorations [6–8]. An adaptation of the CTE mismatch between framework and veneering material is also considered to have an impact on residual stresses in the veneering material [9,10]. The phase transformation mechanism that is present in zirconia is another issue. A phase transformation at the interface between the framework and the veneering material can lead to stress concentration zones that cause chipping in veneered zirconia restorations [4,5,16,17].
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Furthermore, the results presented herein show that a cusp supporting framework design can significantly decrease maximum tensile stresses in the veneering material of single crowns. Therefore, it can be expected that such a design could decrease the risk of chipping in all-ceramic restorations in vivo.
Acknowledgements We thank Prof. Edelhoff and Dr. Güth, Department of Prosthodontics, Ludwig-Maximilians-University, Munich, Germany, who provided the geometrical data for the simulated crown. This work was supported in part by the German Federal Ministry of Education and Research (Grant-No. 13N9658).
references
[1] Sailer I, Pjetursson BE, Zwahlen M, Hämmerle CHF. A systematic review of the survival and complication rates of all-ceramic and metal-ceramic reconstructions after an observation period of at least 3 years. Part II: Fixed dental prostheses. Clin Oral Implants Res 2007;18(Suppl. 3):86–96. [2] Pjetursson BE, Sailer I, Zwahlen M, Hämmerle CHF. A systematic review of the survival and complication rates of all-ceramic and metal-ceramic reconstructions after an observation period of at least 3 years. Part I: Single crowns. Clin Oral Implants Res 2007;18:73–85. [3] Heintze SD, Rousson V. Survival of zirconia-and metal-supported fixed dental prostheses: a systematic review. Int J Prosthodont 2010;23:493–502. [4] Tholey MJ, Swain MV, Thiel N. SEM observations of porcelain Y-TZP interface. Dent Mater 2009;25:857–62. [5] Fischer J, Grohmann P, Stawarczyk B. Effect of zirconia surface treatments on the shear strength of zirconia/veneering ceramic composites. Dent Mater J 2008;27:448–54. [6] Swain MV. Unstable cracking (chipping) of veneering porcelain on all-ceramic dental crowns and fixed partial dentures. Acta Biomater 2009;5:1668–77. [7] Taskonak B, Borges GA, Mecholsky Jr JJ, Anusavice KJ, Moore BK, Yan J. The effects of viscoelastic parameters on residual stress development in a zirconia/glass bilayer dental ceramic. Dent Mater 2008;24:1149–55. [8] Guazzato M, Walton TR, Franklin W, Davis G, Bohl C, Klineberg I. Influence of thickness and cooling rate on development of spontaneous cracks in porcelain/zirconia structures. Aust Dent J 2010;55:306–10. [9] Fischer J, Stawarczyk B, Tomic M, Strub JR, Hämmerle CHF. Effect of thermal misfit between different veneering ceramics and zirconia frameworks on in vitro fracture load of single crowns. Dent Mater J 2007;26:766–72. [10] Bonfante EA, Rafferty B, Zavanelli RA, Silva NRFA, Rekow ED, Thompson VP, et al. Thermal/mechanical simulation and laboratory fatigue testing of an alternative yttria tetragonal zirconia polycrystal core/veneer all-ceramic layered crown design. Eur J Oral Sci 2010;118:202–9. [11] Göstemeyer G, Jendras M, Borchers L, Bach F-W, Stiesch M, Kohorst P. Effect of thermal expansion mismatch on the
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22] [23]
[24]
[25]
[26]
[27]
[28]
[29]
Y-TZP/veneer interfacial adhesion determined by strain energy release rate. J Prosthodont Res 2012;56:93–101. Zarone F, Russo S, Sorrentino R. From porcelain-fused-to-metal to zirconia: clinical and experimental considerations. Dent Mater 2011;27:83–96. Rosentritt M, Steiger D, Behr M, Handel G, Kolbeck C. Influence of substructure design and spacer settings on the in vitro performance of molar zirconia crowns. J Dent 2009;37:978–83. Mainjot AK, Schajer GS, Vanheusden AJ, Sadoun MJ. Influence of zirconia framework thickness on residual stress profile in veneering ceramic: measurement by hole-drilling. Dent Mater 2012;28:378–84. Zhang ZP, Zhou SW, Li Q, Li W, Swain M. Residual stresses in fabrication of core-veneered ceramic prostheses. Adv Mater Res 2010;97–101:2241–4. Allahkarami M, Hanan JC. Mapping the tetragonal to monoclinic phase transformation in zirconia core dental crowns. Dent Mater 2011;27:1279–84. Mainjot AK, Schajer GS, Vanheusden AJ, Sadoun MJ. Influence of veneer thickness on residual stress profile in veneering ceramic: measurement by hole-drilling. Dent Mater 2012;28:160–7. Möllers K, Pätzold W, Parkot D, Kirsten A, Güth J-F, Edelhoff D, et al. Influence of connector design and material composition and veneering on the stress distribution of all-ceramic fixed dental prostheses: a finite element study. Dent Mater 2011;27:e171–5. Fischer H, Weber M, Marx R. Lifetime prediction of all-ceramic bridges by computational methods. J Dent Res 2003;82:238–42. Guazzato M, Proos K, Quach L, Swain MV. Strength, reliability and mode of fracture of bilayered porcelain/zirconia (Y-TZP) dental ceramics. Biomaterials 2004;25:5045–52. Suansuwan N, Swain M. Determination of elastic properties of metal alloys and dental porcelains. J Oral Rehabil 2001;28:133–9. Munz D, Fett T. Ceramics, mechanical properties, failure behavior, materials selection. Berlin: Springer; 1999. Marchack BW, Futatsuki Y, Marchack CB, White SN. Customization of milled zirconia copings for all-ceramic crowns: a clinical report. J Prosthet Dent 2008;99: 169–73. Dittmer MP, Kohorst P, Borchers L, Stiesch M. Influence of the supporting structure on stress distribution in all-ceramic FPDs. Int J Prosthodont 2010;23:63. Möllers K, Parkot D, Kirsten A, Güth J-F, Edelhoff D, Fischer H. Influence of tooth mobility on critical stresses in all-ceramic inlay-retained fixed dental prostheses: a finite element study. Dent Mater 2012;28:146–51. Mahmoud A, Wakabayashi N, Takahashi H, Ohyama T. Deflection fatigue of Ti–6Al–7Nb, Co–Cr, and gold alloy cast clasps. J Prosthet Dent 2005;93:183–8. Kirsten A, Begand S, Oberbach T, Telle R, Fischer H. Subcritical crack growth behavior of dispersion oxide ceramics. J Biomed Mater Res B 2010;95:202–6. Schley J-S, Heussen N, Reich S, Fischer J, Haselhuhn K, Wolfart S. Survival probability of zirconia-based fixed dental prostheses up to 5 yr: a systematic review of the literature. Eur J Oral Sci 2010;118:443–50. Silva NRF, Bonfante E, Rafferty BT, Zavanelli R, Rekow ED, Thompson VP, et al. Modified Y-TZP core design improves all-ceramic crown reliability. J Dent Res 2011;90:104–8.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.intl.elsevierhealth.com/journals/dema
A cusp supporting framework design can decrease critical stresses in veneered molar crowns Armin Kirsten ∗ , Daniel Parkot, Stefan Raith, Horst Fischer Department of Dental Materials and Biomaterials Research, RWTH Aachen University Hospital, Germany
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objectives. Veneered zirconia restorations predominately fail due to veneering fractures. It
Received 25 January 2013
is hypothesized that a cusp-supporting framework design can prevent these catastrophic
Received in revised form
failures in all-ceramic restorations. Therefore, we investigated the influence of framework
14 October 2013
design and framework material on the stress distribution in a single tooth restoration using
Accepted 9 December 2013
the numerical finite element method. Methods. A three-dimensional model of a veneered lower molar (36) crown with constant outer shape was used. The framework design was either cusp supporting or with a constant
Keywords:
framework thickness. Zirconia, alumina, and a gold alloy were used as framework material.
Chipping
A glass ceramic material was used as veneering material for both cases. Two different load
Veneering failure
cases were simulated: terminal occlusion with load distributed over the occlusal surface of
Cusp supporting design
the tooth and a fairly extreme load case with all force concentrated on one cusp.
Framework design
Results. Maximum tensile stresses in the glass ceramic veneering material concentrated
Framework material
in the fissure region for all models. A cusp supporting framework design decreased the
Stress distribution
maximum tensile stresses significantly up to 30.5%. The distolingual load case resulted in
Finite element analysis
an approximately fourfold higher stress level compared to the terminal occlusion load case.
All-ceramic restorations
Significance. A cusp supporting framework design can significantly decrease the maximum tensile stresses in the veneering material of single crowns. Based on the numerical results of this study it can be expected that such a design could decrease the risk of veneering failure in vivo. © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Failure of all-ceramic dental restorations is predominately caused by cohesive fractures of the glass ceramic veneering material. Failure rates up to 13.6% were reported due to this “Chipping” called failure mode [1,2]. Chipping occurs more often for glass ceramic veneers on zirconia frameworks compared to alumina or metal supported restorations [3–15]. One reason for this fact could be the phase transformation mechanism from tetragonal to monoclinic that is present in
zirconia. Therefore, this mechanism was considered to have an impact on the chipping behavior [4,5,16,17]. Other investigations showed an influence of the firing process of the glass ceramic veneering [6–8]. Comparing metal alloys, alumina, and zirconia material properties as thermal conduction k and specific heat capacity C are highly different (gold alloy: k = 200 W m−1 K−1 , C = 130 J K−1 kg−1 ; alumina: k = 30 W m−1 K−1 , C = 775 J K−1 kg−1 , zirconia: k = 2 W m−1 K−1 , C = 450 J K−1 kg−1 ) [6]. Therefore, a slower cooling process was suggested to decrease the stress level within the veneering material [6–8]. Other approaches to reduce these residual
∗ Corresponding author at: Department of Dental Materials and Biomaterials Research, RWTH Aachen University Hospital, Pauwelsstrasse 30, 52074 Aachen, Germany. Tel.: +49 241 80 80931; fax: +49 241 80 82027. E-mail addresses: [email protected], [email protected] (A. Kirsten). 0109-5641/$ – see front matter © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.dental.2013.12.004
322
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thermal stresses focused on the difference in the coefficients of thermal expansion (CTE) [9,10]. It is discussed that the mismatch between the CTE of veneering material and framework material should be adapted for veneered zirconia restorations [11]. Another important factor influencing the chipping behavior of veneered zirconia restorations is the framework design. An anatomical shape of the framework results in a low and nearly constant veneering thickness. This design is considered to prevent chipping in contrast to a thin framework with a thick and irregularly shaped veneering [12,13]. Two different stress types can be considered to explain this behavior: residual thermal stresses due to the firing process and mechanical loading stresses. Residual thermal stresses were shown to be affected by the framework and the veneering thickness. A thin veneering layer tends to a higher stress level using samples with constant zirconia thickness compared to a thicker veneering layer [17]. Compressive stresses occur in the framework due to the CTE mismatch [14]. For a simple bilayer model, stresses can be calculated using equations derived by Swain [6]. However, no clear advice can be given for an adequate thickness ratio because additional residual stresses can be affected by other influences e.g. the phase transformation in zirconia as well [14]. Zhang et al. investigated the residual stress distributions in an anatomical 2D-Model with constant outer shape of the veneering using the finite element method (FEM) [15]. They found decreasing maximum tensile stresses in the glass ceramic material with increasing framework thickness. A cusp supporting design of the framework may therefore be advantageous to prevent chipping. Mechanical stresses that occur during mastication can also be strongly affected by the framework design. In a previous FEM-study we investigated the influence of connector thickness in a dental bridge on the stress profile within the veneers [18]. A strong dependence of the framework design and material on the stress distribution was found for different connector sizes. We hypothesized in this study that a cusp supporting framework design can significantly decrease maximum tensile stresses in the veneering material of a single crown. Therefore, we studied different mastication scenarios using the finite element method. If this hypothesis can be confirmed a cusp supporting design could decrease the risk of veneering failure in vivo.
2.
Materials and methods
Geometrical data of the abutment 36 was generated by scanning a prepared gypsum model in vitro. A lower molar was designed to define the veneering surface. This outer contour of the crown was kept constant for all simulations. The 3D-model was imported in STL-format into a commercial CAD software (3matic 5.1, Materialise, Leuven, Belgium) to fix artifacts and holes in the mesh. Two different framework designs were constructed: a coping with an almost constant framework thickness of approx. 0.8 mm and an anatomically shaped cusp supporting
Fig. 1 – Investigated models. (A) Cross section of the molar crown framework design with almost constant framework thickness. (B) Cross section of the molar crown framework design with cusp supporting framework design, (C) terminal occlusion load case and (D) concentrated load on distolingual cusp.
Table 1 – Material properties of simulated structures. Young’s modulus (GPa) Dentin [19] Glass ceramic [20] Gold alloy [21] Zirconia [19] Alumina [22]
18 64 93 205 410
Poisson’s ratio 0.27 0.21 0.39 0.31 0.23
framework with an almost constant veneering thickness of approx. 0.5 mm (Fig. 1a and b). No cement gap was simulated. The geometric data was meshed using a curvature-based mesh software (ANSYS ICEM CFD, CFX Berlin Software, Berlin, Germany). Approximately 185,000 tetrahedral elements were generated for each model. Finite element calculations were carried out using a commercial software package (ANSYS 14.0, Ansys Inc., Canonsburg, PA, USA). In order to simulate the influence of different framework materials the Young’s moduli and Poisson’s ratios were varied. Zirconia, alumina, and a typical gold alloy were used as framework materials. The material properties of a dental glass ceramic were chosen to define the veneering material. The abutment material was defined as dentin. All material properties used are listed in Table 1 [19–22]. Two different loading cases were assumed. To simulate a physiological mastication behavior nine loading areas were defined on the occlusal surface. Additionally a fairly extreme loading situation was simulated by defining one loading area on the distolingual cusp of the crown. Each defined loading area had a radius of 1 mm (Fig. 1c and d). A force of 600 N in total was allocated to the respected areas as pressure load normal to the surfaces in each model. The bottom of the abutment teeth model was fully constrained for all simulations. The finite element analysis type was linear and quasi-static.
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Stress concentration zones in the framework and in the veneering materials were investigated in post processing. Quasi-brittle materials as glass ceramics, zirconia, and alumina predominately fail because of tensile stresses [22]. Therefore, first principal stress was analyzed for those materials. For the ductile gold alloy von-Mises-Equivalent-Stresses were calculated and used as failure criterion.
3.
Results
Maximum principal stresses were located at the occlusal interface toward the abutment (Fig. 2a and b). The overall stress
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level in the case of distolingual concentrated load was significantly higher compared to the terminal occlusion load case (Figs. 3 and 4). However, a significant influence of the framework design on the maximum stresses was not found in framework tensile stress distributions. Maximum von-MisesStresses in the gold alloy frameworks were about 20 MPa for terminal occlusion and about 145 MPa for the distolingual concentrated load case. Maximum first principal stresses in the zirconia frameworks were about 25 MPa for the terminal occlusion load case and about 160 MPa for distolingual concentrated load case. In the alumina framework even higher first principal stresses of about 39 MPa and 185 MPa could be investigated
Fig. 2 – Stress distributions of the investigated simulations. (A) Von-Mises-Stresses in the framework for terminal occlusion load case with gold alloy as framework material and constant framework thickness, coronal view. (B) First principal stress ( I ) in the framework for concentrated distolingual load case with zirconia as framework material and cusp supporting design, coronal view. (C) First principal stress ( I ) in the veneering material for terminal occlusion load case with gold alloy as framework material, constant framework thickness. (D) First principal stress ( I ) in the veneering material for terminal occlusion load case with gold alloy as framework material, cusp supporting design. (E) First principal stress ( I ) in the veneering material for concentrated distolingual load case with zirconia as framework material, constant framework thickness. (F) First principal stress ( I ) in the veneering material for concentrated distolingual load case with zirconia as framework material, cusp supporting design.
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Fig. 3 – Maximum von-Mises-Stress in gold alloy frameworks depending on load case and framework design.
for the terminal occlusion and the distolingual load, respectively. First principal stresses in the veneering material for terminal occlusion load are presented in Fig. 2c and d. Maximal tensile stresses were located in the fissures between mesiolingual and distobuccal cusps. This stress distribution was similar for the cusp supporting design and the model with constant framework thickness. The stress distributions in the veneering material for concentrated distolingual load case are presented in Fig. 2e and f. The maximal tensile stresses were located in the fissures between distolingual and distobuccal cusps. A comparison of maximal tensile stresses in the veneering material for different framework designs for terminal occlusion load case is presented in Fig. 5. Calculated stresses for this load case were in a range between 16 MPa and 38 MPa. Maximal stresses for the cusp supporting framework design were up to 30.5% lower than the stresses calculated for the constant framework thickness model with alumina as framework material. This dependence was found similar for zirconia and the gold alloy (27.3% and 15.3%, respectively). However, stresses in the veneering on the gold alloy framework were found to be up
Fig. 4 – Maximum first principal stress in zirconia and alumina framework depending on load case and framework design.
Fig. 5 – Maximum first principal stress in the veneering material depending on framework material and design for the terminal occlusion load case.
to 96.9% higher than tensile stresses in the veneering on alumina frameworks (in the case of cusp supporting framework design). Maximum first principal stresses in the veneering material were significantly increased for the distolingual located load case (Fig. 6). Maximum stresses between 87 MPa and 188 MPa were found. By a change in framework design a decrease in maximum tensile stresses of 24.4% (alumina), 18.0% (zirconia), and 11.4% (gold alloy) was observed. However, for this load case an increase in maximum tensile stresses up to 89.6% (cusp supporting framework design) was calculated due to different framework materials.
4.
Discussion
A clear decrease of resulting tensile stresses in the veneering was observed in the model with cusp supporting framework design in comparison to the designs with constant framework thickness. This was found to be true for zirconia, alumina, and
Fig. 6 – Maximum first principal stress in the veneering material depending on framework material and design for the distolingual concentrated load.
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gold alloy framework, and for both the terminal occlusion load case and the fairly extreme distolingual concentrated load case. An explanation for this behavior can be given by the fact that a higher amount of stress is absorbed by the thicker framework material which has a higher stiffness compared to the glass ceramic. A similar result was found in another study on all-ceramic bridges [18]. Anatomically shaped and cusp supporting framework design is recommended by several authors to reduce the risk of chipping in all-ceramic restorations [12,13,23]. This statement can in principle be supported by the results of this study. Cusp supporting framework design can thereby significantly decrease the risk of catastrophic failure in the veneering material. A change of the loading case, however, has a significant influence on the absolute values of tensile stresses. If the overall load of 600 N is concentrated on the distolingual cusp, maximal tensile stresses in the veneering material will increase to the fourfold value compared to the same load uniformly distributed on several points on the occlusal surface. The location of maximum stresses is influenced by the loading case as well. Such an extreme loading situation can appear when an unexpected and stiff element is present in the bolus or a wrongly adjusted occlusion exists. Therefore, such a worst case scenario is suitable to investigate the chipping risk. FEM-simulations are always simplifications of reality. Thus a careful selection of the model is needed to ensure a valuable outcome. In the present study, root and periodontal ligament of the abutment tooth were not simulated. It was shown by several authors that the resilience of abutment teeth can have a big influence on stress level of all-ceramic bridges. For single tooth restorations, however, this influence is negligible [24,25]. The outer geometry of all-ceramic restorations is strongly defined by anatomical and physiological circumstances. However, a modification of the framework design does not affect the outer shape of the restoration which means that a thicker framework automatically results in a thinner veneering and vice versa. Therefore, we decided to create a model with constant outer shape where the framework thickness is either constant or anatomically optimized. In reality, two stress types (residual thermal and mechanical) interfere, which means that the negative effect of one stress type can decrease the positive effect of the other [10]. In the present study, we did not simulate residual thermal stresses that might be present due to a firing process on purpose. Thus we could focus on the stresses that occur during mastication. Stresses in the framework material were concentrated in the occlusal area toward the abutment in all cases (alumina, zirconia, and gold alloy) (Fig. 2a and b). A cusp supporting design had no significant influence on the maximum stresses in the framework material (Figs. 3 and 4). Moreover, these maximum stresses were below the critical stresses of the framework materials, respectively. A maximum vonMises equivalent stress of approx. 148 MPa occurred in the gold alloy framework (Fig. 3). A typical gold alloy exhibits 0.2% yield strength of 620 MPa [26]. Maximum tensile stresses up to 195 MPa were calculated for the alumina frameworks (Fig. 4). This material exhibits a characteristic strength of approx. 350 MPa [22]. In the zirconia framework material a
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maximum tensile stress of 165 MPa was calculated (Fig. 4). Zirconia exhibits a characteristic strength of approx. 1.300 MPa [27]. These results are in accordance with the reported low rate of framework fractures in veneered restorations in vivo [28]. The incidence of chipping on veneered zirconia frameworks is significantly higher compared to veneered metal alloy and alumina frameworks in vivo [1,3]. Therefore the influence of framework material on tensile stress distribution was investigated as well. A remarkable increase in tensile stresses occurred when the gold alloy was chosen as framework material. For the same model and the same loading case the maximum tensile stresses increased up to 96.9% due to the variation of framework material. In our model the framework material affected the stress distribution more than the geometrically optimized design did. Tensile stresses within the veneering material on the gold alloy with a cusp supporting framework design were even higher than the maximum tensile stresses that occurred in the veneering material on the zirconia coping without any cusp support (Figs. 5 and 6). Those unexpected results stand in contrast to the higher chipping incidence of veneered zirconia copings in vivo [1]. Stresses in the veneering material on alumina frameworks were the lowest in our simulations. An explanation of this behavior can be found in the Young’s modulus of the gold alloy (93 GPa) that is much lower than the Young’s modulus of zirconia (205 GPa) and alumina (410 GPa), respectively [19,20]. A stiffer material can absorb more stress with a low deformation. Therefore, higher stresses occur in the veneering material on gold alloy frameworks. As a result, the high stiffness of both zirconia and alumina has a positive effect on the tensile stress distribution in the veneering material. Highest stresses in the veneering material were located in the fissures for all cases. However, cracks were also reported to start at the cusps of a veneering during chipping [29]. This could additionally indicate that chipping cannot only be reasoned in mechanical stresses that result from chewing. Moreover, it should be noted that residual thermal stresses interfere with the simulated loading stresses. Additionally the contact area between antagonist and restoration could be influenced by wear particles, an increased surface roughness, and shear stresses that result from friction. Other influences should be investigated additionally to minimize the risk of cohesive failure in all-ceramic zirconia supported restorations. The thermal conduction coefficient of zirconia is hundredfold lower than that of the gold alloy and still even tenfold lower than that of alumina [6]. This may have a significant influence on the distribution of residual thermal stresses in the veneering material due to the firing process. It was shown already that a lower cooling rate can improve the chipping resistance of veneered zirconia restorations [6–8]. An adaptation of the CTE mismatch between framework and veneering material is also considered to have an impact on residual stresses in the veneering material [9,10]. The phase transformation mechanism that is present in zirconia is another issue. A phase transformation at the interface between the framework and the veneering material can lead to stress concentration zones that cause chipping in veneered zirconia restorations [4,5,16,17].
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Furthermore, the results presented herein show that a cusp supporting framework design can significantly decrease maximum tensile stresses in the veneering material of single crowns. Therefore, it can be expected that such a design could decrease the risk of chipping in all-ceramic restorations in vivo.
Acknowledgements We thank Prof. Edelhoff and Dr. Güth, Department of Prosthodontics, Ludwig-Maximilians-University, Munich, Germany, who provided the geometrical data for the simulated crown. This work was supported in part by the German Federal Ministry of Education and Research (Grant-No. 13N9658).
references
[1] Sailer I, Pjetursson BE, Zwahlen M, Hämmerle CHF. A systematic review of the survival and complication rates of all-ceramic and metal-ceramic reconstructions after an observation period of at least 3 years. Part II: Fixed dental prostheses. Clin Oral Implants Res 2007;18(Suppl. 3):86–96. [2] Pjetursson BE, Sailer I, Zwahlen M, Hämmerle CHF. A systematic review of the survival and complication rates of all-ceramic and metal-ceramic reconstructions after an observation period of at least 3 years. Part I: Single crowns. Clin Oral Implants Res 2007;18:73–85. [3] Heintze SD, Rousson V. Survival of zirconia-and metal-supported fixed dental prostheses: a systematic review. Int J Prosthodont 2010;23:493–502. [4] Tholey MJ, Swain MV, Thiel N. SEM observations of porcelain Y-TZP interface. Dent Mater 2009;25:857–62. [5] Fischer J, Grohmann P, Stawarczyk B. Effect of zirconia surface treatments on the shear strength of zirconia/veneering ceramic composites. Dent Mater J 2008;27:448–54. [6] Swain MV. Unstable cracking (chipping) of veneering porcelain on all-ceramic dental crowns and fixed partial dentures. Acta Biomater 2009;5:1668–77. [7] Taskonak B, Borges GA, Mecholsky Jr JJ, Anusavice KJ, Moore BK, Yan J. The effects of viscoelastic parameters on residual stress development in a zirconia/glass bilayer dental ceramic. Dent Mater 2008;24:1149–55. [8] Guazzato M, Walton TR, Franklin W, Davis G, Bohl C, Klineberg I. Influence of thickness and cooling rate on development of spontaneous cracks in porcelain/zirconia structures. Aust Dent J 2010;55:306–10. [9] Fischer J, Stawarczyk B, Tomic M, Strub JR, Hämmerle CHF. Effect of thermal misfit between different veneering ceramics and zirconia frameworks on in vitro fracture load of single crowns. Dent Mater J 2007;26:766–72. [10] Bonfante EA, Rafferty B, Zavanelli RA, Silva NRFA, Rekow ED, Thompson VP, et al. Thermal/mechanical simulation and laboratory fatigue testing of an alternative yttria tetragonal zirconia polycrystal core/veneer all-ceramic layered crown design. Eur J Oral Sci 2010;118:202–9. [11] Göstemeyer G, Jendras M, Borchers L, Bach F-W, Stiesch M, Kohorst P. Effect of thermal expansion mismatch on the
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22] [23]
[24]
[25]
[26]
[27]
[28]
[29]
Y-TZP/veneer interfacial adhesion determined by strain energy release rate. J Prosthodont Res 2012;56:93–101. Zarone F, Russo S, Sorrentino R. From porcelain-fused-to-metal to zirconia: clinical and experimental considerations. Dent Mater 2011;27:83–96. Rosentritt M, Steiger D, Behr M, Handel G, Kolbeck C. Influence of substructure design and spacer settings on the in vitro performance of molar zirconia crowns. J Dent 2009;37:978–83. Mainjot AK, Schajer GS, Vanheusden AJ, Sadoun MJ. Influence of zirconia framework thickness on residual stress profile in veneering ceramic: measurement by hole-drilling. Dent Mater 2012;28:378–84. Zhang ZP, Zhou SW, Li Q, Li W, Swain M. Residual stresses in fabrication of core-veneered ceramic prostheses. Adv Mater Res 2010;97–101:2241–4. Allahkarami M, Hanan JC. Mapping the tetragonal to monoclinic phase transformation in zirconia core dental crowns. Dent Mater 2011;27:1279–84. Mainjot AK, Schajer GS, Vanheusden AJ, Sadoun MJ. Influence of veneer thickness on residual stress profile in veneering ceramic: measurement by hole-drilling. Dent Mater 2012;28:160–7. Möllers K, Pätzold W, Parkot D, Kirsten A, Güth J-F, Edelhoff D, et al. Influence of connector design and material composition and veneering on the stress distribution of all-ceramic fixed dental prostheses: a finite element study. Dent Mater 2011;27:e171–5. Fischer H, Weber M, Marx R. Lifetime prediction of all-ceramic bridges by computational methods. J Dent Res 2003;82:238–42. Guazzato M, Proos K, Quach L, Swain MV. Strength, reliability and mode of fracture of bilayered porcelain/zirconia (Y-TZP) dental ceramics. Biomaterials 2004;25:5045–52. Suansuwan N, Swain M. Determination of elastic properties of metal alloys and dental porcelains. J Oral Rehabil 2001;28:133–9. Munz D, Fett T. Ceramics, mechanical properties, failure behavior, materials selection. Berlin: Springer; 1999. Marchack BW, Futatsuki Y, Marchack CB, White SN. Customization of milled zirconia copings for all-ceramic crowns: a clinical report. J Prosthet Dent 2008;99: 169–73. Dittmer MP, Kohorst P, Borchers L, Stiesch M. Influence of the supporting structure on stress distribution in all-ceramic FPDs. Int J Prosthodont 2010;23:63. Möllers K, Parkot D, Kirsten A, Güth J-F, Edelhoff D, Fischer H. Influence of tooth mobility on critical stresses in all-ceramic inlay-retained fixed dental prostheses: a finite element study. Dent Mater 2012;28:146–51. Mahmoud A, Wakabayashi N, Takahashi H, Ohyama T. Deflection fatigue of Ti–6Al–7Nb, Co–Cr, and gold alloy cast clasps. J Prosthet Dent 2005;93:183–8. Kirsten A, Begand S, Oberbach T, Telle R, Fischer H. Subcritical crack growth behavior of dispersion oxide ceramics. J Biomed Mater Res B 2010;95:202–6. Schley J-S, Heussen N, Reich S, Fischer J, Haselhuhn K, Wolfart S. Survival probability of zirconia-based fixed dental prostheses up to 5 yr: a systematic review of the literature. Eur J Oral Sci 2010;118:443–50. Silva NRF, Bonfante E, Rafferty BT, Zavanelli R, Rekow ED, Thompson VP, et al. Modified Y-TZP core design improves all-ceramic crown reliability. J Dent Res 2011;90:104–8.
