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Strength estimation of different designs of ceramic inlays and onlays in molars based on the Tsai-Wu failure criterion
Strength estimation of different designs of ceramic inlays and onlays in molars based on the Tsai-Wu failure criterion Beata Dejak, DDS, PhD,a Andrzej Mlotkowski, MEng, PhD,b and Maciej Romanowicz, DMD, PhDc Medical University, Lodz, Poland; Technical University, Lodz, Poland Statement of problem. Successful restoration of large molar defects is a serious clinical problem. Studies on the strength of teeth restored with ceramic restorations of various designs have provided conflicting results. Purpose. The purpose of this study was to determine the shapes of large MOD ceramic restorations in molars most likely to prevent failure and to produce a favorable distribution of contact stresses between the cement and teeth during mastication. Material and methods. The study was performed using a finite element analysis with contact elements. Eight 2-dimensional models of mandibular first molars with the following designs of MOD ceramic restorations were created: an inlay with a butt joint margin, an inlay with a beveled margin, an onlay with a butt joint margin, and an onlay with a rounded shoulder margin. The restorations had 3-mm or 5-mm isthmus widths. Models of opposing maxillary crowns were also developed. Computational simulation of mastication of boluses in the frontal plane was conducted, during which the stresses occurring in the ceramic restorations, cement, and tooth structure were calculated. The Tsai-Wu failure criterion was used to evaluate the strength of the materials. Contact stresses at the adhesive interface between the tooth structure and resin cement around these restorations were analyzed. Results. According to the Tsai-Wu failure criterion, the margin of the beveled inlay and the surrounding tissue could be damaged during masticatory simulation. At the junction of the butt joint margin inlay and enamel, contact tensile stresses appeared. The lowest inverse of the Tsai-Wu strength ratio index appeared in the onlay with a rounded shoulder margin. At the adhesive interfaces around margins of large onlays, compressive contact stresses occurred. Conclusions. For the large molar MOD ceramic restorations tested, the lowest values of the inverse of the Tsai-Wu strength ratio index and a favorable distribution of contact stresses between restoration and tissues appeared in the onlay with a rounded shoulder margin. (J Prosthet Dent 2007; 98: 89-100.)
Clinical Implications
For strength reasons, large defects in molars should be restored with ceramic onlays with a rounded shoulder margin and not inlays. Tooth fracture resistance decreases with increased width1,2 and depth of caries and cavity preparation.3-5 Extensive MOD cavities in molars may be restored with, among other choices, esthetic ceramic inlays and onlays.6,7 The average width of these
restorations is two thirds of the intercuspal distance of teeth.8 Ceramic materials are characterized by low flexural strength9 and fracture toughness.10 Restorations made of these materials are luted with resin cements which have the highest bond strength
to tissue among luting agents.11 The optimum bond of these restorations to teeth enhances the strength of ceramics12 and prepared tissues,13,14 and assists in stabilizing weakened cusps.15 However, these restorations are not as fracture resistant as natu-
Assistant Professor, Department of Prosthetic Dentistry, Medical University. Assistant Professor, Department of Strength of Materials and Structure, Technical University. c Associate Professor, Chairman of Prosthetic Dentistry, Department of Prosthodontics, Medical University. a
b
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Volume 98 Issue 2 ral, intact teeth,16-18 and a large number of ceramic restorations exhibit some marginal deficiency.19 Chipping of restoration margins or changes in the color of surrounding tissues have been observed clinically.20 Another failure of ceramic restorations occurs as a bulk fracture.21 Inlays restore central cavities in teeth. Onlays restore one or more cusps and may completely cover the occlusal surfaces,22 resulting in a favorable distribution of stresses in teeth23,24 and a decreased risk of fractures.25 However, preparation for onlays requires additional tooth reduction relative to inlay restorations. Reports on the strength of teeth with ceramic restorations of various designs are equivocal. Teeth with inlays appeared more resistant to fractures than those with onlays in an in vitro study.26 Clinically, however, a higher number of failures in an inlay group was observed.27 Controversy exists as to what type of ceramic restoration should be used for the restoration of large defects in an attempt to prevent fracture and microleakage. To better understand this issue, a finite element analysis of stresses associated with various designs of ceramic restorations in molars was performed. There are various criteria that are used to assess the possibility of failure of a material.28,29 For isotropic materials with similar values of compressive and tensile strength, the most commonly used is the von Mises criterion.28 However, dental tissues and enamel, in particular, have anisotropic properties.30,31 Possible failure of the anisotropic material can be evaluated by the Tsai-Wu failure criterion.32,33,34 According to this criterion, if the inverse of the Tsai-Wu strength ratio index in the tested material is lower than 1, the material will not fracture. However, if this value is over 1, then damage to the material may occur.35 The criterion was used to estimate the strength of teeth with ceramic inlays and onlays. The purpose of this study was to determine the shapes of large MOD
ceramic restorations in molars most likely to prevent their failure and produce a favorable distribution of contact stresses between the cement and teeth during mastication.
MATERIAL AND METHODS The study of stresses during mastication in first molars with ceramic restorations was conducted by finite element analysis (FEA)36 (ANSYS version 10; ANSYS Inc, Canonsburg, Pa). Basing the analysis on frontal sections of molars with surrounding tissues and using dental anatomy textbooks37,38 as guides, 2-dimensional (2-D) computer models of a right first mandibular molar embedded in periodontium and bone were created (Fig. 1). Eight molar tooth models with various ceramic intracoronal restorations were developed. Four restorations with a 3-mm-wide isthmus (two thirds of the intercuspal distance) were shaped as follows: 3IBJ, inlay with a butt joint margin (Fig. 2, A); 3IB, inlay with a beveled margin (Fig. 2, B); 3OBJ, onlay with a butt joint margin (Fig. 2, C); and 3ORS, onlay with a rounded shoulder marginal preparation (Fig.
2, D). The additional 4 models were developed for inlays and onlays of a 5-mm isthmus width (up to the tops of cusps) with the same preparation design as previously described (Fig. 2, E through H). The restorations were designed according to the assumed rules of marginal tooth preparation for an inlay (cavosurface butt joints or a bevel for occlusal margins) and for an onlay (a heavy chamfer or a rounded shoulder for axial surface margins).39,40 The restorations were bonded to the tooth structure using resin cement, 0.1 mm thick. A model of the opposing maxillary molar crown was also created (Fig. 1). According to anatomical conditions, the mandibular first molar had a 20-degree axial lingual inclination, and the crown of the maxillary tooth had an 8-degree buccal inclination in the faciolingual plane.37 Anisotropic properties were applied to the enamel in the study.41 The values of the elastic modulus for the enamel (Table I),30 shear modulus for enamel (32,895 MPa parallel to the prism and 27,331 MPa perpendicular to the prism),42 its tensile strength (42.2 MPa along the prisms, 11.5
1 Model of mandibular first molar with fragment of mandible and crown of maxillary molar in frontal plane. Opposing teeth are in lateral contact position. Bolus is placed between opposing teeth.
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A
B
C
D
E
F
G
H
2 Models of mandibular first molars restored with various ceramic restorations. A, Inlay with butt joint, 3-mm-wide isthmus (3IBJ). B, Inlay with beveled margin, 3-mm-wide isthmus (3IB). C, Onlay with butt joint margin, 3-mm-wide isthmus (3OBJ). D, Onlay with rounded shoulder margin, 3-mm-wide isthmus (3ORS). E, Inlay with 5-mm-wide isthmus (5IBJ). F, Onlay with beveled margin, 5-mm-wide isthmus (5OB). G, Onlay with butt joint margin, 5-mm-wide isthmus (5OBJ). H, Onlay with rounded shoulder margin, 5-mm-wide isthmus (5ORS).
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Table I. Materials used in models of molars with ceramic inlays and onlays Material
Modulus of Elasticity (Mpa)
Poisson’s Ratio
Enamel (perpendicular to prism)
72,70030
0.33
Enamel (parallel to prism)
87,50030
0.33
Dentin
18,60045
0.31
Periodontium
5046
0.45
Cortical bone
11,50047
0.30
Cancellous bone
43148
0.30
Leucite ceramic
65,00051
0.19
Resin cement
8,30052
0.35
MPa perpendicular to the prisms),31 compressive strength (384 MPa),43 and shear strength (90.2 MPa)44 were entered into the analysis program. The modulus of elasticity for the dentin,45 periodontium,46 cortical bone,47 and cancellous bone48 is presented in Table I. Additionally, tensile strength (105.5 MPa),49 compressive strength (297 MPa),45 and shear strength (52.7 MPa)50 of dentin were considered. An elastic modulus of 65 GPa for Empress ceramic (Ivoclar Vivadent, Schaan, Leichtenstein)51 and 8.3 GPa for Variolink II resin cement (Ivoclar Vivadent) 52 were used. Computational simulation of the clenching phase of mastication was performed in the frontal plane.53 The upper part of the maxillary molar crown was fixed. The opposing teeth were placed in a lateral contact position; the buccal cusp of the mandibular molar was situated opposite the lingual slope of the buccal maxillary tooth.54 A bolus, with an elastic modulus of 33.84 MPa55 (similar to a nut), was placed between the teeth. An increasing force, from 0 to 200 N, acting upward along the mandibular
molars axis, was evenly distributed at the lower margin of the mandible.56 At the same time, medial displacement (1 mm) of the mandible was performed.54 Lingual cusps of the mandibular molar glided over the bolus, along the occlusal surfaces of the maxillary teeth, until maximum intercuspal position of the opposing teeth was achieved.57 To perform calculations, each model was divided into almost 10,000 triangular 6-node elements (minimum, 9090, and maximum, 11,379 elements) joined at almost 20,000 nodes (minimum, 17,557, and maximum, 21,986 nodes). At the interface between the occlusal surfaces of the molars and the bolus, pairs of contact elements were used. The coefficient of friction at the contact surfaces was assumed to be 0.05.58 The contact elements between the bolus and enamel of the studied teeth allowed for calculation of the combined pressure exerted on the occlusal surface of the mandibular first molars during mastication. It was assumed that the tooth was in a plane strain state (the strain directed perpendicularly toward the
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analyzed cross-section equaled zero). This type of contact simulation by means of FEA requires a nonlinear analysis with the load and displacement being applied in a number of steps. Automatic time stepping was applied in the finite element program (ANSYS, Inc). The pressure exerted on the occlusal surface of the mandibular first molar and the stress components (normal stress, shear stress, principal stress) were calculated for each model. The Tsai-Wu failure criterion was used to evaluate the effort of the materials in the models.35 The criterion can be described by the formula: Fij σi σj + Fi σi =1 where i, j = 1,...,6 (1) F i and F ij are coefficients dependent on the strength properties of materials to tension, compression, and shear in the x, y, z direction, where these coordinate axes are directed according to main directions of the material anisotropy. σi and σj are stresses corresponding to principal directions in the material. The strength ratio R could be defined as: σi(a) =R σi (2) where the stress σi is applied or im-
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August 2007 posed, σi(a) means the allowed or ultimate stress. Substituting expression (2) to equation (1), the following is obtained: [Fij σiσj]R 2 + [Fi σi]R =1(3) One of the solutions to equation (3) is the Tsai-Wu strength ratio R. The Tsai-Wu strength ratio R can range from 1 to ∞. For a more convenient interpretation of results, the inverse of the Tsai-Wu strength ratio index was introduced (below referred to as the ITWSR): 1/R= σi / σi(a) (4) If the value of formula (4) and the ITWSR is less than 1, then the material will not fracture; however, if this value is higher than 1, then damage to the material may occur.35 The results were presented as maps of the distribution of the ITWSR for the models of ceramic restorations and enamel in molars. The pairs of bonded contact elements were used at the cement-tissue junction around the studied restorations. Tensile and compressive contact stresses perpendicular to the bonded cement-tooth surfaces and contact shear stresses parallel to the surfaces were calculated during the
simulation of mastication. The highest values of tensile contact stresses occurring at the adhesive interface in each model were compared to the values of tensile bond strength (TBS) of the Variolink II cement to enamel (49.3 MPa) and dentin (1.1 MPa).11 The highest values of shear contact stresses were compared to the values of shear bond strength (SBS) of the cement to enamel (32.8 MPa) and to dentin (15.1 MPa).59 When the contact stresses exceed the TBS or SBS of the cement to tooth structure, adhesive failure may occur. In these areas, restorations will be sheared from teeth, the bonds could be damaged, and microleakage may occur. Compressive contact stresses indicate the compressing of restorations to the tooth structures. The bond between an inlay and the tooth structure is significantly more resistant to compressive than tensile or shear forces. Under compression, no microleakage should occur.
RESULTS During the mastication of a hard bolus, the highest values of the IT-
A
WSR in teeth and ceramic restorations occurred in the clenching phase, in the moment preceding maximum intercuspation. These values were analyzed. For the ceramic inlay with a 3-mm isthmus (3IBJ), the highest value of 0.449 for the ITWSR appeared around the central groove (Fig. 3, A) (Table II). At the adhesive interface, along the inlay preparation lingual wall, tensile contact stresses reached 4.98 MPa (Fig. 3, B) (Table III). Contact shear stresses did not exceed 1.93 MPa (Table III). In the inlay with the beveled margins (3IB), the ITWSR was higher by 77% than in 3IBJ (Table II). Its highest value, 0.796, arose in the thin margin of the inlay, near the lingual molar cusps (Fig. 4, A). In the enamel around this inlay, the ITWSR exceeded 1 (Fig. 4, B). Between the cement and tooth structure surrounding the inlay margins, contact compressive stresses of 13.92 MPa developed (Fig. 4, C) and contact shear stresses of 4.64 MPa (Table III). In the central groove of the 3OBJ onlay, the ITWSR was 0.584 (Fig. 5, A). For the enamel around the inlay, the stresses were small in comparison
B
3 A, Distribution of highest values of inverse of Tsai-Wu strength ratio index (ITWSR) in 3IBJ ceramic inlay during mastication. Maximum value of ITWSR is denoted as MX, in red color. B, Distributions of contact tensile and compressive stresses in adhesive interface between cement and tooth around 3IBJ inlay during mastication (MPa). Areas of highest tensile contact stress are marked in blue color and as MN. Tensile contact stresses can be seen around margin of restoration.
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Table II. Maximum values of inverse of Tsai-Wu strength ratio index in ceramic restorations, cement, and enamel in molars during mastication
Inverse of Tsai-Wu Strength Ratio Index Group Code
Restoration
Ceramic
Resin Cement
3IBJ
Inlay with butt joint margin
0.449
0.224
0.21
3IB
Inlay with beveled margin
0.796
0.232
1.29
3OBJ
Onlay with butt joint margin
0.584
0.194
0.03
3ORS
Onlay with rounded shoulder margin
0.642
0.211
0.25
5IBJ
Inlay with butt joint margin
0.617
0.181
0.35
5OB
Onlay with beveled margin
0.501
0.177
0.13
5OBJ
Onlay with butt joint margin
0.596
0.152
0.02
5ORS
Onlay with rounded shoulder margin
0.437
0.156
0.07
with the other models (Table II). Close to the margins of the onlay at the cement-enamel junction, compressive contact stresses of 6.93 MPa formed (Fig. 5, B). With the 3ORS onlay, the highest value of the ITWSR (0.642) was observed at the internal side of the inlay over the lingual cusp (Fig. 6, A) (Table II). The distribution of contact tensile and compressive stresses between the cement and tooth structure around the onlay is presented in Figure 6, B. For the inlay with a 5-mm-wide isthmus (3IBJ), the ITWSR was higher by 37% than in the 3IBJ inlay (Table II) (Fig. 7, A). In contrast to the nar-
Enamel Around Margin of Restoration
rower 3IBJ inlay, compressive stresses appeared at the cement- enamel junction along the inlay preparation lingual wall (Fig. 7, B). For the 5-mm inlay with the beveled margins (5OB), the ITWSR was smaller by 38% than its narrower counterpart (3IB) (Table II). The maximum value was localized around the central groove and not in the inlay margin. In the enamel, the value of the index was almost 10 times lower than that associated with the 3IB inlay. For the wider onlay with butt joint margins (5OBJ), the ITWSR was similar to that found with 3OBJ. In the cement and enamel, the index values were the smallest of all the
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models studied (Table II). Among all of the studied ceramic restorations, the ITWSR was lowest in the 5ORS onlay (Table II). Around the margins of the wider restorations, compressive contact stresses, not tensile, occurred (Table III). The contact shear stresses around restorations studied did not exceed the SBS of Variolink II cement to tooth tissues (Table III).59 For the resin cement, the Tsai-Wu indices reached a value lower than 0.23. ITWSR were lower around the wider restorations compared with the narrower restorations (Table II).
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Table III. Maximum contact stresses in adhesive interface between cement and enamel around margins of ceramic restorations (MPa) Group Code
Maximum Contact Stresses Restoration
Tensile
Compressive
Shear
3IBJ
Inlay with butt joint margin
4.983
3.713
1.932
3IB
Inlay with beveled margin
–––
13.923
4.642
3OBJ
Onlay with butt joint margin
–––
6.927
2.090
3ORS
Onlay with rounded shoulder margin
–––
7.982
1.330
5IBJ
Inlay with butt joint margin
–––
6.891
3.941
5OB
Onlay with beveled margin
–––
8.477
1.705
5OBJ
Onlay with butt joint margin
–––
5.159
1.903
5ORS
Onlay with rounded shoulder margin
–––
4.915
1.516
A
B
4 A, Distribution of highest values of ITWSR in 3IB ceramic inlay during mastication. Maximum values of ITWSR are indicated as MX, in red color. B, Distributions of contact tensile and compressive stresses in adhesive interface between cement and tooth around ITWSR 3IB inlay during mastication (MPa). Areas of highest tensile contact stress are indicated in blue color and as MN. Areas of highest compressive contact stress are indicated in red color and as MX in same figure. Compressive contact stresses are seen around margins of restoration.
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C 4 continued C, Distribution of ITWSR in enamel around 3IB ceramic inlay during mastication. Maximum values of Tsai-Wu ratio are indicated in red color.
A
B
5 A, Distribution of highest values of ITWSR in 3OBJ ceramic onlay during mastication. Maximum values of ITWSR are indicated as MX, in red color. B, Distributions of contact tensile and compressive stresses in adhesive interface between cement and tooth around 3OBJ onlay during mastication (MPa). Areas of highest tensile contact stress are indicated in blue color and as MN. Areas of highest compressive contact stress are indicated in red color and as MX in same figure. Compressive contact stresses around margins of restoration are indicated in yellow and green color.
A
B
6 A, Distribution of highest values of ITWSR in 3ORS ceramic onlay during mastication. Maximum values of ITWSR are indicated as MX, in red color. B, Distributions of contact tensile and compressive stresses in adhesive interface between cement and tooth around 3ORS onlay during mastication (MPa). Areas of highest tensile contact stress are indicated in blue color and as MN. Areas of highest compressive contact stress are indicated in red color and as MX in same figure. Compressive contact stresses around margins of restoration are indicated by yellow and green color.
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A
B
7 A, Distribution of highest values of ITWSR in 5IBJ ceramic inlay during mastication. Maximum value of ITWSR is indicated as MX, in red color. B, Distributions of contact tensile and compressive stresses in adhesive interface between cement and tooth around 5IBJ inlay during mastication (MPa). Areas of highest tensile contact stress are indicated in blue color and as MN. Areas of highest compressive contact stress are indicated in red color and as MX in same figure. Compressive contact stresses around margins of restoration are indicated in yellow and green color.
DISCUSSION The study presents computational simulations of mastication of a hard bolus, during which the ITWSR was calculated for intracoronal ceramic restorations of various designs. Among restorations with a width equal to two thirds of the intercuspal distance, the lowest ITWSR was seen in the inlay with the butt joint margin (3IBJ). Simultaneously, between the cement and surrounding tooth structure, along the inlay preparation lingual wall, a tensile contact stress of 4.98 MPa occurred. This value did not exceed the adhesion of the resin cement to enamel (49.3 MPa), but was higher than the tensile bond strength to dentin (1.1 MPa).11 Consequently, in subsequent masticatory cycles, the tooth-cement junction could be damaged. This situation may also predispose the restoration to microleakage. An unfavorable distribution of stresses between ceramics and tooth structure may result in marginal deterioration around ceramic inlays.6,19,21 The highest Tsai-Wu ratio was seen in the thin margin of the beveled inlay, and in the surrounding enamel, the index exceeded 1 (Table II). According to the Tsai-Wu criterion, the sharp edge of the ceramics and the tooth around it may chip during mas-
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tication. This investigation confirms that ceramic restorations should not have knife-edged margin preparations, particularly, in places exposed to significant loads.39 Clinically, this may result in marginal fracture of the restoration.20 Among ceramic molar restorations with a 5-mm isthmus width, the lowest ITWSR was seen in the onlay (5ORS) with a rounded shoulder margin and in the surrounding enamel. Compressive contact stresses occurred in the adhesive interfaces between cement and teeth structures near the margins of onlays. The restorations were pressed to the tooth structures in these areas. The calculations performed within this study are consistent with the 2-D FEA calculations by Magne and Belser.24 These authors reported that compressive interfacial stresses forming around wider ceramic onlays provided potential protection against debonding at the dentin-restoration interface and increased crown stiffness. The Tsai-Wu failure criterion is a general theory of strength for anisotropic materials. It was developed and validated for fiber-reinforced, multilayered, multidirectional composites.32 Unlike the existing quadratic approximation of failure, the Tsai-Wu theory considers an interaction of in-
dependent components, considering a difference in strength due to positive and negative stresses, and can be modified to account for different materials.32 This criterion allows for the consideration of anisotropic materials, which might be much weaker in one direction than another. Enamel is composed of prisms oriented perpendicularly to the dentino-enamel junction, joined by the cementing substance.41 The tissue has 4 times lower tensile strength perpendicular to prisms than the strength along prisms.31 The structure and properties of dentin are similar to bone tissue.41 The Tsai-Wu criterion has been used to evaluate the risk of bone fracture.33,34 Keaveny et al33 concluded that the Tsai-Wu quadratic criterion was a reasonable predictor of the multiaxial failure behavior of bone. The strength of materials used in the present study was recalculated according to the Mohr-Coulomb failure criterion and the criterion of maximum stresses. These criteria do not consider the anisotropic stiffness of the materials studied, but they allow for consideration of differences in tensile and compressive strength of materials. The results of the Tsai-Wu criterion were compared with the simple failure criteria and turned out to be similar (Table IV). Based on these
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Table IV. Comparison of values of Tsai-Wu, Mohr-Coulomb, and maximum stresses failure criteria in enamel of teeth models with various ceramic restorations (MPa) Criteria Group Code
Restoration
Tsai-Wu
Mohr-Coulomb
Maximum Stresses
3IBJ
Inlay with butt joint margin
0.449
0.393
0.379
3IB
Inlay with beveled margin
0.796
1.062
0.613
3OBJ
Onlay with butt joint margin
0.584
0.521
0.541
3ORS
Onlay with rounded shoulder margin
0.642
0.670
0.612
5IBJ
Inlay with butt joint margin
0.617
0.552
0.535
5OB
Onlay with beveled margin
0.501
0.504
0.464
5OBJ
Onlay with butt joint margin
0.596
0.601
0.563
5ORS
Onlay with rounded shoulder margin
0.437
0.451
0.390
criteria, the same conclusions can be drawn. It is not possible to consider within an FEA study all of the variables operating in an oral environment. In this study, it was assumed that ceramic material is homogenous, without artifacts. Simplified 2-D models in a plane strain state of the mandibular molar models connected to mandibular alveolar bone by a periodontium were used in the study. Anisotropic properties of enamel were accounted for in the model. Simulations of a cycle of mastication were performed in the frontal plane. Based on these assumptions, under the studied load conditions and according to the TsaiWu failure criterion, wider ceramic
restorations with a 5-mm-wide isthmus should generally not be subject to failure. These results require further confirmation in 3-D model studies and clinical verification.
CONCLUSIONS Within the limitations of this study, the following conclusions were drawn: 1. During simulation of mastication among wide MOD ceramic restorations in molars, the lowest values of the inverse of the Tsai-Wu strength ratio index occurred in the onlay with a rounded shoulder margin, and the highest values occurred in the 3-mmwide inlay with a beveled margin. Ac-
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cording to the Tsai-Wu failure criterion, thin occlusal margins with inlays and the surrounding enamel are prone to chipping during mastication. 2. In the adhesive interface between the cement and enamel surrounding the majority of the restoration margins studied, compressive contact stresses occurred. Tensile contact stresses appeared only around inlays with butt joint margins. 3. Wide preparations in molars should be restored with ceramic onlays, not inlays, because of the lower inverse of the Tsai-Wu strength ratio index, and a favorable distribution of contact stresses between the cement and enamel during mastication.
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August 2007 REFERENCES 1. Cavel WT, Kelsey WP, Blankenau RJ. An in vivo study of cuspal fracture. J Prosthet Dent 1985;53:38-42. 2. Eakle WS, Maxwell EH, Braly BF. Fractures of posterior teeth in adults. J Am Dent Assoc 1986;112:215-8. 3. Blaser PK, Lund MR, Cochran MA, Potter RH. Effect of designs of Class II preparations on resistance of teeth to fracture. Oper Dent 1983;8:6-10. 4. Lin CL, Chang CH, Wang CH, Ko CC, Lee HE. Numerical investigation of the factors affecting interfacial stresses in an MOD restored tooth by auto-meshed finite element method. J Oral Rehabil 2001;28:517-25. 5. Goel VK, Khera SC, Gurusami S, Chen RC. Effect of cavity depth on stresses in a restored tooth. J Prosthet Dent 1992;67:17483. 6. Reich SM, Wichmann M, Rinne H, Shortall A. Clinical performance of large, all-ceramic CAD/CAM-generated restorations after three years: a pilot study. J Am Dent Assoc 2004;135:605-12. 7. Meyer A Jr, Cardoso LC, Araujo E, Baratieri LN. Ceramic inlays and onlays: clinical procedures for predictable results. J Esthet Restor Dent 2003;15:338-51. 8. Etemadi S, Smales RJ, Drummond PW, Goodhart JR. Assessment of tooth preparation designs for posterior resin-bonded porcelain restorations. J Oral Rehabil 1999;26:691-7. 9. Cattell MJ, Clarke RL, Lynch EJ. The biaxial flexural strength and reliability of four dental ceramics-- Part II. J Dent 1997;25:40914. 10.Holand W, Schweiger M, Frank M, Rheinberger V. A comparison of the microstructure and properties of the IPS Empress 2 and the IPS Empress glass-ceramics. J Biomed Mater Res 2000;53:297-303. 11.Hikita K, Van Meerbeek B, De Munck J, Ikeda T, Van Landuyt K, Maida T, et al. Bonding effectiveness of adhesive luting agents to enamel and dentin. Dent Mater 2007;23:71-80. 12.Burke FJ, Fleming GJ, Nathanson D, Marquis PM. Are adhesive technologies needed to support ceramics? An assessment of the current evidence. J Adhes Dent 2002;4:722. 13.Denehy GE, Torney DL. Internal enamel reinforcement through micromechanical bonding. J Prosthet Dent 1976;36:171-5. 14.Bremer BD, Geurtsen W. Molar fracture resistance after adhesive restoration with ceramic inlays or resin-based composites. Am J Dent 2001;14:216-20. 15.Mehl A, Kunzelmann KH, Folwaczny M, Hickel R. Stabilization effects of CAD/CAM ceramic restorations in extended MOD cavities. J Adhes Dent 2004;6:239-45. 16.St-Georges AJ, Sturdevant JR, Swift EJ Jr, Thompson JY. Fracture resistance of prepared teeth restored with bonded inlay restorations. J Prosthet Dent 2003;89:551-7. 17.Dalpino PH, Francischone CE, Ishikiriama A, Franco EB. Fracture resistance of teeth directly and indirectly restored with composite resin and indirectly restored with
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ceramic materials. Am J Dent 2002;15:38994. 18.Santos MJ, Bezerra RB. Fracture resistance of maxillary premolars restored with direct and indirect adhesive techniques. J Can Dent Assoc 2005;71:585. 19.Kramer N, Frankenberger R. Clinical performance of bonded leucite-reinforced glass ceramic inlays and onlays after eight years. Dent Mater 2005;21:262-71. 20.Hayashi M, Tsuchitani Y, Kawamura Y, Miura M, Takeshige F, Ebisu S. Eight-year clinical evaluation of fired ceramic inlays. Oper Dent 2000;25:473-81. 21.Otto T, De Nisco S. Computer-aided direct ceramic restorations: a 10-year prospective clinical study of Cerec CAD/CAM inlays and onlays. Int J Prosthodont 2002;15:1228. 22.Shillingburg HT. Fundamentals of fixed prosthodontics. 3rd ed. Chicago: Quintessence; 1997. p.171-9. 23.Fisher DW, Caputo AA, Shillingburg HT, Duncanson MG Jr. Photoelastic analysis of inlay and onlay preparations. J Prosthet Dent 1975; 33, 47-53. 24.Magne P, Belser UC. Porcelain versus composite inlays/onlays: effects of mechanical loads on stress distribution, adhesion, and crown flexure. Int J Periodontics Restorative Dent 2003;23:543-55. 25.Mondelli J, Steagall L, Ishikiriama A, de Lima Navarro MF, Soares FB. Fracture strength of human teeth with cavity preparations. J Prosthet Dent 1980;43:419-22. 26.Stappert CF, Guess PC, Gerds T, Strub JR. All-ceramic partial coverage premolar restorations. Cavity preparation design, reliability and fracture resistance after fatigue. Am J Dent 2005;18:275-80. 27.Arnelund CF, Johansson A, Ericson M, Hager P, Fyrberg KA. Five-year evaluation of two resin-retained ceramic systems: a retrospective study in a general practice setting. Int J Prosthodont 2004;17:302-6. 28.Boresi AP, Schmidt RJ. Advanced mechanics of materials. 6th ed. New York: John Wiley & Sons; 2003. p. 113-22. 29.Yu M. Advances in strength theories for materials under complex stress state in the 20th Century. Appl Mech Rev 2002;55:169-218. 30.Habelitz S, Marshall SJ, Marshall GW Jr, Balooch M. Mechanical properties of human dental enamel on the nanometre scale. Arch Oral Biol 2001;46:173-83. 31.Giannini M, Soares JC, de Carvalho RM. Ultimate tensile strength of tooth structures. Dent Mater 2004;20:322-9. 32.Tsai SW, Wu EM. A general theory of strength for anisotropic materials. J Composite Mat 1971;5:58-80. 33.Keaveny TM, Wachtel EF, Zadesky SP, Arramon YP. Application of the Tsai-Wu quadratic multiaxial failure criterion to bovine trabecular bone. J Biomech Eng 1999;121:99-107. 34.Natali AN, Pavan PG. A comparative analysis based on different strength criteria for evaluation of risk factor for dental implants. Comput Methods Biomech Biomed Engin 2002;5:127-33. 35.Tsai SW, Hahn HT. Introduction to composite materials. Westport: Technomic
Publishing Co; 1980. p. 276-81, 302-6. 36.Zienkiewicz OC, Taylor RL. The finite element method. Volume 1. 5th ed. St. Louis: Elsevier; 2000. p. 87-110. 37.Kraus BS, Jordan RE, Abrams L. Dental anatomy and occlusion. Baltimore: Williams and Wilkins Co; 1969. p. 197, 223-62. 38.Ash MM Jr. Wheeler’s atlas of tooth form. 5th ed. Philadelphia: Elsevier; 1984. p. 26, 68. 39.Banks RG. Conservative posterior ceramic restorations: a literature review. J Prosthet Dent 1990;63:619-26. 40.Deines DN. The etched porcelain inlay/onlay restoration. Mo Dent J. 1986;66:26-8. 41.Provenza DV, Seitel W. Oral histology: inheritance and development, 2nd ed. Philadelphia: Lippincott, Williams, & Wilkins; 1986. p. 243-63, 342-65. 42.Arikawa H. Dynamic shear modulus in torsion of human dentin and enamel. Dent Mater J 1989;8:223-35. 43.Craig RG, Peyton FA, Johnson DW. Compressive properties of enamel, dental cements and gold. J Dent Res 1961;40:93640. 44.Smith DC, Cooper WE. The determination of shear strength. A method using a micro-punch apparatus. Brit Dent J 1971;130:333-7. 45.Craig RG, Peyton FA. Elastic and mechanical properties of human dentin. J Dent Res 1958;37:710-8. 46.Rees JS, Jacobsen PH. Elastic modulus of the periodontal ligament. Biomaterials 1997;18:995-9. 47.Lettry S, Seedhom BB, Berry E, Cuppone M. Quality assessment of the cortical bone of the human mandible. Bone 2003;32:3544. 48.Giesen EB, Ding M, Dalstra M, van Eijden TM. Mechanical properties of cancellous bone in human mandibular condyle are anisotropic. J Biomech 2001;34:799-803. 49.Sano H, Ciucchi B, Matthews WG, Pashley DH. Tensile properties of mineralized and demineralized human and bovine dentin. J Dent Res 1994;73:1205-11. 50.Konishi N, Watanabe LG, Hilton JF, Marshall GW, Marshall SJ, Staninec M. Dentin shear strength: effect of distance from the pulp. Dent Mater 2002;18:516-20. 51.Albakry M, Guazzato M, Swain MV. Biaxial flexural strength, elastic moduli, and x-ray diffraction characterization of three pressable all-ceramic materials. J Prosthet Dent 2003;89:374-80. 52.Magne P, Perakis N, Belser UC, Krejci I. Stress distribution of inlay-anchored adhesive fixed partial dentures: a finite element analysis of influence of restorative materials and abutment preparation design. J Prosthet Dent 2002;87:516-27. 53.Dejak B, Mlotkowski A, Romanowicz M. Finite element analysis of stresses in molars during clenching and mastication. J Prosthet Dent 2003:90:591-7. 54.Gibbs CH, Lunden HC, Mahan PE, Fujimoto J. Chewing movements in relation to border movements at the first molar. J Prosthet Dent 1981;46:308-22. 55.Agrawal KR, Lucas PW, Printz JF, Bruce IC. Mechanical properties of foods responsible
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Volume 98 Issue 2 for resisting food breakdown in the human mouth. Arch Oral Biol 1997;42:1-9. 56.Gibbs CH, Mahan PE, Lundeen HC, Brehnan K, Walsh EK, Holbrook WB. Occlusal forces during chewing and swallowing as measured by sound transmission. J Prosthet Dent 1981;46:443-9. 57.Suit SR, Gibbs CH, Benz ST. Study of gliding tooth contact during mastication. J Periodontol 1976;47:331-4. 58.Katona TR. A mathematical analysis of the
role of friction in occlusal trauma. J Prosthet Dent 2001;86:636-43. 59.Abo-Hamar SE, Hiller KA, Jung H, Federlin M, Friedl KH, Schmalz G. Bond strength of a new universal self-adhesive resin luting cement to dentin and enamel. Clin Oral Investig 2005;9:161-7.
Corresponding author: Dr Beata Dejak Department of Prosthetic Dentistry Medical University of Lodz 251 Pomorska str 92-213 Lodz POLAND Fax: 00 48 42 675-74-50 E-mail: [email protected] Copyright © 2007 by the Editorial Council of The Journal of Prosthetic Dentistry.
Noteworthy Abstracts of the Current Literature Fracture resistance of implant-supported screw- versus cement-retained porcelain fused to metal single crowns: SEM fractographic analysis Zarone F, Sorrentino R, Traini T, Di lorio D, Caputi S. Dent Mater 2007;23:296-301.
Objectives. The present in vitro study aimed at evaluating the fracture resistance of both implant-supported screwand cement-retained porcelain fused to metal (PFM) single crowns. A scanning electron microscope (SEM) evaluation of the mode of failure of the specimens was also performed. Methods. Forty PFM premolar-shaped identical single crowns were realized. The restorations were divided into two groups: cement-retained (group 1) and screw-retained (group 2) prostheses. Compressive loading tests and SEM fractographic analyses were performed. The data were statistically analysed by means of the Student’s t-test, with a confidence interval of 95%. Results. The mean fracture load value was 1657 (±725) N in group 1 and 1281 (±747) N in group 2; the statistical analysis pointed out no significant differences between the two groups (P=.115). The mean work at maximum load value was 0.775 (±0.619) J in group 1 and 0.605 (±0.526) J in group 2; the statistical analysis pointed out no significant differences between the two groups (P=.355). All the samples were affected by cohesive fractures of the porcelain. Screw-retained crowns showed microcracks at the level of the occlusal access to the screw and extensive fractures in the whole thickness of the ceramics. On the contrary, cement-retained restorations were affected by less wide paramarginal fractures of the porcelain. Significance. A stronger implant-prosthetic connection was noticed in cemented restorations group than in screwretained single crowns. Even though negatively influenced by the presence of the occlusal access to the screw, the metal–ceramics bond can be considered predictable in both the implant-prosthetic connection systems analysed. Reprinted with permission from The Academy of Dental Materials.
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Clinical Implications
For strength reasons, large defects in molars should be restored with ceramic onlays with a rounded shoulder margin and not inlays. Tooth fracture resistance decreases with increased width1,2 and depth of caries and cavity preparation.3-5 Extensive MOD cavities in molars may be restored with, among other choices, esthetic ceramic inlays and onlays.6,7 The average width of these
restorations is two thirds of the intercuspal distance of teeth.8 Ceramic materials are characterized by low flexural strength9 and fracture toughness.10 Restorations made of these materials are luted with resin cements which have the highest bond strength
to tissue among luting agents.11 The optimum bond of these restorations to teeth enhances the strength of ceramics12 and prepared tissues,13,14 and assists in stabilizing weakened cusps.15 However, these restorations are not as fracture resistant as natu-
Assistant Professor, Department of Prosthetic Dentistry, Medical University. Assistant Professor, Department of Strength of Materials and Structure, Technical University. c Associate Professor, Chairman of Prosthetic Dentistry, Department of Prosthodontics, Medical University. a
b
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Volume 98 Issue 2 ral, intact teeth,16-18 and a large number of ceramic restorations exhibit some marginal deficiency.19 Chipping of restoration margins or changes in the color of surrounding tissues have been observed clinically.20 Another failure of ceramic restorations occurs as a bulk fracture.21 Inlays restore central cavities in teeth. Onlays restore one or more cusps and may completely cover the occlusal surfaces,22 resulting in a favorable distribution of stresses in teeth23,24 and a decreased risk of fractures.25 However, preparation for onlays requires additional tooth reduction relative to inlay restorations. Reports on the strength of teeth with ceramic restorations of various designs are equivocal. Teeth with inlays appeared more resistant to fractures than those with onlays in an in vitro study.26 Clinically, however, a higher number of failures in an inlay group was observed.27 Controversy exists as to what type of ceramic restoration should be used for the restoration of large defects in an attempt to prevent fracture and microleakage. To better understand this issue, a finite element analysis of stresses associated with various designs of ceramic restorations in molars was performed. There are various criteria that are used to assess the possibility of failure of a material.28,29 For isotropic materials with similar values of compressive and tensile strength, the most commonly used is the von Mises criterion.28 However, dental tissues and enamel, in particular, have anisotropic properties.30,31 Possible failure of the anisotropic material can be evaluated by the Tsai-Wu failure criterion.32,33,34 According to this criterion, if the inverse of the Tsai-Wu strength ratio index in the tested material is lower than 1, the material will not fracture. However, if this value is over 1, then damage to the material may occur.35 The criterion was used to estimate the strength of teeth with ceramic inlays and onlays. The purpose of this study was to determine the shapes of large MOD
ceramic restorations in molars most likely to prevent their failure and produce a favorable distribution of contact stresses between the cement and teeth during mastication.
MATERIAL AND METHODS The study of stresses during mastication in first molars with ceramic restorations was conducted by finite element analysis (FEA)36 (ANSYS version 10; ANSYS Inc, Canonsburg, Pa). Basing the analysis on frontal sections of molars with surrounding tissues and using dental anatomy textbooks37,38 as guides, 2-dimensional (2-D) computer models of a right first mandibular molar embedded in periodontium and bone were created (Fig. 1). Eight molar tooth models with various ceramic intracoronal restorations were developed. Four restorations with a 3-mm-wide isthmus (two thirds of the intercuspal distance) were shaped as follows: 3IBJ, inlay with a butt joint margin (Fig. 2, A); 3IB, inlay with a beveled margin (Fig. 2, B); 3OBJ, onlay with a butt joint margin (Fig. 2, C); and 3ORS, onlay with a rounded shoulder marginal preparation (Fig.
2, D). The additional 4 models were developed for inlays and onlays of a 5-mm isthmus width (up to the tops of cusps) with the same preparation design as previously described (Fig. 2, E through H). The restorations were designed according to the assumed rules of marginal tooth preparation for an inlay (cavosurface butt joints or a bevel for occlusal margins) and for an onlay (a heavy chamfer or a rounded shoulder for axial surface margins).39,40 The restorations were bonded to the tooth structure using resin cement, 0.1 mm thick. A model of the opposing maxillary molar crown was also created (Fig. 1). According to anatomical conditions, the mandibular first molar had a 20-degree axial lingual inclination, and the crown of the maxillary tooth had an 8-degree buccal inclination in the faciolingual plane.37 Anisotropic properties were applied to the enamel in the study.41 The values of the elastic modulus for the enamel (Table I),30 shear modulus for enamel (32,895 MPa parallel to the prism and 27,331 MPa perpendicular to the prism),42 its tensile strength (42.2 MPa along the prisms, 11.5
1 Model of mandibular first molar with fragment of mandible and crown of maxillary molar in frontal plane. Opposing teeth are in lateral contact position. Bolus is placed between opposing teeth.
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A
B
C
D
E
F
G
H
2 Models of mandibular first molars restored with various ceramic restorations. A, Inlay with butt joint, 3-mm-wide isthmus (3IBJ). B, Inlay with beveled margin, 3-mm-wide isthmus (3IB). C, Onlay with butt joint margin, 3-mm-wide isthmus (3OBJ). D, Onlay with rounded shoulder margin, 3-mm-wide isthmus (3ORS). E, Inlay with 5-mm-wide isthmus (5IBJ). F, Onlay with beveled margin, 5-mm-wide isthmus (5OB). G, Onlay with butt joint margin, 5-mm-wide isthmus (5OBJ). H, Onlay with rounded shoulder margin, 5-mm-wide isthmus (5ORS).
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Table I. Materials used in models of molars with ceramic inlays and onlays Material
Modulus of Elasticity (Mpa)
Poisson’s Ratio
Enamel (perpendicular to prism)
72,70030
0.33
Enamel (parallel to prism)
87,50030
0.33
Dentin
18,60045
0.31
Periodontium
5046
0.45
Cortical bone
11,50047
0.30
Cancellous bone
43148
0.30
Leucite ceramic
65,00051
0.19
Resin cement
8,30052
0.35
MPa perpendicular to the prisms),31 compressive strength (384 MPa),43 and shear strength (90.2 MPa)44 were entered into the analysis program. The modulus of elasticity for the dentin,45 periodontium,46 cortical bone,47 and cancellous bone48 is presented in Table I. Additionally, tensile strength (105.5 MPa),49 compressive strength (297 MPa),45 and shear strength (52.7 MPa)50 of dentin were considered. An elastic modulus of 65 GPa for Empress ceramic (Ivoclar Vivadent, Schaan, Leichtenstein)51 and 8.3 GPa for Variolink II resin cement (Ivoclar Vivadent) 52 were used. Computational simulation of the clenching phase of mastication was performed in the frontal plane.53 The upper part of the maxillary molar crown was fixed. The opposing teeth were placed in a lateral contact position; the buccal cusp of the mandibular molar was situated opposite the lingual slope of the buccal maxillary tooth.54 A bolus, with an elastic modulus of 33.84 MPa55 (similar to a nut), was placed between the teeth. An increasing force, from 0 to 200 N, acting upward along the mandibular
molars axis, was evenly distributed at the lower margin of the mandible.56 At the same time, medial displacement (1 mm) of the mandible was performed.54 Lingual cusps of the mandibular molar glided over the bolus, along the occlusal surfaces of the maxillary teeth, until maximum intercuspal position of the opposing teeth was achieved.57 To perform calculations, each model was divided into almost 10,000 triangular 6-node elements (minimum, 9090, and maximum, 11,379 elements) joined at almost 20,000 nodes (minimum, 17,557, and maximum, 21,986 nodes). At the interface between the occlusal surfaces of the molars and the bolus, pairs of contact elements were used. The coefficient of friction at the contact surfaces was assumed to be 0.05.58 The contact elements between the bolus and enamel of the studied teeth allowed for calculation of the combined pressure exerted on the occlusal surface of the mandibular first molars during mastication. It was assumed that the tooth was in a plane strain state (the strain directed perpendicularly toward the
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analyzed cross-section equaled zero). This type of contact simulation by means of FEA requires a nonlinear analysis with the load and displacement being applied in a number of steps. Automatic time stepping was applied in the finite element program (ANSYS, Inc). The pressure exerted on the occlusal surface of the mandibular first molar and the stress components (normal stress, shear stress, principal stress) were calculated for each model. The Tsai-Wu failure criterion was used to evaluate the effort of the materials in the models.35 The criterion can be described by the formula: Fij σi σj + Fi σi =1 where i, j = 1,...,6 (1) F i and F ij are coefficients dependent on the strength properties of materials to tension, compression, and shear in the x, y, z direction, where these coordinate axes are directed according to main directions of the material anisotropy. σi and σj are stresses corresponding to principal directions in the material. The strength ratio R could be defined as: σi(a) =R σi (2) where the stress σi is applied or im-
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August 2007 posed, σi(a) means the allowed or ultimate stress. Substituting expression (2) to equation (1), the following is obtained: [Fij σiσj]R 2 + [Fi σi]R =1(3) One of the solutions to equation (3) is the Tsai-Wu strength ratio R. The Tsai-Wu strength ratio R can range from 1 to ∞. For a more convenient interpretation of results, the inverse of the Tsai-Wu strength ratio index was introduced (below referred to as the ITWSR): 1/R= σi / σi(a) (4) If the value of formula (4) and the ITWSR is less than 1, then the material will not fracture; however, if this value is higher than 1, then damage to the material may occur.35 The results were presented as maps of the distribution of the ITWSR for the models of ceramic restorations and enamel in molars. The pairs of bonded contact elements were used at the cement-tissue junction around the studied restorations. Tensile and compressive contact stresses perpendicular to the bonded cement-tooth surfaces and contact shear stresses parallel to the surfaces were calculated during the
simulation of mastication. The highest values of tensile contact stresses occurring at the adhesive interface in each model were compared to the values of tensile bond strength (TBS) of the Variolink II cement to enamel (49.3 MPa) and dentin (1.1 MPa).11 The highest values of shear contact stresses were compared to the values of shear bond strength (SBS) of the cement to enamel (32.8 MPa) and to dentin (15.1 MPa).59 When the contact stresses exceed the TBS or SBS of the cement to tooth structure, adhesive failure may occur. In these areas, restorations will be sheared from teeth, the bonds could be damaged, and microleakage may occur. Compressive contact stresses indicate the compressing of restorations to the tooth structures. The bond between an inlay and the tooth structure is significantly more resistant to compressive than tensile or shear forces. Under compression, no microleakage should occur.
RESULTS During the mastication of a hard bolus, the highest values of the IT-
A
WSR in teeth and ceramic restorations occurred in the clenching phase, in the moment preceding maximum intercuspation. These values were analyzed. For the ceramic inlay with a 3-mm isthmus (3IBJ), the highest value of 0.449 for the ITWSR appeared around the central groove (Fig. 3, A) (Table II). At the adhesive interface, along the inlay preparation lingual wall, tensile contact stresses reached 4.98 MPa (Fig. 3, B) (Table III). Contact shear stresses did not exceed 1.93 MPa (Table III). In the inlay with the beveled margins (3IB), the ITWSR was higher by 77% than in 3IBJ (Table II). Its highest value, 0.796, arose in the thin margin of the inlay, near the lingual molar cusps (Fig. 4, A). In the enamel around this inlay, the ITWSR exceeded 1 (Fig. 4, B). Between the cement and tooth structure surrounding the inlay margins, contact compressive stresses of 13.92 MPa developed (Fig. 4, C) and contact shear stresses of 4.64 MPa (Table III). In the central groove of the 3OBJ onlay, the ITWSR was 0.584 (Fig. 5, A). For the enamel around the inlay, the stresses were small in comparison
B
3 A, Distribution of highest values of inverse of Tsai-Wu strength ratio index (ITWSR) in 3IBJ ceramic inlay during mastication. Maximum value of ITWSR is denoted as MX, in red color. B, Distributions of contact tensile and compressive stresses in adhesive interface between cement and tooth around 3IBJ inlay during mastication (MPa). Areas of highest tensile contact stress are marked in blue color and as MN. Tensile contact stresses can be seen around margin of restoration.
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Table II. Maximum values of inverse of Tsai-Wu strength ratio index in ceramic restorations, cement, and enamel in molars during mastication
Inverse of Tsai-Wu Strength Ratio Index Group Code
Restoration
Ceramic
Resin Cement
3IBJ
Inlay with butt joint margin
0.449
0.224
0.21
3IB
Inlay with beveled margin
0.796
0.232
1.29
3OBJ
Onlay with butt joint margin
0.584
0.194
0.03
3ORS
Onlay with rounded shoulder margin
0.642
0.211
0.25
5IBJ
Inlay with butt joint margin
0.617
0.181
0.35
5OB
Onlay with beveled margin
0.501
0.177
0.13
5OBJ
Onlay with butt joint margin
0.596
0.152
0.02
5ORS
Onlay with rounded shoulder margin
0.437
0.156
0.07
with the other models (Table II). Close to the margins of the onlay at the cement-enamel junction, compressive contact stresses of 6.93 MPa formed (Fig. 5, B). With the 3ORS onlay, the highest value of the ITWSR (0.642) was observed at the internal side of the inlay over the lingual cusp (Fig. 6, A) (Table II). The distribution of contact tensile and compressive stresses between the cement and tooth structure around the onlay is presented in Figure 6, B. For the inlay with a 5-mm-wide isthmus (3IBJ), the ITWSR was higher by 37% than in the 3IBJ inlay (Table II) (Fig. 7, A). In contrast to the nar-
Enamel Around Margin of Restoration
rower 3IBJ inlay, compressive stresses appeared at the cement- enamel junction along the inlay preparation lingual wall (Fig. 7, B). For the 5-mm inlay with the beveled margins (5OB), the ITWSR was smaller by 38% than its narrower counterpart (3IB) (Table II). The maximum value was localized around the central groove and not in the inlay margin. In the enamel, the value of the index was almost 10 times lower than that associated with the 3IB inlay. For the wider onlay with butt joint margins (5OBJ), the ITWSR was similar to that found with 3OBJ. In the cement and enamel, the index values were the smallest of all the
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models studied (Table II). Among all of the studied ceramic restorations, the ITWSR was lowest in the 5ORS onlay (Table II). Around the margins of the wider restorations, compressive contact stresses, not tensile, occurred (Table III). The contact shear stresses around restorations studied did not exceed the SBS of Variolink II cement to tooth tissues (Table III).59 For the resin cement, the Tsai-Wu indices reached a value lower than 0.23. ITWSR were lower around the wider restorations compared with the narrower restorations (Table II).
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Table III. Maximum contact stresses in adhesive interface between cement and enamel around margins of ceramic restorations (MPa) Group Code
Maximum Contact Stresses Restoration
Tensile
Compressive
Shear
3IBJ
Inlay with butt joint margin
4.983
3.713
1.932
3IB
Inlay with beveled margin
–––
13.923
4.642
3OBJ
Onlay with butt joint margin
–––
6.927
2.090
3ORS
Onlay with rounded shoulder margin
–––
7.982
1.330
5IBJ
Inlay with butt joint margin
–––
6.891
3.941
5OB
Onlay with beveled margin
–––
8.477
1.705
5OBJ
Onlay with butt joint margin
–––
5.159
1.903
5ORS
Onlay with rounded shoulder margin
–––
4.915
1.516
A
B
4 A, Distribution of highest values of ITWSR in 3IB ceramic inlay during mastication. Maximum values of ITWSR are indicated as MX, in red color. B, Distributions of contact tensile and compressive stresses in adhesive interface between cement and tooth around ITWSR 3IB inlay during mastication (MPa). Areas of highest tensile contact stress are indicated in blue color and as MN. Areas of highest compressive contact stress are indicated in red color and as MX in same figure. Compressive contact stresses are seen around margins of restoration.
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C 4 continued C, Distribution of ITWSR in enamel around 3IB ceramic inlay during mastication. Maximum values of Tsai-Wu ratio are indicated in red color.
A
B
5 A, Distribution of highest values of ITWSR in 3OBJ ceramic onlay during mastication. Maximum values of ITWSR are indicated as MX, in red color. B, Distributions of contact tensile and compressive stresses in adhesive interface between cement and tooth around 3OBJ onlay during mastication (MPa). Areas of highest tensile contact stress are indicated in blue color and as MN. Areas of highest compressive contact stress are indicated in red color and as MX in same figure. Compressive contact stresses around margins of restoration are indicated in yellow and green color.
A
B
6 A, Distribution of highest values of ITWSR in 3ORS ceramic onlay during mastication. Maximum values of ITWSR are indicated as MX, in red color. B, Distributions of contact tensile and compressive stresses in adhesive interface between cement and tooth around 3ORS onlay during mastication (MPa). Areas of highest tensile contact stress are indicated in blue color and as MN. Areas of highest compressive contact stress are indicated in red color and as MX in same figure. Compressive contact stresses around margins of restoration are indicated by yellow and green color.
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A
B
7 A, Distribution of highest values of ITWSR in 5IBJ ceramic inlay during mastication. Maximum value of ITWSR is indicated as MX, in red color. B, Distributions of contact tensile and compressive stresses in adhesive interface between cement and tooth around 5IBJ inlay during mastication (MPa). Areas of highest tensile contact stress are indicated in blue color and as MN. Areas of highest compressive contact stress are indicated in red color and as MX in same figure. Compressive contact stresses around margins of restoration are indicated in yellow and green color.
DISCUSSION The study presents computational simulations of mastication of a hard bolus, during which the ITWSR was calculated for intracoronal ceramic restorations of various designs. Among restorations with a width equal to two thirds of the intercuspal distance, the lowest ITWSR was seen in the inlay with the butt joint margin (3IBJ). Simultaneously, between the cement and surrounding tooth structure, along the inlay preparation lingual wall, a tensile contact stress of 4.98 MPa occurred. This value did not exceed the adhesion of the resin cement to enamel (49.3 MPa), but was higher than the tensile bond strength to dentin (1.1 MPa).11 Consequently, in subsequent masticatory cycles, the tooth-cement junction could be damaged. This situation may also predispose the restoration to microleakage. An unfavorable distribution of stresses between ceramics and tooth structure may result in marginal deterioration around ceramic inlays.6,19,21 The highest Tsai-Wu ratio was seen in the thin margin of the beveled inlay, and in the surrounding enamel, the index exceeded 1 (Table II). According to the Tsai-Wu criterion, the sharp edge of the ceramics and the tooth around it may chip during mas-
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tication. This investigation confirms that ceramic restorations should not have knife-edged margin preparations, particularly, in places exposed to significant loads.39 Clinically, this may result in marginal fracture of the restoration.20 Among ceramic molar restorations with a 5-mm isthmus width, the lowest ITWSR was seen in the onlay (5ORS) with a rounded shoulder margin and in the surrounding enamel. Compressive contact stresses occurred in the adhesive interfaces between cement and teeth structures near the margins of onlays. The restorations were pressed to the tooth structures in these areas. The calculations performed within this study are consistent with the 2-D FEA calculations by Magne and Belser.24 These authors reported that compressive interfacial stresses forming around wider ceramic onlays provided potential protection against debonding at the dentin-restoration interface and increased crown stiffness. The Tsai-Wu failure criterion is a general theory of strength for anisotropic materials. It was developed and validated for fiber-reinforced, multilayered, multidirectional composites.32 Unlike the existing quadratic approximation of failure, the Tsai-Wu theory considers an interaction of in-
dependent components, considering a difference in strength due to positive and negative stresses, and can be modified to account for different materials.32 This criterion allows for the consideration of anisotropic materials, which might be much weaker in one direction than another. Enamel is composed of prisms oriented perpendicularly to the dentino-enamel junction, joined by the cementing substance.41 The tissue has 4 times lower tensile strength perpendicular to prisms than the strength along prisms.31 The structure and properties of dentin are similar to bone tissue.41 The Tsai-Wu criterion has been used to evaluate the risk of bone fracture.33,34 Keaveny et al33 concluded that the Tsai-Wu quadratic criterion was a reasonable predictor of the multiaxial failure behavior of bone. The strength of materials used in the present study was recalculated according to the Mohr-Coulomb failure criterion and the criterion of maximum stresses. These criteria do not consider the anisotropic stiffness of the materials studied, but they allow for consideration of differences in tensile and compressive strength of materials. The results of the Tsai-Wu criterion were compared with the simple failure criteria and turned out to be similar (Table IV). Based on these
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Table IV. Comparison of values of Tsai-Wu, Mohr-Coulomb, and maximum stresses failure criteria in enamel of teeth models with various ceramic restorations (MPa) Criteria Group Code
Restoration
Tsai-Wu
Mohr-Coulomb
Maximum Stresses
3IBJ
Inlay with butt joint margin
0.449
0.393
0.379
3IB
Inlay with beveled margin
0.796
1.062
0.613
3OBJ
Onlay with butt joint margin
0.584
0.521
0.541
3ORS
Onlay with rounded shoulder margin
0.642
0.670
0.612
5IBJ
Inlay with butt joint margin
0.617
0.552
0.535
5OB
Onlay with beveled margin
0.501
0.504
0.464
5OBJ
Onlay with butt joint margin
0.596
0.601
0.563
5ORS
Onlay with rounded shoulder margin
0.437
0.451
0.390
criteria, the same conclusions can be drawn. It is not possible to consider within an FEA study all of the variables operating in an oral environment. In this study, it was assumed that ceramic material is homogenous, without artifacts. Simplified 2-D models in a plane strain state of the mandibular molar models connected to mandibular alveolar bone by a periodontium were used in the study. Anisotropic properties of enamel were accounted for in the model. Simulations of a cycle of mastication were performed in the frontal plane. Based on these assumptions, under the studied load conditions and according to the TsaiWu failure criterion, wider ceramic
restorations with a 5-mm-wide isthmus should generally not be subject to failure. These results require further confirmation in 3-D model studies and clinical verification.
CONCLUSIONS Within the limitations of this study, the following conclusions were drawn: 1. During simulation of mastication among wide MOD ceramic restorations in molars, the lowest values of the inverse of the Tsai-Wu strength ratio index occurred in the onlay with a rounded shoulder margin, and the highest values occurred in the 3-mmwide inlay with a beveled margin. Ac-
The Journal of Prosthetic Dentistry
cording to the Tsai-Wu failure criterion, thin occlusal margins with inlays and the surrounding enamel are prone to chipping during mastication. 2. In the adhesive interface between the cement and enamel surrounding the majority of the restoration margins studied, compressive contact stresses occurred. Tensile contact stresses appeared only around inlays with butt joint margins. 3. Wide preparations in molars should be restored with ceramic onlays, not inlays, because of the lower inverse of the Tsai-Wu strength ratio index, and a favorable distribution of contact stresses between the cement and enamel during mastication.
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Volume 98 Issue 2 for resisting food breakdown in the human mouth. Arch Oral Biol 1997;42:1-9. 56.Gibbs CH, Mahan PE, Lundeen HC, Brehnan K, Walsh EK, Holbrook WB. Occlusal forces during chewing and swallowing as measured by sound transmission. J Prosthet Dent 1981;46:443-9. 57.Suit SR, Gibbs CH, Benz ST. Study of gliding tooth contact during mastication. J Periodontol 1976;47:331-4. 58.Katona TR. A mathematical analysis of the
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Corresponding author: Dr Beata Dejak Department of Prosthetic Dentistry Medical University of Lodz 251 Pomorska str 92-213 Lodz POLAND Fax: 00 48 42 675-74-50 E-mail: [email protected] Copyright © 2007 by the Editorial Council of The Journal of Prosthetic Dentistry.
Noteworthy Abstracts of the Current Literature Fracture resistance of implant-supported screw- versus cement-retained porcelain fused to metal single crowns: SEM fractographic analysis Zarone F, Sorrentino R, Traini T, Di lorio D, Caputi S. Dent Mater 2007;23:296-301.
Objectives. The present in vitro study aimed at evaluating the fracture resistance of both implant-supported screwand cement-retained porcelain fused to metal (PFM) single crowns. A scanning electron microscope (SEM) evaluation of the mode of failure of the specimens was also performed. Methods. Forty PFM premolar-shaped identical single crowns were realized. The restorations were divided into two groups: cement-retained (group 1) and screw-retained (group 2) prostheses. Compressive loading tests and SEM fractographic analyses were performed. The data were statistically analysed by means of the Student’s t-test, with a confidence interval of 95%. Results. The mean fracture load value was 1657 (±725) N in group 1 and 1281 (±747) N in group 2; the statistical analysis pointed out no significant differences between the two groups (P=.115). The mean work at maximum load value was 0.775 (±0.619) J in group 1 and 0.605 (±0.526) J in group 2; the statistical analysis pointed out no significant differences between the two groups (P=.355). All the samples were affected by cohesive fractures of the porcelain. Screw-retained crowns showed microcracks at the level of the occlusal access to the screw and extensive fractures in the whole thickness of the ceramics. On the contrary, cement-retained restorations were affected by less wide paramarginal fractures of the porcelain. Significance. A stronger implant-prosthetic connection was noticed in cemented restorations group than in screwretained single crowns. Even though negatively influenced by the presence of the occlusal access to the screw, the metal–ceramics bond can be considered predictable in both the implant-prosthetic connection systems analysed. Reprinted with permission from The Academy of Dental Materials.
The Journal of Prosthetic Dentistry
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