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Stress analysis of cemented or resin-bonded loaded porcelain inlays
Stress analysis of cemented or resin-bonded loaded porcelain inlays T. Derand Department of Oral Technology School of Dentistry University of Lund S-214 21 MalmO, Sweden Received November 30, 1989 Accepted September 4, 1990 Dent Mater 7:21-24, January, 1991
Abstract-Ceramic inlays have become an interesting alternative to amalgam fillings. There are two main ways to affix the inlay to the tooth: by use of either a cement or a composite adhesion system. The aim of the investigation was to examine the two methods' influence on stresses in the inlay and the shear-stress state in the gluing materials. The finite element method (FEM) was used to calculate the stresses and displacements. A two-dimensional inlay was modeled with a 200-N point load on the occlusal surface just over the isthmus. Composite and cement linings were simulated with and without adhesion, and the stresses were calculated. The results showed a marked compression of the dentin below the proximal part of the inlay. The direct effects of the different elastic constants of the two lining materials influenced the stresses in only a minor way. Complete adhesion reduced stresses in the inlay, compared with cemented inlays, with no adhesion along the pulpal wall. Higher shear stresses were also calculated in the cement compared with the composite.
he use of ceramic inlays is becoming increasingly more popular, especially since some patients are concerned about metal constructions. Great hopes were originally set on composites as a first-choice alternative to amalgams. However, disadvantages-such as lack of wear resistance, discoloration, and leaka g e - c a u s e d clinical problems, most pronounced in molars (Lambrechts et al., 1987; Davidson, 1987). The improvements in ceramic materials now make it possible for alternatives to amalgams, composites, and cast metal to be offered for posterior teeth. The increased interest in esthetic and cosmetic dentistry has led to significant patient acceptance of ceramic inlays. There are two types of materials available today, porcelains and glass ceramics. Porcelain inlays are fabricated with the brush technique, and most glass ceramics are fabricated by the casting method. A computeraided milling technique has also been introduced into the market (Moerman et al., 1989). All ceramic materials are characterized by brittleness and low tensile strength. They are also weakened by small defects in critical areas. Therefore, great care must be taken in the construction of an inlay or crown. An important clinical consideration is the way in which inlays are fixed to the teeth. They can be c e m e n t e d with either zinc phosphate, polyalcenoate cements, or with adhesive resin composites. The latter method has become popular, since it has cosmetic advantages, but it may also strengthen the construction by offering better support. There are, however, several advantages and disadvantages with each of these methods. The adhesive technique implies bonding to both ceramic and/ or enamel and dentin (Jensen et al., 1987; Nicholls, 1988; Calamia, 1989). The aim of this investigation was to
T
determine how adhesive bonding influences the stress distribution in a loaded ceramic inlay as compared with cementation. The stresses in the fLxation materials were also examined. Stresses were calculated by the finite element method (FEM). As a verification of the stress analysis, f r a c t u r e experiments were conducted with true ceramic inlays in extracted teeth to examine which f'Lxation method resisted the highest load and whether this agreed with the stress analysis. MATERIALSAND METHODS A symmetrical L-wo-dimensional M O D
inlay was modeled, with shape and dimensions as given in Fig. 1. The load (200 N) was applied just over JI
r'4 se~
so~
~os
sol
502
50~
502 ~
SO3
50~
i !
401
~02U."
4O3
~0~
i
303
3O4
5o6
I, "!'r::~[l'l I i :~!Ll ....
301
l,
302~
i 201
102
SOS
SOS
,i !
, 203
206
Fig. I. The central (mesio-distal) section of a twodimensional model of a porcelain inlay. Dimensions in ram. Smaller elements (1000-1022) define the inner surface of the ceramic inlay. Elements 11001122 represent the cement of the resin layer (100 pro). Elements 900-922 represent smaller elements of dentin. Elastic properties of the different materials are presented in "Materials and Methods". In cases where "no bonding" was modeled, small elements with very low elastic properties {not shown) were placed between series 900 and 1100.
Dental Materials~January 1991 21
the isthmus in the direction of the long axis of the tooth. The Abaqus (version 4, 1982) finite element prog r a m was based on rectangular elements with four integration points for output, so they are not included in the i n t e r - e l e m e n t a s s e m b l y process. Stress invariants (von Mises' equivalent stress) and principal stresses and strain components were calculated. Smaller elements were used around the joint and in the adhesive or cement layer. The three components in the model were simplified to isotropic linear elastic materials, and the elastic constants E (Young's modulus) were 18/70 GPa and v (Poisson's ratio) 0.31/0.28 for dentin and porcelain, respectively (Anusavice et al., 1986). Values for the luting materials were chosen as follows: a high-modulus material E = 20 GPa, v = 0.35, which corresponded to a good cement (Powers et al., 1976), and a low-modulus material E = 6 GPa, v = 0.36, corres p o n d i n g to a low-filler loaded composite material (Braem et al., 1986). The calculations consisted of cases with and without adhesion to the axial pulpal wall. This was done by establishment of an intermediate layer of elements with e x t r e m e l y low
m | (
,m=
, (lit
lie
ip
o n l D
n
n ~
e
' i l | ° i l l
h i '
Young's modulus values. The cervical part of the proximal box was also modeled with and without elements, corresponding to a cement layer in the bottom. This would imitate a m e c h a n i c a l l y , cervically locked proximal wing of the inlay. Model experiments were also conducted with porcelain inlays dimensioned as given above. Ten extracted orthodontic pre-molars from the upper jaw were mounted in acrylic and oriented in a milling machine. The cavities were made with an opening angle of 20 °. Minor details were adjusted by hand with use of diamond burs. The porcelain inlays were made of Vitadur (Vita Zahnfabrik, H. Rauter, Bad S~ickingen, Germany). Five inlays were c e m e n t e d with glass-ionomer cement (Ketac Bond, Espe, Germany) and five with a composite luting material (DiCor, Dentsply Intl., York, PA). The inlays were loaded over the isthmus until fractured in a testing machine (Alvetron, Stockholm, Sweden). The adhesive bond with the composite material was made by etching of the porcelain surface, silane treatment, cleaning of the dentin surface, and coating it with additional bonding material (Gluma, Bayer, Germany). The specimens were stored in tap water one day before being loaded. When the glass-ionomer cement was
~,
Inlay
- ' ' J -
Dentin
Fig, 2. Displacements of a loaded model. Dotted line = inlay loaded; solid line = unloaded model. Displacements of elements under the loading could also be seen. The displacements are magnified by 2.639 × 104.
Fig. 3. Equivalent stresses along the axial pulpal wall (horizontal grid) and the isthmus area (vertical grid) of an inlay. Solid lines show a cemented porcelain inlay and the dotted line an inlay fixed with a resin composite material.
22 DI~RAND/STRESS ANALYSIS OF PORCELAIN INLAYS
used, the inlays and teeth w e r e cleaned before cementation (Tubulicid, Dental Therapeutics, Nacka, Sweden).
RESULTS The program created a picture of enlarged displacements of the loaded structure, shown in Fig. 2. From that, a uniform bending of the occlusal bulk of the inlay and compression of the dentin (especially beneath the proximal box) can be seen. The stress invariants (yon Mises') are shown in Table 1 from elements around the inner pulpal walls of the inlay. The calculated equivalent stresses are also shown graphically in Fig. 3. The magnitudes of the stresses show, at most points, very small differences between the two luting systems. This indicates that if adhesion occurs for both of them, the Young's modulus has a minor effect on the calculated stresses in the inlay. When the proximal box was cervically locked to the dentin, the stresses were reduced by about 20%. The equivalent stresses in the occlusal part of the isthmus were approximately 10% lower in models with full adhesion compared with the case lacking adhesion along the axial pulpal wall. The principal stresses in elements around the isthmus angle showed components of tensile stresses (Table 2). The maximum tensile stresses were higher for resin-bonded compared with cemented cases in the transverse plane (occlusal), but this difference was r e d u c e d when no adhesion was present along the pulpal wall. The shear stresses in the adhesive were seen to be highest most often in the occlusal element next to the isthmus. The m a g n i t u d e s w e r e greatest when the proximal box was locked to the dentin (Table 3). The highest stresses were found in the occlusal element for the model with the cement material, but along the axial pulpal wall the increase was small. In the occlusal part, close to the isthmus angle, comparatively higher stresses were found in the cement layer than in the sample with the resin adhesive. The fracture strengths of true inlays fixed on extracted pre-molars showed h i g h e r values for resin-
bonded than cemented specimens [570 (23)/470 (50) N, mean and SD]. In all cases, the rupture occurred in the isthmus area. In three cases of cemented inlays, a slight sliding of the inlays was noticed in the testing machine just before fracture. DISCUSSION In this model, the total number of elements was 159, with a concentration of smaller elements along the interface between tooth and inlay. A two-dimensional model is, in this case, rather close to a true inlay and its central section. Knowledge of how the fLxation techniques influence the stresses in the inlay could be found in this central plane of the inlay. A literature review of material properties yielded a range of values, but the values used may be accepted for this calculation (with the possible exception of the cement and resin). Luting materials are subjected to mostly shear forces, and Young's moduli and Poisson's ratio are not documented for the situation where voids and porosity in the joint may lead to a decrease in stiffness, which can influence the clinical situation. The highest value found for a cement was chosen for maximum span between the figures in the calculations (Powers et al., 1976). The stresses at the nodes were calculated by use of the values at the integration points and extrapolation to the nodes. Equivalent stresses are meaningful for indication of yield stresses in a model. Here, no failure criterion was appropriate for the materials, and the equivalent stresses were used for comparative purposes only. When the two models with cement and resin luting materials were compared, both with perfect adhesion, the equivalent stress distribution in the porcelain inlay was quite similar but had different magnitudes. Resin composite created higher stresses in the cervical part of the box. All the differences, however, were small, and it could be stated that the influence of the modulus of elasticity of the luting material on the stresses in the ceramic inlay was < 10%. When the proximal box was locked in the cervical part, the stresses were decreased in both examples. This model could be compared with a clinical case
TABLE 1 EQUIVALENTSTRESSES(MPa) (AT TWO POINTSFOR EACH ELEMENT) IN THE INLAY ALONG THE PULPAL WALLS UNDER DIFFERENTCONDITIONS Condition Element C CL ON CLN R RN RL RLN 1008 0.10 0.10 0.11 0.01 0.10 0.11 0.10 0.11 1008 0.09 0.09 0.11 0.11 0.08 0.12 0.10 0.11 1007 0.08 0.08 0.11 0.11 0.10 0.12 0.09 0.11 1007 0.09 0.08 0.10 0.10 0.10 0.10 0.09 0.10 1006 0.11 0.09 0.07 0.06 0.10 0.07 0.09 0.06 1006 0.10 0.09 0.06 0.05 0.10 0.07 0.08 0.05 1005 0.10 0.08 0.07 0.08 0.10 0.07 0.08 0.06 1005 0.09 0.08 0.07 0.06 0.10 0.07 0.08 0.06 1004 0.09 0.08 0.08 0.07 0.10 0.08 0.08 0.07 1004 0.09 0.07 0.07 0.07 0.09 0.07 0.08 0.07 1003 0.09 0.07 0.08 0.07 0.09 0.08 0.07 0.07 1003 0.09 0.07 0.09 0.08 0.10 0.09 0.07 0.08 1002 0.10 0.07 0.09 0.08 0.09 0.09 0.07 0.08 1002 0.09 0.07 0.09 0.08 0.09 0.09 0.07 0.09 1001 0.10 0.07 0.10 0.09 0.09 0.11 0.08 0.11 1001 0.09 0.08 0.13 0.12 0.11 0.14 0.09 0.12 1000 0.08 0.09 0.12 0.12 0.10 0.12 0.10 0.13 1000 0.15 0.12 0.21 0.18 0.20 0.26 0.14 0.18 C = cemented inlay; CL = cemented inlay with cervically locked proximal box; CN = cemented inlay with no adhesion along the vertical (axial) pulpal wall; CLN = locked proximal box and no adhesion; R = adhesive-resin-fixed inlay; RL = adhesive-resin-fixed inlay with cervically locked proximal box; RLN -- same as RL, without adhesion. Elements are identified in Fig. 1.
where the luting material is very thin cervically and where there is mechanical locking. In the model where no adhesion to the pulpal wall was used, the stresses in the inlay were greater in the occlusal and cervical elements, where the stresses were about 30% higher. This situation could be comparable with cases when low adhesion exists, e.g., when zincphosphate or glass-ionomer cements are used, perhaps with improperly cleaned dentin surfaces. A strong adhesion between cements and ceramics is probably not to be expected, since only mechanical locking occurs. Glass-ionomer cement adheres well only to substrates such as enamel, dentin, and base metals, where attractive forces are electrostatic (Hotz et al., 1977). The tensile stresses in the isthmus angle were not critical for a dental ceramic at the applied load, but varied with the experimental conditions. With full adhesion to the tooth, they were somewhat higher when resin material was used compared with cement, but this difference was reduced when no adhesion was present along the axial pulpal wall. Again, this shows that the Young's modulus of the luting material is of minor importance to the stresses in the inlay. The differences in elastic properties
between the adhesive and the ceramic are, in both cases, great, and the relatively thin lining may be the explanation. In the elements representing the luting materials, larger shear stresses arose, somewhat greater along the pulpal wall when the cervical part of the proximal box was locked. In the occlusal part of the isthmus area, the stresses were higher when cement was used because of lower compliance, and the difference was seen clearly. In this area, the stresses were also higher in cases with locked proximal boxes. This indicates that the resins could function better than cements under loaded inlays in this respect. Comparison of cemented inlays without adhesion and resinbonded inlays with and without adhesion showed that, without adhesion, lower shear stresses were found in the resin material than in the cements. Resin materials without bonding to the dentin, however, may be a risky clinical situation, since leakage may be deleterious to the tooth. The fracture experiments were few, but resin-bonded inlays demonstrated higher fracture resistance than did cemented ones. Together with the calculations, it would be consistent to conclude that this dif-
Dental Materials~January 1991 23
TABLE 2
COMPARISON OF MAXIMAL TENSILE PRINCIPAL STRESSES (MPa) AROUND THE ISTHMUS ANGLE (IN ELEMENTS 1006-1008) UNDER DIFFERENTCONDITIONS Elements Condition 1006 1007 1008 C 0.01 0.06 0.07 CL 0.01 0.06 0.07 CN 0.02 0.09 0.07 CLN 0.03 0.09 0.07 R 0.06 0.07 0.08 RL 0.08 0.07 0.09 RN 0.02 0.09 0.08 RLN 0.03 0.09 0.08 C = cemented inlay, CL = cemented inlay with a cervically locked proximal box, CN = cemented inlay without any bonding to the axial pulpal wall, CLN = cemented inlay with a cervically locked proximal box and without any bonding to the axial pulpal wall, R = resin-bonded inlay, RL = resinbonded inlay with a cervically locked proximal box, RN = resin without bonding to the axial wall, and RLN = the same with locked proximal box. TABLE 3
MEAN SHEAR STRESSES (MPa) IN CEMENT/ADHESIVELAYER Condition Element
C
CL
CN
R
RL
RN
1100 1101
0.018
0.017
-
0.012
0.011
-
0.007 0.010 0.009 0.010 1102 0.011 0.010 0.012 0.010 1103 0.008 0.009 0.010 0.010 1104 0.009 0.008 0.010 0.009 1105 0.005 0.007 0.007 0.007 1106 0.010 0.025 0.008 0.007 1107 0.028 0.038 0.020 0.028 0.034 0.006 1108 0.104 0.120 0.021 0.035 0.048 0.005 1109 0.082 0.037 0.012 0.016 0.014 0.004 1110 0.032 0.018 0.009 0.006 0.009 0.004 With (CL, RL) or without (C,R) locked proximal box and without adhesion along the pulpal wall CN, RN. Element 1100 (cervical) to 1108 along the pulpal wall and 1107-1110, occlusal.
ference is due to the fact that clinically high loads are generally not observed to create critical stress failure in the inlays, but, rather more often, in the luting materials. When high shear stresses arise in a cement
film at dynamic loading of an inlay, pulverization of this rather weak and brittle material may occur. If this happens, the ceramic inlay will have both decreased support and reduced fLxation to the tooth, consistent with
24 DI~RAND/STRESSANALYSIS OF PORCELAIN INLAYS
the situation. Distortions of some inlays were seen in the fracture experiments with cemented inlays. REFERENCES
ANUSAVICE, K.J.; HOJJATIE, B.; and DEHOFF, P.H. (1986): Influence of Metal Thickness on Stress Distribution in Metal-Ceramic Crowns, J Dent Res 65:1173--1178. BRAEM, M.; LAMBRECHTS, P.; VAN DOREN, V.; and VANHERLE,G. (1986): The Impact of Composite Structure on its Elastic Response, J Dent Res 65:648-653. CALAM~A,J. (1989): High-strength Porcelain Bonded Restorations: Anterior and Posterior, Quint Int 20:717-726. DAVIDSON,C.L. (1987): Posterior Composites: Criteria for Assessment, Quint Int 18:515-519. JENSEN, M.; REDFORD, D.; WILLIAMS, B.; and GARDNER,F. (1987). Posterior Etched-Porcelain Restorations: an in vitro Study, Compend Contin Educ Dent 8:615--622. Howz, P.; McLEAN, J.W.; and SCED,I. (1977): The Bonding of Glass-Ionomer Cements to Metal and Tooth Substrates, Br Dent J 142:41-47. LAMBRECHTS, P.; BRAEM, M.; and VANHERLE, G. (1987): Evaluation of Clinical Performance for Posterior Composite Resins and Dentin Adhesives, Oper Dent 12:53-78. MOERMAN, W.H.; BRANDESTINI, M.; Ltrrz, F.; and BARBAKOW,F. (1989): Chairside Computer-aided Direct Ceramic Inlays, Quint Int 20:329-339. NmHOLLS, J.I. (1988): Tensile Bond of Resin Cements to Porcelain Veneers, J Prosthet Dent 60:443-445. POWERS, J.M.; FAR)H, J.W.; and CmuG, R.G. (1976): Modulus of Elasticity and Strength Properties of Dental Cements, J Am Dent Assoc 92:588-591.
Abstract-Ceramic inlays have become an interesting alternative to amalgam fillings. There are two main ways to affix the inlay to the tooth: by use of either a cement or a composite adhesion system. The aim of the investigation was to examine the two methods' influence on stresses in the inlay and the shear-stress state in the gluing materials. The finite element method (FEM) was used to calculate the stresses and displacements. A two-dimensional inlay was modeled with a 200-N point load on the occlusal surface just over the isthmus. Composite and cement linings were simulated with and without adhesion, and the stresses were calculated. The results showed a marked compression of the dentin below the proximal part of the inlay. The direct effects of the different elastic constants of the two lining materials influenced the stresses in only a minor way. Complete adhesion reduced stresses in the inlay, compared with cemented inlays, with no adhesion along the pulpal wall. Higher shear stresses were also calculated in the cement compared with the composite.
he use of ceramic inlays is becoming increasingly more popular, especially since some patients are concerned about metal constructions. Great hopes were originally set on composites as a first-choice alternative to amalgams. However, disadvantages-such as lack of wear resistance, discoloration, and leaka g e - c a u s e d clinical problems, most pronounced in molars (Lambrechts et al., 1987; Davidson, 1987). The improvements in ceramic materials now make it possible for alternatives to amalgams, composites, and cast metal to be offered for posterior teeth. The increased interest in esthetic and cosmetic dentistry has led to significant patient acceptance of ceramic inlays. There are two types of materials available today, porcelains and glass ceramics. Porcelain inlays are fabricated with the brush technique, and most glass ceramics are fabricated by the casting method. A computeraided milling technique has also been introduced into the market (Moerman et al., 1989). All ceramic materials are characterized by brittleness and low tensile strength. They are also weakened by small defects in critical areas. Therefore, great care must be taken in the construction of an inlay or crown. An important clinical consideration is the way in which inlays are fixed to the teeth. They can be c e m e n t e d with either zinc phosphate, polyalcenoate cements, or with adhesive resin composites. The latter method has become popular, since it has cosmetic advantages, but it may also strengthen the construction by offering better support. There are, however, several advantages and disadvantages with each of these methods. The adhesive technique implies bonding to both ceramic and/ or enamel and dentin (Jensen et al., 1987; Nicholls, 1988; Calamia, 1989). The aim of this investigation was to
T
determine how adhesive bonding influences the stress distribution in a loaded ceramic inlay as compared with cementation. The stresses in the fLxation materials were also examined. Stresses were calculated by the finite element method (FEM). As a verification of the stress analysis, f r a c t u r e experiments were conducted with true ceramic inlays in extracted teeth to examine which f'Lxation method resisted the highest load and whether this agreed with the stress analysis. MATERIALSAND METHODS A symmetrical L-wo-dimensional M O D
inlay was modeled, with shape and dimensions as given in Fig. 1. The load (200 N) was applied just over JI
r'4 se~
so~
~os
sol
502
50~
502 ~
SO3
50~
i !
401
~02U."
4O3
~0~
i
303
3O4
5o6
I, "!'r::~[l'l I i :~!Ll ....
301
l,
302~
i 201
102
SOS
SOS
,i !
, 203
206
Fig. I. The central (mesio-distal) section of a twodimensional model of a porcelain inlay. Dimensions in ram. Smaller elements (1000-1022) define the inner surface of the ceramic inlay. Elements 11001122 represent the cement of the resin layer (100 pro). Elements 900-922 represent smaller elements of dentin. Elastic properties of the different materials are presented in "Materials and Methods". In cases where "no bonding" was modeled, small elements with very low elastic properties {not shown) were placed between series 900 and 1100.
Dental Materials~January 1991 21
the isthmus in the direction of the long axis of the tooth. The Abaqus (version 4, 1982) finite element prog r a m was based on rectangular elements with four integration points for output, so they are not included in the i n t e r - e l e m e n t a s s e m b l y process. Stress invariants (von Mises' equivalent stress) and principal stresses and strain components were calculated. Smaller elements were used around the joint and in the adhesive or cement layer. The three components in the model were simplified to isotropic linear elastic materials, and the elastic constants E (Young's modulus) were 18/70 GPa and v (Poisson's ratio) 0.31/0.28 for dentin and porcelain, respectively (Anusavice et al., 1986). Values for the luting materials were chosen as follows: a high-modulus material E = 20 GPa, v = 0.35, which corresponded to a good cement (Powers et al., 1976), and a low-modulus material E = 6 GPa, v = 0.36, corres p o n d i n g to a low-filler loaded composite material (Braem et al., 1986). The calculations consisted of cases with and without adhesion to the axial pulpal wall. This was done by establishment of an intermediate layer of elements with e x t r e m e l y low
m | (
,m=
, (lit
lie
ip
o n l D
n
n ~
e
' i l | ° i l l
h i '
Young's modulus values. The cervical part of the proximal box was also modeled with and without elements, corresponding to a cement layer in the bottom. This would imitate a m e c h a n i c a l l y , cervically locked proximal wing of the inlay. Model experiments were also conducted with porcelain inlays dimensioned as given above. Ten extracted orthodontic pre-molars from the upper jaw were mounted in acrylic and oriented in a milling machine. The cavities were made with an opening angle of 20 °. Minor details were adjusted by hand with use of diamond burs. The porcelain inlays were made of Vitadur (Vita Zahnfabrik, H. Rauter, Bad S~ickingen, Germany). Five inlays were c e m e n t e d with glass-ionomer cement (Ketac Bond, Espe, Germany) and five with a composite luting material (DiCor, Dentsply Intl., York, PA). The inlays were loaded over the isthmus until fractured in a testing machine (Alvetron, Stockholm, Sweden). The adhesive bond with the composite material was made by etching of the porcelain surface, silane treatment, cleaning of the dentin surface, and coating it with additional bonding material (Gluma, Bayer, Germany). The specimens were stored in tap water one day before being loaded. When the glass-ionomer cement was
~,
Inlay
- ' ' J -
Dentin
Fig, 2. Displacements of a loaded model. Dotted line = inlay loaded; solid line = unloaded model. Displacements of elements under the loading could also be seen. The displacements are magnified by 2.639 × 104.
Fig. 3. Equivalent stresses along the axial pulpal wall (horizontal grid) and the isthmus area (vertical grid) of an inlay. Solid lines show a cemented porcelain inlay and the dotted line an inlay fixed with a resin composite material.
22 DI~RAND/STRESS ANALYSIS OF PORCELAIN INLAYS
used, the inlays and teeth w e r e cleaned before cementation (Tubulicid, Dental Therapeutics, Nacka, Sweden).
RESULTS The program created a picture of enlarged displacements of the loaded structure, shown in Fig. 2. From that, a uniform bending of the occlusal bulk of the inlay and compression of the dentin (especially beneath the proximal box) can be seen. The stress invariants (yon Mises') are shown in Table 1 from elements around the inner pulpal walls of the inlay. The calculated equivalent stresses are also shown graphically in Fig. 3. The magnitudes of the stresses show, at most points, very small differences between the two luting systems. This indicates that if adhesion occurs for both of them, the Young's modulus has a minor effect on the calculated stresses in the inlay. When the proximal box was cervically locked to the dentin, the stresses were reduced by about 20%. The equivalent stresses in the occlusal part of the isthmus were approximately 10% lower in models with full adhesion compared with the case lacking adhesion along the axial pulpal wall. The principal stresses in elements around the isthmus angle showed components of tensile stresses (Table 2). The maximum tensile stresses were higher for resin-bonded compared with cemented cases in the transverse plane (occlusal), but this difference was r e d u c e d when no adhesion was present along the pulpal wall. The shear stresses in the adhesive were seen to be highest most often in the occlusal element next to the isthmus. The m a g n i t u d e s w e r e greatest when the proximal box was locked to the dentin (Table 3). The highest stresses were found in the occlusal element for the model with the cement material, but along the axial pulpal wall the increase was small. In the occlusal part, close to the isthmus angle, comparatively higher stresses were found in the cement layer than in the sample with the resin adhesive. The fracture strengths of true inlays fixed on extracted pre-molars showed h i g h e r values for resin-
bonded than cemented specimens [570 (23)/470 (50) N, mean and SD]. In all cases, the rupture occurred in the isthmus area. In three cases of cemented inlays, a slight sliding of the inlays was noticed in the testing machine just before fracture. DISCUSSION In this model, the total number of elements was 159, with a concentration of smaller elements along the interface between tooth and inlay. A two-dimensional model is, in this case, rather close to a true inlay and its central section. Knowledge of how the fLxation techniques influence the stresses in the inlay could be found in this central plane of the inlay. A literature review of material properties yielded a range of values, but the values used may be accepted for this calculation (with the possible exception of the cement and resin). Luting materials are subjected to mostly shear forces, and Young's moduli and Poisson's ratio are not documented for the situation where voids and porosity in the joint may lead to a decrease in stiffness, which can influence the clinical situation. The highest value found for a cement was chosen for maximum span between the figures in the calculations (Powers et al., 1976). The stresses at the nodes were calculated by use of the values at the integration points and extrapolation to the nodes. Equivalent stresses are meaningful for indication of yield stresses in a model. Here, no failure criterion was appropriate for the materials, and the equivalent stresses were used for comparative purposes only. When the two models with cement and resin luting materials were compared, both with perfect adhesion, the equivalent stress distribution in the porcelain inlay was quite similar but had different magnitudes. Resin composite created higher stresses in the cervical part of the box. All the differences, however, were small, and it could be stated that the influence of the modulus of elasticity of the luting material on the stresses in the ceramic inlay was < 10%. When the proximal box was locked in the cervical part, the stresses were decreased in both examples. This model could be compared with a clinical case
TABLE 1 EQUIVALENTSTRESSES(MPa) (AT TWO POINTSFOR EACH ELEMENT) IN THE INLAY ALONG THE PULPAL WALLS UNDER DIFFERENTCONDITIONS Condition Element C CL ON CLN R RN RL RLN 1008 0.10 0.10 0.11 0.01 0.10 0.11 0.10 0.11 1008 0.09 0.09 0.11 0.11 0.08 0.12 0.10 0.11 1007 0.08 0.08 0.11 0.11 0.10 0.12 0.09 0.11 1007 0.09 0.08 0.10 0.10 0.10 0.10 0.09 0.10 1006 0.11 0.09 0.07 0.06 0.10 0.07 0.09 0.06 1006 0.10 0.09 0.06 0.05 0.10 0.07 0.08 0.05 1005 0.10 0.08 0.07 0.08 0.10 0.07 0.08 0.06 1005 0.09 0.08 0.07 0.06 0.10 0.07 0.08 0.06 1004 0.09 0.08 0.08 0.07 0.10 0.08 0.08 0.07 1004 0.09 0.07 0.07 0.07 0.09 0.07 0.08 0.07 1003 0.09 0.07 0.08 0.07 0.09 0.08 0.07 0.07 1003 0.09 0.07 0.09 0.08 0.10 0.09 0.07 0.08 1002 0.10 0.07 0.09 0.08 0.09 0.09 0.07 0.08 1002 0.09 0.07 0.09 0.08 0.09 0.09 0.07 0.09 1001 0.10 0.07 0.10 0.09 0.09 0.11 0.08 0.11 1001 0.09 0.08 0.13 0.12 0.11 0.14 0.09 0.12 1000 0.08 0.09 0.12 0.12 0.10 0.12 0.10 0.13 1000 0.15 0.12 0.21 0.18 0.20 0.26 0.14 0.18 C = cemented inlay; CL = cemented inlay with cervically locked proximal box; CN = cemented inlay with no adhesion along the vertical (axial) pulpal wall; CLN = locked proximal box and no adhesion; R = adhesive-resin-fixed inlay; RL = adhesive-resin-fixed inlay with cervically locked proximal box; RLN -- same as RL, without adhesion. Elements are identified in Fig. 1.
where the luting material is very thin cervically and where there is mechanical locking. In the model where no adhesion to the pulpal wall was used, the stresses in the inlay were greater in the occlusal and cervical elements, where the stresses were about 30% higher. This situation could be comparable with cases when low adhesion exists, e.g., when zincphosphate or glass-ionomer cements are used, perhaps with improperly cleaned dentin surfaces. A strong adhesion between cements and ceramics is probably not to be expected, since only mechanical locking occurs. Glass-ionomer cement adheres well only to substrates such as enamel, dentin, and base metals, where attractive forces are electrostatic (Hotz et al., 1977). The tensile stresses in the isthmus angle were not critical for a dental ceramic at the applied load, but varied with the experimental conditions. With full adhesion to the tooth, they were somewhat higher when resin material was used compared with cement, but this difference was reduced when no adhesion was present along the axial pulpal wall. Again, this shows that the Young's modulus of the luting material is of minor importance to the stresses in the inlay. The differences in elastic properties
between the adhesive and the ceramic are, in both cases, great, and the relatively thin lining may be the explanation. In the elements representing the luting materials, larger shear stresses arose, somewhat greater along the pulpal wall when the cervical part of the proximal box was locked. In the occlusal part of the isthmus area, the stresses were higher when cement was used because of lower compliance, and the difference was seen clearly. In this area, the stresses were also higher in cases with locked proximal boxes. This indicates that the resins could function better than cements under loaded inlays in this respect. Comparison of cemented inlays without adhesion and resinbonded inlays with and without adhesion showed that, without adhesion, lower shear stresses were found in the resin material than in the cements. Resin materials without bonding to the dentin, however, may be a risky clinical situation, since leakage may be deleterious to the tooth. The fracture experiments were few, but resin-bonded inlays demonstrated higher fracture resistance than did cemented ones. Together with the calculations, it would be consistent to conclude that this dif-
Dental Materials~January 1991 23
TABLE 2
COMPARISON OF MAXIMAL TENSILE PRINCIPAL STRESSES (MPa) AROUND THE ISTHMUS ANGLE (IN ELEMENTS 1006-1008) UNDER DIFFERENTCONDITIONS Elements Condition 1006 1007 1008 C 0.01 0.06 0.07 CL 0.01 0.06 0.07 CN 0.02 0.09 0.07 CLN 0.03 0.09 0.07 R 0.06 0.07 0.08 RL 0.08 0.07 0.09 RN 0.02 0.09 0.08 RLN 0.03 0.09 0.08 C = cemented inlay, CL = cemented inlay with a cervically locked proximal box, CN = cemented inlay without any bonding to the axial pulpal wall, CLN = cemented inlay with a cervically locked proximal box and without any bonding to the axial pulpal wall, R = resin-bonded inlay, RL = resinbonded inlay with a cervically locked proximal box, RN = resin without bonding to the axial wall, and RLN = the same with locked proximal box. TABLE 3
MEAN SHEAR STRESSES (MPa) IN CEMENT/ADHESIVELAYER Condition Element
C
CL
CN
R
RL
RN
1100 1101
0.018
0.017
-
0.012
0.011
-
0.007 0.010 0.009 0.010 1102 0.011 0.010 0.012 0.010 1103 0.008 0.009 0.010 0.010 1104 0.009 0.008 0.010 0.009 1105 0.005 0.007 0.007 0.007 1106 0.010 0.025 0.008 0.007 1107 0.028 0.038 0.020 0.028 0.034 0.006 1108 0.104 0.120 0.021 0.035 0.048 0.005 1109 0.082 0.037 0.012 0.016 0.014 0.004 1110 0.032 0.018 0.009 0.006 0.009 0.004 With (CL, RL) or without (C,R) locked proximal box and without adhesion along the pulpal wall CN, RN. Element 1100 (cervical) to 1108 along the pulpal wall and 1107-1110, occlusal.
ference is due to the fact that clinically high loads are generally not observed to create critical stress failure in the inlays, but, rather more often, in the luting materials. When high shear stresses arise in a cement
film at dynamic loading of an inlay, pulverization of this rather weak and brittle material may occur. If this happens, the ceramic inlay will have both decreased support and reduced fLxation to the tooth, consistent with
24 DI~RAND/STRESSANALYSIS OF PORCELAIN INLAYS
the situation. Distortions of some inlays were seen in the fracture experiments with cemented inlays. REFERENCES
ANUSAVICE, K.J.; HOJJATIE, B.; and DEHOFF, P.H. (1986): Influence of Metal Thickness on Stress Distribution in Metal-Ceramic Crowns, J Dent Res 65:1173--1178. BRAEM, M.; LAMBRECHTS, P.; VAN DOREN, V.; and VANHERLE,G. (1986): The Impact of Composite Structure on its Elastic Response, J Dent Res 65:648-653. CALAM~A,J. (1989): High-strength Porcelain Bonded Restorations: Anterior and Posterior, Quint Int 20:717-726. DAVIDSON,C.L. (1987): Posterior Composites: Criteria for Assessment, Quint Int 18:515-519. JENSEN, M.; REDFORD, D.; WILLIAMS, B.; and GARDNER,F. (1987). Posterior Etched-Porcelain Restorations: an in vitro Study, Compend Contin Educ Dent 8:615--622. Howz, P.; McLEAN, J.W.; and SCED,I. (1977): The Bonding of Glass-Ionomer Cements to Metal and Tooth Substrates, Br Dent J 142:41-47. LAMBRECHTS, P.; BRAEM, M.; and VANHERLE, G. (1987): Evaluation of Clinical Performance for Posterior Composite Resins and Dentin Adhesives, Oper Dent 12:53-78. MOERMAN, W.H.; BRANDESTINI, M.; Ltrrz, F.; and BARBAKOW,F. (1989): Chairside Computer-aided Direct Ceramic Inlays, Quint Int 20:329-339. NmHOLLS, J.I. (1988): Tensile Bond of Resin Cements to Porcelain Veneers, J Prosthet Dent 60:443-445. POWERS, J.M.; FAR)H, J.W.; and CmuG, R.G. (1976): Modulus of Elasticity and Strength Properties of Dental Cements, J Am Dent Assoc 92:588-591.