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1990 Perpmoa

Press pk

THREE-DIMENSIONAL FINITE ELEMENT ANALYSIS OF GLASS-CERAMIC DENTAL CROWNS B. HOJJATIE’ and K. J. ANUSAVICE Department of Dental Biomaterials, College of Dentistry, University of Florida, Box J4t6, J.H.M.H.C.. Gainesville, FL 3261&0446, U.S.A. Abstract-Because of the improved esthetic potential of glass-ceramic crowns as dental restorations. they arc sometimes preferred over metal-ceramic crowns for restoration of anterior teeth. Because of their relatively high strength. these aramic crowns are also frequently used for restoration of posterior teeth. However, due to the larger magnitude of biting forces on posterior teeth, intraoral fracture of all-ceramic crowns tends to occur more frequently in posterior crowns (MotTa, 1988). The objective of this study was to determine the relative influence of load orientation and the occlusal thickness of posterior ceramic crowns on the stress distribution which develops under these loading and design conditions. Three-dimensional finite element models for a molar crown were developed to determine the stressdistribution under simulated applied loads. Glass-ceramic crowns with occlusal thicknessesof 0.5.1.5. and 3.0 mm were considered. The largest principal tensile stressesinduced in aramic due to a distributed load of 600 N applied in a cuspal region were approximately I2 and 182 MPa for vertical and horizontal loading orientations, respectively. Stresses which developed in the facial and lingual marginal regions were primarily compressive under vertical loads. However, tensile stressesdeveloped when the load was applied horizontally. Dilferences in stress distribution within crowns with the three occlusal thicknessesoccurred only near the site of loading. Because of the relatively large failure rams of ceramic crowns in the posteriorregions.theserestorations shouldbe strengthenedby improvementin daign. composition, and thermal processingconditions. Before any significant progress is made in these areas. these rcstorations should bc used for the anterior teeth. The results ofthis study suggestthat orientation of the applied load has a more important effect on development of large tensile stressesthan the occlusal thickness of aramic.

INTRODUcTION

various types of applied loading which are not nccessarily axisymmctric. Since the analysis and design A castable glass product, which is strengthened during of dental prostheses should be based on the most heat treatment by the growth of tetrasilicic Ruormica relevant loading condition. a three-dimensional tinite crystals to form a glass-ceramic. was developed by element analysis of these restorations should be Grossman (1973) and was tirst used for dental appli- employed. cations by Adair and Hoekstra (1982). This product is Anusavice and Hojjatie (1988) used a two-dimengaining in popularity as the material of choice for sional finite clement model to determine the influence jacket crown applications. Due to its higher modulus of the prepared tooth height and applied loading on of rupture compared with conventional feldspathic the stress distribution in ceramic crowns on prepared porcelain, this material is used frequently to construct maxillary central incisors. It was concluded that horirestorations for posterior teeth. Finite element stress zontal load components were major determinants of analysis has been employed previously to determine tensile stressesinduced in the ceramic. However, stresthe stress distribution in castable ceramic crowns ses along the mesiodistal direction were not analystd under spccitic loading conditions. Starling and Cook in this previous study. (1983) used axisymmetric and plane-stress models of a It is generally believed that if the occlusal thickness ceramic crown to determine the influence of elastic of posterior ceramic crowns is less than I.5 mm, the modulus, cement layer thickness, loading orientation, risk of failure would increase markedly. The objective and loading configuration of the gingival preparation of this study was to use three-dimensional finite on the resulting stress state. The authors concluded element analysis to test the hypothesis that the orithat the stress values determined from the axisym- entation of simulated intraoral forces, and not the metric model were in better agreement with the results occlusal thickness, is the principal determinant of high obtained from mechanical testing and strain gage stressesin ceramic crowns. measurements than the values obtained from a planestressmodel. In their analyses, it was assumed that the FtNtTE ELEMENT MODUS applied loading was axisymmetric. However, ceramic crowns used fot the posterior teeth are subjected to Three-dimensional finite element models for a manReceived in jW/Orm 30 May 1990. l Author to whbm correspondena should be addressed. This study was supported by NIDR Grant DE06672.

dibular second molar crown were developed and the overall dimensions were selected to be consistent with the values identified by Wheeler (1965) for an average molar crown. In these models it was assumed that the 1157

1158

B. HOJJATIEand K. J. AHUSAVICE

enamel in the prepared areas was completely removed and was replaced by castable ceramic crowns with occlusal thicknessesof 0.5 mm (Case I), 1.5 mm (Case II) and 3.0 mm (Case III). Except for this variation in ceramic thickness at the biting (occlusal) region, the three models had identical dimensions in other locations ofthecrown. The shaded areas for Cases 1, II and III shown in Fig. 1 correspond to occlusal regions of dentin. The assumptions used in this study are as follows: (I) the materials were assumed to be homogeneous, linearly elastic, and isotopic, (2) the influences of a cement layer and the periodontal ligament were negligible: (3) residual stresseswhich are induced in castable ceramic because of contraction differences between the cast crown and shading porcelain and nonuniform distribution of temperature during processing were negligible; (4) no critical structural flaws were present; (5) perfect bonding existed between ceramic and dentin; (6) the external veneer of shading porcelain, which is usually required to achieve acccptablc esthetics, was not present. Mesh generation of the models was accomplished by the use of the MTAB*PRE prc-processing softwart (1987). This software is capable of gcncrating finite elcmcnt models using IBM-PC and compatible microcomputers. For preliminary analyses, crown models with 226 nodes and 171 three-dimensional solid elements were developed. Each element consisted of eight nodes and each node could be assigned

Fig. 1. Cross-sectional view of a mandibular second molar showing the three design cases. Stress distributions were obtained using finite element models with ceramic thicknessesof03 mm (Case I). I.5 mm (Case II) and 3.0 mm (Case 1x1)in the bifing region and for a distribured load of 600 N.

three translational degrees of freedom (DOF). To improve the geometry of the crown models and to create more realistic topography at the cusp regions. the finite element model for the Case I design was refined. In this refined model, a total of 586 nodes and 456 three-dimensional solid elements (eight-node brick) were employed (Fig. 2). The element-shrink and the hidden-line-removal options of the pre-processing program have been used to generate this figure. All of the nodes in the x-y plane. which correspond to the root portion of dentin, were assumed to be fixed and no translation was allowed in any direction of the Cartesian coordinate system. Locations of some of these fixed nodes are also identified in Fig. I. The elastic modulus values chosen for ceramic, dentin and pulp were 7.03 x lo’, 1.86 x 10. and 2.0 MPa, respectively, and the corresponding Poisson’s ratios were 0.28.0.31 and 0.45, respectively(Anusavice et aI., 1986; Anusavice and Hojjatie, 1987, 1988). After generating the finite element model, input data were translated for the SAP86 (1986) microcomputer program. The following analyses were considered in this study: (a) in the preliminary model, a load of 600 N was distributed along the vertical (:) direction on one cusp and the stressand displacement values were compared for the three design cases; (b) the analysts described in part (a) were pcrformed except that the load was applied along the horizontal direction; (c) the finite element model for Case I was refined and the stressand displacement induced in the crown due to the vertical and horizontal loading configurations were compared with those obtained from the previous models; (d) to determine the influence of the pulp chamber, the same analyses as part (c) were considered by substituting a void region for the pulp chamber. This study assumed an average biting force of 600 N (Fig. 3) based on the data reported by Craig(l980) and Finn (1978) for second molars under normal mastication. In general, biting forces of this magnitude occur along a vertical direction. However, to determine the influence of loading orientation on the level of stresses, the same amount of load was also applied along the horizontal direction. In static analysis, when the materials are homogeneous, linearly elastic and isotropic, the stresses are directly proportional to the applied loads. Therefore, the stressescalculated in this study for a load of 600 N can also be used to predict the stressesfor other magnitudes of applied loads. The three-dimensional crown models for a mandibular second molar were developed to evaluate the manufacturer’s recommendations on the design of castable ceramic crowns and to examine the findings from previous studies which are as follows: (I) the manufacturer of [email protected] castable ceramic crowns recommends maintaining a minimum occlusal thickness of 1.5 mm (Clinical Procedures Manual, Dentsply International, 1984). To determine the influence of ceramic thickness on the magnitude of applied

Fig. 2. Three-dimensional

finite elcmcnl mtdcl using 586 no&s and 456 solid clement (refined mdcl) showing poreclain, dentin and pulp regions.

1159

Stressanalysisof dental ceramic crowns

It61 RESULTS

A 2

X

Y

Fig. 3. Locationsof the appliedloadsfor the finite element model.

stresses in the csown. three design cases were analysed [analyses in part (a)]; (2) two-dimcn6ional. finite element stress analysis of ceramic crowns for anterior teeth indicate that the loading oricntaqion was a major cause of tensile stresses(Anusavice and Hojjatic, 1988). Analyses in part (b) were pedformcd 10 evaluate this finding by a three-dimensional model; (3) The results from finite element analysis arc associated with discretization errors which are due to the replacement ofa continuous structure by a discrete model and this error should bc reduced by mesh refinement (Anusavice and Hojjatie. 1988). Therefore, in the analyses of part (c) the stresseswere calculated for a more relined model and the results were compared with those of the preliminary model; (4) because of the negligibly small elastic modulus of the pulp char&r, it may be hypothesized (hat the absence or pretince of this region within the linite element model will have a negligible influence on the stress distribution in ceramic and dentin. This hypothesis was tested’in the analyses of part (d). The analyses were performed on an IBM PC-AT microcomputer and the outputs from SAP86 ftnite element analyses were entered into the MTAB*POST post-processing $oftware (1987) to determine the peak values of stress and displacement and to generate stressconlours. All components of normal stress (uI, CT,.a,). shear stress (T*,, T,*, r,.), principal stress (u,. oz. a,), and maximum shear stress (I,_) and the displacement alang the three directions of the global coordinate system were examined by means of stress contours. The results were summarized graphically in terms of u,, u2, and r,,,.,. For better visualization of the stress magnjtudes at the interior points of the crown, the contours were plotted along various crosssections of the crpwns on the color monitor and, with the use of color &ding, stressesand displacements at the critical areasisuch as marginal and pulpal regions were analysed.

For analysis {a) in which the three crown designs were subjected to a vertical load of 600 N, the stress values for all three design cases were nearly idenrical. The focus of this study is to determine the influence of ceramic thickness and loading condition on the induced stressesin various locations of the molar crown. To accomplish this, the results are presented in terms of principal tensile, compressive and maximum shear stresscontours. The peak value of the principal tensile stress (a,) for the design Case I (ceramic thickness =O.S mm) was 7.7 MPa which occurred at the marginal region (Fig. 4). The stresscontours identified by the same letters correspond to the same stress values. The stressmagnitudes corresponding to each letter are shown in the table above the figure. The thicker lines identify the location of the nodal points at the crown surface. The stress contours near the marginal and cusp areas which arc closer to each other correspond to steeper stress gradients compared with other Iocations. Similar stress distributions for the principal stress (a,) were obtained for the design Cases II and 111. For the vertically applied load, the largest compressive stresseswere obtained along the z direction. The peak values of the principal compressive stress (a,) at the surface for Case f (ceramic thickness =O.S mm) was 74.2 MPa (Fig. 5). The corresponding values for Case II (ceramic thickness= I.5 mm) and Case III (ceramic thickness= 3.0 mm) were 73.8 MPa and 73.3 MPa. respectively. The principal stress distributions (al) for all three design cases were similar.

I

B a-- -3.9 7.7

fb-4.0 - -6.8

g c-I -9.7 1.9

h d.I -12.6 -1.0 I

Fig. 4. o,-Stress contours for a crown with a ceramic thickness of 0.5 mm in the biting region (Case I) for a disrributed vertical load of 600 N. These surface stresseswere obtained using a finite element model consisting of 226 nodes and I71 solid elements (preliminary model).

B. HOJJATIEand K. J. A~uuv~cx

1162

a-

5.3

e-40.1

b --6.1

c -67.4

f = -51.5

6 I -62.9

.

d --26.6 h I -74.2

*I,..

f s 3.7 k s-4.0

b = 9.9 g a 2.2 I v9.s

c s 9.3 n * 0.7 m z-7.0

d = 9.9 1 n-0.9 n *-a.9

. , 0

s 6.3 . -2.0 s -10.1

I

I 900

Fig. 5. o,-Stress contours for a crown with ceramic thickness of0.S mm in the biting region (Case 111)for a vertical load of 600 N. A finite clement model with 226 nodes and 171 solid elements was used for these analyses.

In analysis(b), the 600 N load was distributed along the horizontal direction at the same location as part (a). Under this loading condition, the peak values of the principal tensile (a,) and principal compressive (a,) stresses for the Case I were 178.3 MPa and 102.5 MPa, respectively. These stresses were similar for all design cases. To verify the accuracy of these stress values, the model corresponding to Case I was refined and analyses were performed for the same vertical and horizontal loading conditions (analyses in part (c)]. The peak value of principal tensile stress (a,) due to a vertical load of 600 N for the refined model was 11.4 MPa (Fig. 6). In this figure. the stress contours ‘0’ and ‘b’ are hidden from view and do not appear on the figure. However, the location for contour ‘a’(maximum tension) is shown by an arrow. The location of contour ‘b’ is near contour ‘a’. Comparison of principal tensile stress values (a,) for the refined and unrefined models showed that only a small improvement in accuracy was obtained due to model refinement. Under the horizontally applied load of 600 N, relatively large magnitudes of tensile stresses occurred in both dentin and ceramic surfaces (Figs 7 and 8). The largest tensile stresses in dentin were produced around the fixed nodes which were located directly below the site of loading. The peak value of tensile stress (a,) in ceramic at the marginal area was 69.7 MPa (contour h in Fig. 7). The corresponding value in dentin was 171.9 MPa (contour a). The largest, principal compressive stress value (u,) in ceramic was 116.2 MPa which occurred at the ceramic-dentin boundary (contour o in Fig. 8). In general, the stresses developed at the interior of the ceramic and dentin were similar to

N

Fig. 6. a,-Stress contours for a crown with ceramic thickness of 0.5 mm (Case I) in the biting region for a vertical load of 600 N. These surface stresses were obtained using a finite element model with 586 nodes and 456 three-dimensional solid elements. Contours ‘a’ (which represent maximum tension) and ‘b’ are hidden from the view of this figure.

a - 171.9 e -113.5 k . 25.9

b m157.3 I - 98.9 I . 11.3

c -142.7 h I 69.7 Ill. - 3.3

cjI 128.1 .j I 40.5 0 . -32 5

U,=60

Fig. 7. o,-Stress contours for crown with ceramic thickness 010.5 mm in the biting region (Case I) for a horizontal load of 600 N. A finite ekment model with 586 nodes and 456 thrccdimensional solid ckmcnts was used for these analyses.

the surface strcsscs. Thus, for better visualization of the stress contours, only the surface stresses arc used to compare the various design and loading conditions. Analyses performed in part (d) indicated that the pulp chamber had a negligible influence on the stress magnitude for all design conditions.

Stress analysis of dental aramic crowns

P = e--

36.6 6.7

I m-499

b I

f

27.5

o-16.7

g =-27.6

h.-

366

CcI -72.0

1163

l

=667

b I

62.6

c-

505

d.

544

e

= 50.2

g .

42.0

h.

379

k.

260

ml

17.3

n=

132

o=

90

I-214

~e~lmum

Shew

Fig. 9. r,,- Stress contours for a crown with aramic thickFig. 8. o,-Stresscontours for a crown with ceramic thickness nessof 0.5 mm in the biting region for a horizontal load of of 0.5 mm in the titing region for a horizontal load of 600 N. 600 N. A finite element model with 586 nodes and 456 solid A finite element mbdcl with 586 nodes and 456 solidcltimcnts elemcnls was used for these analyses. was used for thcsc analyses.

The magnitude of the shear stressesdue to a vertically applied load were relatively small. However, when the load was applied along the horizontal direction, larger values of shear stresseswere observed. The maximum value of shear stress in ceramic which occurred at the marginal area was 54.4 MPa (Fig. 9).

DISCUSSION

A second molar crown has a geometry which is approximately gymmetrical with respect to an axis along the occlu~ogingival direction (z-axis in Fig. 3). However, an axisymmetric finite element model can be used to calculatt the stress distribution when loading configurations dre also symmetrical about this axis. If cylindrical cooqdinates (r, 8, t), with z as the axis of symmetry and r!as the radial direction are considered. then in the axisymmetric model all the stress and displacement cdmponents are independent of angle 0 (Timoshenko abd Goodier, 1970). An axisymmetric stress condition has only four independent components of stress.In general, intraoral forces which act on dental prosthe& are not symmetrically oriented. Therefore, axisbmmetric finite element models for molar tooth anblyses used previously by Farah et 01. (1973. l975), +lna et al. (1975), Starting and Cook (1983). and by ck Vree et 01.(1984) have considered an ideal and possidly clinically unrealistic loading condition. Finite e#nent analysis of dental restorations should be bad on the most general oral conditions. When generali&g the results from such an analytical study, specific dttention should be given to the assumptions and simplifications used (Anusavice and

Hojjatie, 1988). In general, biological materials such as dentin are anisotropic. inhomogeneous and exhibit a nonlinear stress-strain relationship. However, in this study dentin was treated like an isotropic, homogeneous and linear material and was assumed to bond perfectly to ceramic. These assumptions were considered because of the lack of reliable mechanical property data for dentin under this condition. For simplification of the finiteelement model, the influence of the cement layer and critical structural flaws were not considered in this study. It is clear that more accurate stress distributions can be obtained from a three-dimensional model which takes the cement layer into account. However, the model employed in this study was used for a relative comparison of various design geometries in a ceramic crown under comparable loading conditions. Increase in capabilities of microcomputer based finite element programs in the future can make it possible to develop a three-dimensional finite element model that takes the cement layer and the periodontal ligament into account. Numerous reports exists in the dental literature which describe biting forces on human teeth (Craig, 1980; Gibbs et al.. 1986; Proffit et 01.. 1983). However, most of these reports correspond to axially directed occlusal forces. The maximum biting forces during ordinary chewing vary and may depend on sex, age, tooth location and type of food. Due to the large variability among human subjects, measurement of biting forces is usually conducted on large number of subjects. Gibbs et al. (1986) reported that in some bruxerclencher patients the biting force can be as much as six times larger than that of non-bruxer. A maximum biting force of 4345 N was determined for a

1164

B. HOJJATIEand K. J. ANUMVICE

subject, which was the load applied on the posterior teeth. Graf PCal. (1974) developed a three-component force transducer to measure occlusal forces in the axial, buccolingual and mesiodistal directions of a first molar tooth in a normal subject. They reported that every chewing stroke was associated with a combination of axial and horizontal forces. In one experiment they measured biting forces performed by chewing medium hard Swiss rye bread. For a biting force of 49 N measured along the vertical direction, the corresponding force along the horizontal direction was 19.6 N which corresponds to a ratio of 2.5. Therefore, for a vertical biting force of 600 N used in the present study, a horizontal force of 240 N is expected to be developed. As stated earlier, under the conditions analysed in the present study the stressesare directly proportional to the applied load. Thus, the maximum tensile stress induced in ceramic due to a horizontal load of 240 N is expected to be 72.8 MPa. However, for relative comparison of stresses.produced by vertical and horizontal loads. the same load magnitude of 600 N was applied for each condition. A comparison of stresscontours for the three design cases revealed that reduction of occlusal thickness of ceramic from 3.0 to 0.5 mm had a small influence on the stress distribution. particularly with increasing distance from the occlusal area. For a vertically applied load of 600 N, only small amounts of tensile stress were induced in the ceramic along the vertical direction. The largest compressive strcsscsoccurred in the marginal region whcrc the stress contours for all design caseswere nearly identical. Analyses pcrformcd in part (a) revealed that stressand displacement for the three design cases were not significantly different. The tensile and compressive strengths of castable ceramic are 69 and 828 M Pa, respectively (Clinical Proccdurcs Manual, Dentsply International, 1984). The stresses induced in ceramic due to a vertical load of 600 N applied on a cusp were well below these strength values. However, the analyses in part (b)showed that if the load is applied along a horizontal direction, the tensile stresses induced in ceramic at the marginal region rise above its strength level (Fig. 7). This indicates that loading orientation has a significant influence on longevity of ceramic crowns. The purpose of analysis(c) was to verify the quantitative results from the previous analyses by increasing the number of nodes and elements. In the refined model, the curvature of the crown at the occlusal region is more precisely modeled. Comparison of the stress contours for u, in the refined and unrefined models showed only a small difference in stresses within cuspal areas. Since the stress contours at the marginal and dcntinal regions were similar, the difference in stresses within occlusal regions probably is more related to the change in crown geometry at this region and not to the reduction in discretization error. The results of analysis (c) indicate that the values obtained for analyses (a) and (b) were not associated with large values of the discretization error.

The result obtained from analysis (d) is important relative to the efficiency of the finite element models. When the pulp chamber was replaced by a void region, no significant changes in stress and displacement values were obtained. This implies that for finite element analyses of similar dental restorations, it is not necessaryto model the pulp chamber. However, if the pulp chamber is included in the model, relatively larger sized elements can be selected in this region. Therefore, the limited number of nodes and elements which are usually associated with microcomputer programs can be used for more critical areas such as within ceramic marginal regions. From these analyses, it can be inferred that regions with a relatively small elastic modulus which are located farther away from the site of loading can have large elements or in some cases they may be ignored completely in the finite element model. In the previous two-dimensional finite element stress analysis of natural tooth by Atmaram and Mohammed (1981) and ceramic crown by Anusavice and Hojjatie (1988). the influence of the pulp chamber was considered to be negligible. Also, in a three-dimensional finite element analysis performed by Rubin et al. (1983). it was found that the pulp chamber had no major influence on the stressdistributions. The analysts in part (d) of the present study support this finding. When the vertical load of 600 N was applied along one cusp, the largest tcnsilc stress which developed in ceramic was 12.0 MPa and occurred near the cuspal region (Case I). The corresponding tensile stressin the marginal area was 4.0 MPa (contour k in Fig. 6). However, when the load was applied along the horizontal direction. the tensile stressesinduced in cuspal and marginal regions increased to 25.9 and 113.5 M Pa, respectively (contours k and c in Fig. 7). The maximum compressive stressesin ceramic due to vertical and horizontal loading were 70.9 MPa and 116.2 MPa, respectively, in the marginal area. For the horizontally oriented force, the peak value of the shear stressat the marginal area was 54.4 M Pa (Fig. 9). If the shear strength of ceramic is considered to be 20,000 psi (137.8 M Pa), the ratio of the peak shear stressvalue to this strength value is 0.39, while the maximum tensile stress of 113.5 MPa induced in ceramic at the marginal area, is approximately 1.6 times higher than the tensile strength value of 69.0 MPa. These results suggest that, in the absence of ceramic flaws along the interior surface or voids within dentin (or cement layer), the regions of castable ceramic crowns which are associated with the highest risk of failure are located near marginal regions and not near cuspal regions. For [email protected], a tetrasilic fluormica glassceramic, Moffa (1988) reported a failure rate for molar crowns of 35.3 % during the first three years. However, little information is available on the mode of failure of these restorations. Mcfnnes-Ledoux et al. (1989) and Grossman (1989) have associated the longevity of these crowns with the bond strength of various adhesive

materials

with

ceramic

and dentin.

In a

Stress analysis of dental ceramic crowns

recent study, Kelly et al. (1989) have used quantitative fractography by scanning electron microscopy to determine the source of fracture and stress values responsible for Qacture in five clinically failed [email protected] aramic crowns. They concluded that the source of failure in these crowns was at the internal surface of aramic. often at an intersection of two internal walls of the proposed teeth. The fracture stress in Dice+ was reported to be 55.4+ 10.6 MPa. In an in oitro study, Dickinson (1988) reported that fracture of an anterior [email protected] crown initiated from the incisal edge at the point of loading. However, Hoekstra (1988) showed that under in oioo conditions, fracture initiated from the lingual surfaa and propagated to the marginal area. They reported that failure of a molar [email protected] crown originated from inside the occlusal surface. Unfortunately, these clinical results were reported only for a single crown. In general, clinical failures ofceramic restorations are statistical in nature and determination of the failure modes should be based on a large number of subjects. Since the glass-ceramic material was introduced to dentistry for clinical use only four years ago, few clinical reports on failure are available. At the present time the only reliable study which reports the clinical failure of these DicoF restoration based on five ceramic crowns, is by Kelly er al. (1989). However, to determine the mode of failure

of these restorations

fractographic

additional

clinical

and

d#ta arc necdcd.

It should bc emphasiscd

that in the finite clement

model analysed in this study, the influence of the flaws and the cement layer were assumed to be negligible. Because of these assumptions, no conclusion can be made regarding the failure mode and fracture mechanism of these restorations. The results of this study support the hypothesis that the orientation of applied forces is a dominant factor in the development of tensile stresses.The reduction of the occlusal thickness of ceramic from 3.0 to 0.5 mm has only a minimal etTecton the induced tensile stress state. This insensitivity of induced stressesto changes in the crown dimensions does not appear to justify the recommendation of a minimal occlusal thickness of 1.5 mm. Howevur. to draw a conclusion regarding the mode

of failure

dimensional

of these restorations,

future

three-

studies should also consider the influence

of the cement layer, surface flaws, periodontal

liga-

merit. and other factors which may be associated with a higher risk of clinical failure.

REFERENCFS

Adair, P. J. and Mockstra, K. E. (1982) Fit evaluation of a castablc ceramic. /. drnr. Res.. IADR Pros. Absfr. 61, No. lsoo. p. 345. Anusavicc. K. J. aed Hojjalie. B. (1987) Stress distribution in metal-ceramic icrowns with a facial porcelain margin. 1. Dent. Res. M, 1493-1498. Anusavicc, K. J. .Ind Hojjatic, B. (1988) Influence of in&al length of ceraaic and loading orientalion on stress distribution in ceramic crowns. 1. Dent. Res. 67, 1371-I 375.

1165

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ANUSAVICE

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