Effects of Labial Mar in Design on Stress Distribution o a Porcelain-Fused-to-MetalCrown
P
John Y. Chai, BDS, AdS, * andJohn W. Steege, MS3MET Purpose: This study compared the stress distribution of three porcelain-fused-to-metal labial margins on a central incisor under simulated occlusal force. Materials and Methods: The margin designs were rounded-shoulder, rounded-shoulder with a bevel, and a chamfer. Results: Evaluation of mean equivalent Mises tensile stress did not show any difference at the cement-dentin and metal-cement interfaces of the three margins. The mean equivalent Mises tensile stress at the porcelain-metal interface was found t o be significantly higher for rounded-shoulder when compared with the chamfer. There was no significant difference in the axial stresses along the three interfaces among the three margin designs. Statistically significant differences in radial stresses at some interfaces of the three margin designs were found. Conclusion: The change of cement thickness of the chamfer margin is significantly greater than that of either the rounded-shoulder or the bevelled-shoulder margin. JProsthod 1: 18-23. Copyright o 1992 by the American College of Prosthodontists.
INDEX WORDS: PFM stress, stress analysis, porcelain-fused-to-metal restoration
F
actors that govern the rationale and usage of different margin designs include marginal accuracy, provision of adequate room for restorative material, avoidance of the pulp, and conservation of tooth structure.'-6 Ofparticular interest is the behavior of different margins during the fabrication process and under occlusal load.
Review of the Literature Although marginal distortion of different porcelainfused-to-metal (PFM) margins during fabrication have been do~umented,'-'~ recent studies have shown that neither degassing nor porcelain firing resulted in significant marginal distortion for various alloys and margin designs.'"I8 One study showed that an increase in faciolingual dimension of the castings after degassing decreased after porcelain firing and the end result had no significant change from the initial readings.IqDeHoff and Anusavice2"performed finite element analysis of the effect of thermal stress
on four PFM margin designs. Radial and axial marginal distortion for all four designs were very similar and the magnitudes were well above clinically acceptable limits.2' Contrasting results between the earlier and recent studies were probably due to the advent of better understanding of materials and techniques. O n the other hand, information on the effects of different PFM margin designs during function is scarce.22-24 Variation in alloy type and coping thickness was found not to significantly affect the stress distribution of a PFM crown with a chamfer marNeither the alloy type, coping thickness, nor coping termination significantly changed the stress distribution around a facial porcelain margin of a PFM crown.14 The purpose of this study was to quantify the effect of margin design on the stress distribution and margin distortion.
Materials and Methods * h i s t a n t PruJessor and Director, Advanced Education Prnrthodonticc, .h'a&westem L'nzuersity Dental School, Cfiicago, II.. TDesign Engnem, Rehabilitalion Engineering Propurn, i$'oorthwestm UniuersiQ Medical School, Chicago, IL. Address reprint reguests 10: john Chni, BDs, M s , Advanced Education Prosthodontiw, l'orlhuiest?m C'nioarity Dental School, 240 E Huron S1, Chicqo, IL 60611. Co?vright 0 1992 the American College uJPmthodontists 1059-941Xl921Ol0l-0003$5.00/0
18
All materials in this study were assumed to be isotropic and linearly elastic. Three designs of the labial metal margin were studied: (1) chamfer margin with a knife-edge metal finish, (2) rounded shoulder with a metal finish, (3) rounded shoulder with a bevelled metal finish. A twodimensional sagittal cross section of a central incisor with a PFM restoration was modeled according to
Journal ofProsthodontics,Vol 1,N o I (SeptembeqL 1992:pp 18-23
19
September 1992, Volume I , Number I
Table 1. Moduli ofElasticity and Poisson's Ratio for Various Materials Dentin
Porcelain
ZOP Cement
Pd-Ag Ally
18.6 .3 1
69 .28
11 .35
138 .33
Modulus of Elasticity (GPa) Poisson's Ratio
anatomical d i m e n s ~ o n s The . ~ ~ thicknesses of metal and porcelain followcd recommended values.26The thickness of porcelain was maintdined between 1.2 to 1.5 mm. The thickness of the alloy was kept at 0.3 mm which terminated at the lingual aspect as a 3-mm collar. The metal thicknesses of the roundedshoulder and the chamfer designs tapered to a knife-edge finish of 0.1-mm thickness at their margins. The bevelled-shoulder has a metal margin of a 45" bewl which is about 0.5 mm in width. Porcelain extended above the labial metal margin, covered the entire labial surface, and terminated to a lingual metal collar 3 mm from the lingual margin?7 A cement thickness of 25 p,m was allowed between the crown and the tooth. This corresponded to the minimum thickness of zinc phosphatc cement specified by the American Dental Association.28hloduli of elasticity and Poisson's ratio for the materials in this study are outlined in Table 1?9,30 The modeling of a cement layer has been particularly difficult because or its extreme thinness compared with the dimension of its adjacent components. The resultant cement elements inevitably appear slender, hence, the accuracy of computation is often questioned. Eight-noded quadrilateral plane stress elements were uscd throughout the model to increase the number of integration (calculation) points within each element, thus increasing the accuracy. Large numbers of small elements were used in interfaces where sharp stress gradients arc likely to appear. The quadrilateral elements have the advantage over triangular elements of requiring
Table 2.
fewer elements in regions of abrupt change of material proper tie^.^^ Five hundred forty-seven elements and 1,73 1 nodes were used to model the PFM crown with a rounded shoulder; 548 elements and 1,737 nodes were used for the PFM crown with a bevellcd shoulder margin; 549 elements and 1,745nodes were used for the PFM crown with a chamfer margin. A point load o f 320 N, representing the average maximum biting force,32was applied at a 45" angle on porcelain 2 mm coronal to the lingual porcelainmetal junction. The nodes on the most apical horizontal line werp fixed. A continuous junction is assumed between elements of all materials. The problems were solved with the aid of a finite element code (MARC, Marc Analysis Research Corporation, Palo Alto, CA) on a minicomputer (SPARC station I + , Sun Microsystem, Mountain View CA). Equivalent Mises tensile stresses were plotted diagrammatically (the von Mises criterion states that yield occurs when the cquivalent stress equals the yield stress). The equivalent Mises tensile stresses, stresses in the radial (x) and axial (y) directions along the cementdentin, metal-cement, and porcelain-metal interfaces were computed at the three labial margins. Values of these parameters along these interfaces were compared up to a length of approximately 2.5 mm from their labial termination. It was believed that failure of the restoration initiates from these interfaces. Strain of the cement thickness was calculated by dividing the change in cement thickness by the original thickness. This parameter providcs an indication of the likelihood of cement failure. Analysis of variance and Tukey multiple comparisons were applied.
Results Subjective comparison of the hfises tensile stresses plots (Figs 1 through 3) showed even stress distribu-
Mean Equivalent Mises Tensile Stresses (ma)Along Three Interfaces
Cement-dentin Me tal-cement
Porcelain-me tal
Rounded-Shoulder
Herielled-Shoulder
Chamfer
96.47 t 39.65 (n = 32) 123.8 +- 27.13. (n = 32) 154.2 t 18.19* (n = 29)
98.14 ? 44.90 (n = 31) 131.1 ? 37.54 (n = 31) 150.8 ? 15.36 (n = 28)
94.59 -t- 44.37 (n = 29) 133.9 ? 25.45 (n = 29) 139.4 ? 18.1 1 * (n = 29)
Values expressed as mean f SD. n is the number ofcalculation points along an interface. *Significantdifferenrc between groups (P< .01).
20
Eficts ofMaqin De+y an PFM Crowns
Chai and Steqe
Figure 1. Equivalent von Mises tensile stress plot for round shoulder (unitsin megapascal).
Figure 2. Equivalent von hlises tensile stress plot for bevelled shoulder (units in megapascal).
Figure 3. Equivalent von Mises tensile stress plot for chamfer (units in megapascal).
tion along the three interfaces of the three labial margins. As expected, stress concentration is observed in areas close to the point of application of the occlusal load and those diagonally opposing it. Table 2 depicts means and standard deviations of the calculated figures of the three interfaces along a length of approximately 2.5 mm from their labial termination. Statistical analysis of these values did not show any significant difference among the three margin designs at the cement-dentin and metalcement interfaces (P> .01). The porcelain-metal interface at the round shoulder margin sustained significantly higher Mises tensile stress than that of the chamfer margin (P< .01). There was no significant difference in the axial stresses along the three interfaces among the three margin designs (P> .Ol), and all axial stresses have negative values and hence were compressive in nature (Table 3). At the cement-dentin interface, the radial tensile stresses of the chamfer were significantly higher (P< .01) than those of the rounded-shoulder; no difference was found between bevelled-shoulder and either of the other two designs (P> .01). At the metal-cement interface, all designs display similar
21
September 1992, Volume 1;Number 1
Table 3. Mean Axial Stresses (ma)Along Three Interfaces Cementdentin Metalcement Porcelain-metal
RounddShoulder
Beaelled-Shoulder
Chamfer
-61.19
-66.25 f 55.67 (n = 31) -101.0 f 42.75 (n = 31) - 117.8 f 50.24 (n = 28)
-70.30 5 54.47 (n = 29) - 108.1t 35.64 (n = 29) -122.6 15.81 (n = 29)
5
51.17
(n = 32) -98.64 t 30.20 (n = 32) - 124.3 5 33.74 (n = 29)
*
Values exprcsscd as mean f SD. Negative values denote compression; positive values denote tension. n is the number of calculation points along an interface.
radial stresses (P> .01). At the porcelain-metal interface, the radial tensile stresses of both the shoulder and the bevelled-shoulder were higher than those of the chamfer (P< .01) (Table 4). The mean thickness of the cement layers at the rounded-shoulder and the bevelled-shoulder margin decreased whereas that of the chamfer margin increased (Table 5). The change ofcement thickness of the chamfer margin is significantlygreater than that of either the rounded-shoulder or the bevelledshoulder margin (P< .O 1).
Discussion Comparison of the equivalent Mises tensile stresses gives an impression of the likelihood of materials to yield in response to stress. The only significant finding is between rounded-shoulder (154.2 MPa) and chamfer (139.4 MPa) at the porcelain-metal interface. It appears that failure of porcelain-metal interface is more likely at the rounded-shoulder margin than the chamfer margin. The presence of a 0.5-mm wide metal margin in the form of a 45" bevel decreases the equivalent Mises tensile stress at the porcelain-metal interface (150.8 MPa) to the statistical equivalent of that of the chamfer. The advantage of the bevel could be attributed to the provision of extra bulk of metal at the margin.
Mean axial stress at the three interfaces of all margins did not differ statistically. Some significant differences between the mean radial stresses along the cement-dentin and porcelain-metal interfaces were observed, their values were too low to be of clinical significance. Calculation of the change of cement thickness at the margins showed that the mean cement thicknesses of the shoulder and the bevelled shoulder margin decreased whereas that of the chamfer increased. There is a statistically significant difference between the change of cement thickness of the chamfer when compared with that of the shoulder. Calculation of the actual change in thickness at the chamfer margin, under the parameters of this study, showed that an increase of about 0.056 p m (0.223% X 25 pm = 0.056 pm) had taken place (Table 5). Although a change of this magnitude does not seem to be significant, one should consider the mode of failure of the cement layer. Dental cement is a brittle material that fails by propagation of cracks. Strain or a change in the thickness of the cement in practice would be expressed as opening of inherent microcracks. The mechanism is such that the stress field is concentrated in the material in front of the crack; propagation of the crack occurs when the equivalent von Mises tensile stress exceeds that of yield stress of the material. Also important in the
Table 4. Mean Radial Stresses (MPa) Along Three Interfaces Cement-dentin
Rounded-Shoulder
Bevelled-Shoulder
-1.950
5.638 f 15.44
5
20.41*
Metalcement
(n = 32) 1.209 t 16.19
Porcelain-metal
(n = 32) 1.799t 7.181* (n = 29)
(n = 31) 5.966 f 15.10 (n = 31) 3.812 t 5.995** (n = 28)
Chamfer
17.72 f 11.87* (n = 29) 0.331 ? 6.993 (n = 29) -5.980 t 9.276** (n = 29)
Values expressed as mean t- SD. Negative values denote compression; positive values denote tension. n is the number of calculation points along an interface. * o r **Significant diffcrcncc bctween groups (P< .01).
Table 5. Mean Strain of C e m e n t Thickness Rounded-Shoulder
Becelled-Shoulder
Chnmfm ~~
-0.00292 f 0.00557 (n = 32)
-0.00514 2 0.0106* (n = 31)
0.00223 t 0.00620* (n = 29)
Values expressed as mean 2 SD. Negative values denote decrease in cement thickness, positive values denote increase in cement thickness. n is the number of calculation points along an interface *Significant difference betwcen groups (P< .Ol).
discussion of materials failure is the effect of fatigue and the size of a crack. The magnitude of repeated loads necessary to induce failure in a materid is lower than a static load. According to the Griffith’s Law, the critical stress for crack propagation is proportional to the reciprocal of the square root of the crack length.33 In other words, the larger the crack, the lower the stress required to initiate crack propagation. Thus, the clinical significance of the change in cement thicknesses of the margins requires further investigation. Other than the chamfer margin showing significantly lower mean equivalent von Mises tensile stress at the porcelain-metal interface than the shoulder margin, there is no conclusive evidence, using the parameters of this study, to show that one margin design is superior to any other. The choice of a margin is dependent on other factors that are as important as the effects of the margin on stress distribution. Examples are the provision of adequate thickness of porcelain for esthetics, conservation of tooth structure, accuracy of fabrication, location of the restoration in the arch, and depth of the gingival sulcus. All of these factors should be considered in the clinical selection of a margin design.
Conclusion In comparing the rounded-shoulder, bevelled-shoulder, and chamfer, the following can be concluded. (1) Mean equivalent Mises tensile stress at the cementdentin and metal-cements interfaces of the three margins did not differ. The mean equivalent Mises tensile stress at the porcelain-metal interface was found to he significantlyhigher for rounded-shoulder when compared with the chamfer. (2) Mean axial stresses along the three interfaces of the three margin designs were all compressive in nature and did not differ statistically. (3) Mean radial stresses along the cement-dentin and porcelain-metal interfaces of the three margin designs differed statistically. However, the clinical significance of the differences is unknown. (4) Statistically significant difference in the change of cement thickness be-
tween the chamfer and the shoulder was found. This finding requires further investigation.
References 1. Kanders RF: Simple technic for imprmjng the gingival bevel
ofgoldor acryliccrowns. NYUnivJDent 1957;15:1O7-108
2. Smith CG:’The marginal fit ofthe full cast shoulderless crown. JProsthet Dent 1957;7:231-243 3. Roscnsticl SF, Land MF, Fujimoto J: Contemporary Fixed Prosthodontics (cd I ) . St Louis, MO, Mosby, 1988, pp 123.124 4. Rosner D: Function, placement, and reproductionof bevels for gold castings.J Prosthet Dent 1963;13:1160-1166 5. Fusayama T, Ide K, Hosoda H: Relief of resistance of cement of full cast crowns.J Prosthet Dent 1964;1495-106 6. Gavelis JR, MorencyJD, Riley ED, et al: The cffcct of various finish line preparations on the marginal seal and occlusal seat of crown preparations. J Prosthct Dent 1981;45:138-145 7. Fairhurst CW, Anusavice KJ, Ringle KD, et al: Porcelainmetal thermal compatibi1ity.J Dent Res 1981;60815-819 8. Silver M, Klcin G, Howard MG: An r.valuation and comparison of porcelain fused to cast mctal.J Prosthct Dent 1960;lO: 1055-1064 9. Shillingburg HT, Hobo S, Fisher D W Preparation design and margin distortion in porcelain-fused-to-metal restor-ations.J Prosthct Dent 1973;29:276-284 10. Faucher KK, Nicholls J I Distortion related to margin design in porcelain-fiised-to-metal rcst0rations.J Prosthet Dent 1980; 43: 149-15.5 11. Ando N, Nakamura y Namiki T, ct al: Deformation of porcelain bonded gold alloys. J Japan Soc Appar Mater 1972;13:237-248 12. Buchanan WT,Svare CW, Turner Kik The effect of repeated firings and strength on marginal distortion in two ceramometal systems.J Prosthet Dent 1981;45:502-506 13. Mumford G: The porcelain fused to metal restoration. Dent Clin North Am 1965;2:241-249 14. Dcderirh DN, Svare CW, Peterson LC, et al: The effect of repeated firings on the margins of nonprecious ceramometals. J Prosthet Dent 1984;51:628-630 15. Belser UC, MacTntee MI; Richter W A Fit of three porcelainfused-to-metal marginal designs in vivo: A scanning electron microscope study.J Prosthet Dent 1985;53:24-29 16. kchterSnapp K, Aquilino SA, Stare CW, et al: Change in marginal fit as related to rnargin design, alloy type, and porcelain proximity in porcelain-fiised-to-mctal restorations. J Prosthet Dent 1988;60435-4% 17. Hamaguchi,J, Cacciatore A, Tueller VM: Marginal distortion of the porcelain-bonded-to metal complete crown: An SEM Study.J Prosthet Dent 1982;47:146-153
September 1992, Volume I , Number I
18. Strating H, Pameijer CH, Gildenhuys RR: Evaluation of the marginal integrity of ceramometal restorations. Part I. J Prosther Dent 3981;46:59-65 19. Fisher UW, Hobo S, fichter WK: Behavior of the cast metal coping during the porcelain firing q-CIS [Abstract].,J Dent Res 1984;63215 20. DeHolfPH, Anusavice KJ: Effect of metal design on marginal distortion of metal-ceramic crowns.J Dent Kes 1984;63:13271331 21. Christensen GJ: Marginal fit ofgold inlay castings. J Prosthet Dent 1966;16297-305 22. FarahJW, Craig KG: Distribution ofstresses in porcelain-fusedto-metal and porcelain jacket crowns. J Dent Re?; 1975;54 10-15 23. Anusavice KJ, Hojjatie B, DcHoff PH: Influence of metal thickness on strcss distribution in metal-ceramic crowns. .J Dent Res 1986;65:1173-1178 24. Anusavice KJ, Hojjatie B: Stress distribution in metal-ceramic ct-ownswith a facial porcelain margin.J Dent Res 1987;66:14931498 25. Wheeler KC: A texlbook of dental anatomy and physiology (ed 4). Philadelphia, PA, Saunders, 1965, p 22
23
26. Rosensticl SF, Land MF, Fujimoto J: Contemporary Fixed Prosthodontics (ed 1). St Louis, MO, Mosby, 1988, p 155-161 27. Shilirigburg m J r , Hobo S, Whitsett LU: Fundamentals of Fixed Prosthodontics (ed 2). Chicago, IL,Quintessence, 1981, p 424 28. Council on materials and Devices: Revised American National Standards Institute/American Dental Association Specification No. 8 for zinc phosphate cement. J Am Dent Assoc 1978;96 12 1- 123 29. Reinhard1 KA, Krejci KF, Pao YC, et al: Dentin stresses in post-reconstructed teeth with diniinished bone support. J Dent Res 1983;62:1002-1008 30. Rosenstiel SF, Land MF, Fujimoto J: Contemporary Fixed Prosthodontics (ed 1). St Louis, hfO, Mosby, 1988, pp 308-309 3 I. Williams KR, Edrnundson J T A finite element stress analyxis ofan endodontically restored tooth. Eng Med 1984;13:167-173 32. Lundgren D, Laurel1 L: Occlusal force pattern duringcheiring and biting in dentitions restored with fixed bridges of crossarch extension. J Oral Kchabil 1986;13:57-71 33. Darvell BM7: hfatcrials Science in lkntistr);. Faculty of Dentistry, University ofHong Kong, pp 8-9
P
John Y. Chai, BDS, AdS, * andJohn W. Steege, MS3MET Purpose: This study compared the stress distribution of three porcelain-fused-to-metal labial margins on a central incisor under simulated occlusal force. Materials and Methods: The margin designs were rounded-shoulder, rounded-shoulder with a bevel, and a chamfer. Results: Evaluation of mean equivalent Mises tensile stress did not show any difference at the cement-dentin and metal-cement interfaces of the three margins. The mean equivalent Mises tensile stress at the porcelain-metal interface was found t o be significantly higher for rounded-shoulder when compared with the chamfer. There was no significant difference in the axial stresses along the three interfaces among the three margin designs. Statistically significant differences in radial stresses at some interfaces of the three margin designs were found. Conclusion: The change of cement thickness of the chamfer margin is significantly greater than that of either the rounded-shoulder or the bevelled-shoulder margin. JProsthod 1: 18-23. Copyright o 1992 by the American College of Prosthodontists.
INDEX WORDS: PFM stress, stress analysis, porcelain-fused-to-metal restoration
F
actors that govern the rationale and usage of different margin designs include marginal accuracy, provision of adequate room for restorative material, avoidance of the pulp, and conservation of tooth structure.'-6 Ofparticular interest is the behavior of different margins during the fabrication process and under occlusal load.
Review of the Literature Although marginal distortion of different porcelainfused-to-metal (PFM) margins during fabrication have been do~umented,'-'~ recent studies have shown that neither degassing nor porcelain firing resulted in significant marginal distortion for various alloys and margin designs.'"I8 One study showed that an increase in faciolingual dimension of the castings after degassing decreased after porcelain firing and the end result had no significant change from the initial readings.IqDeHoff and Anusavice2"performed finite element analysis of the effect of thermal stress
on four PFM margin designs. Radial and axial marginal distortion for all four designs were very similar and the magnitudes were well above clinically acceptable limits.2' Contrasting results between the earlier and recent studies were probably due to the advent of better understanding of materials and techniques. O n the other hand, information on the effects of different PFM margin designs during function is scarce.22-24 Variation in alloy type and coping thickness was found not to significantly affect the stress distribution of a PFM crown with a chamfer marNeither the alloy type, coping thickness, nor coping termination significantly changed the stress distribution around a facial porcelain margin of a PFM crown.14 The purpose of this study was to quantify the effect of margin design on the stress distribution and margin distortion.
Materials and Methods * h i s t a n t PruJessor and Director, Advanced Education Prnrthodonticc, .h'a&westem L'nzuersity Dental School, Cfiicago, II.. TDesign Engnem, Rehabilitalion Engineering Propurn, i$'oorthwestm UniuersiQ Medical School, Chicago, IL. Address reprint reguests 10: john Chni, BDs, M s , Advanced Education Prosthodontiw, l'orlhuiest?m C'nioarity Dental School, 240 E Huron S1, Chicqo, IL 60611. Co?vright 0 1992 the American College uJPmthodontists 1059-941Xl921Ol0l-0003$5.00/0
18
All materials in this study were assumed to be isotropic and linearly elastic. Three designs of the labial metal margin were studied: (1) chamfer margin with a knife-edge metal finish, (2) rounded shoulder with a metal finish, (3) rounded shoulder with a bevelled metal finish. A twodimensional sagittal cross section of a central incisor with a PFM restoration was modeled according to
Journal ofProsthodontics,Vol 1,N o I (SeptembeqL 1992:pp 18-23
19
September 1992, Volume I , Number I
Table 1. Moduli ofElasticity and Poisson's Ratio for Various Materials Dentin
Porcelain
ZOP Cement
Pd-Ag Ally
18.6 .3 1
69 .28
11 .35
138 .33
Modulus of Elasticity (GPa) Poisson's Ratio
anatomical d i m e n s ~ o n s The . ~ ~ thicknesses of metal and porcelain followcd recommended values.26The thickness of porcelain was maintdined between 1.2 to 1.5 mm. The thickness of the alloy was kept at 0.3 mm which terminated at the lingual aspect as a 3-mm collar. The metal thicknesses of the roundedshoulder and the chamfer designs tapered to a knife-edge finish of 0.1-mm thickness at their margins. The bevelled-shoulder has a metal margin of a 45" bewl which is about 0.5 mm in width. Porcelain extended above the labial metal margin, covered the entire labial surface, and terminated to a lingual metal collar 3 mm from the lingual margin?7 A cement thickness of 25 p,m was allowed between the crown and the tooth. This corresponded to the minimum thickness of zinc phosphatc cement specified by the American Dental Association.28hloduli of elasticity and Poisson's ratio for the materials in this study are outlined in Table 1?9,30 The modeling of a cement layer has been particularly difficult because or its extreme thinness compared with the dimension of its adjacent components. The resultant cement elements inevitably appear slender, hence, the accuracy of computation is often questioned. Eight-noded quadrilateral plane stress elements were uscd throughout the model to increase the number of integration (calculation) points within each element, thus increasing the accuracy. Large numbers of small elements were used in interfaces where sharp stress gradients arc likely to appear. The quadrilateral elements have the advantage over triangular elements of requiring
Table 2.
fewer elements in regions of abrupt change of material proper tie^.^^ Five hundred forty-seven elements and 1,73 1 nodes were used to model the PFM crown with a rounded shoulder; 548 elements and 1,737 nodes were used for the PFM crown with a bevellcd shoulder margin; 549 elements and 1,745nodes were used for the PFM crown with a chamfer margin. A point load o f 320 N, representing the average maximum biting force,32was applied at a 45" angle on porcelain 2 mm coronal to the lingual porcelainmetal junction. The nodes on the most apical horizontal line werp fixed. A continuous junction is assumed between elements of all materials. The problems were solved with the aid of a finite element code (MARC, Marc Analysis Research Corporation, Palo Alto, CA) on a minicomputer (SPARC station I + , Sun Microsystem, Mountain View CA). Equivalent Mises tensile stresses were plotted diagrammatically (the von Mises criterion states that yield occurs when the cquivalent stress equals the yield stress). The equivalent Mises tensile stresses, stresses in the radial (x) and axial (y) directions along the cementdentin, metal-cement, and porcelain-metal interfaces were computed at the three labial margins. Values of these parameters along these interfaces were compared up to a length of approximately 2.5 mm from their labial termination. It was believed that failure of the restoration initiates from these interfaces. Strain of the cement thickness was calculated by dividing the change in cement thickness by the original thickness. This parameter providcs an indication of the likelihood of cement failure. Analysis of variance and Tukey multiple comparisons were applied.
Results Subjective comparison of the hfises tensile stresses plots (Figs 1 through 3) showed even stress distribu-
Mean Equivalent Mises Tensile Stresses (ma)Along Three Interfaces
Cement-dentin Me tal-cement
Porcelain-me tal
Rounded-Shoulder
Herielled-Shoulder
Chamfer
96.47 t 39.65 (n = 32) 123.8 +- 27.13. (n = 32) 154.2 t 18.19* (n = 29)
98.14 ? 44.90 (n = 31) 131.1 ? 37.54 (n = 31) 150.8 ? 15.36 (n = 28)
94.59 -t- 44.37 (n = 29) 133.9 ? 25.45 (n = 29) 139.4 ? 18.1 1 * (n = 29)
Values expressed as mean f SD. n is the number ofcalculation points along an interface. *Significantdifferenrc between groups (P< .01).
20
Eficts ofMaqin De+y an PFM Crowns
Chai and Steqe
Figure 1. Equivalent von Mises tensile stress plot for round shoulder (unitsin megapascal).
Figure 2. Equivalent von hlises tensile stress plot for bevelled shoulder (units in megapascal).
Figure 3. Equivalent von Mises tensile stress plot for chamfer (units in megapascal).
tion along the three interfaces of the three labial margins. As expected, stress concentration is observed in areas close to the point of application of the occlusal load and those diagonally opposing it. Table 2 depicts means and standard deviations of the calculated figures of the three interfaces along a length of approximately 2.5 mm from their labial termination. Statistical analysis of these values did not show any significant difference among the three margin designs at the cement-dentin and metalcement interfaces (P> .01). The porcelain-metal interface at the round shoulder margin sustained significantly higher Mises tensile stress than that of the chamfer margin (P< .01). There was no significant difference in the axial stresses along the three interfaces among the three margin designs (P> .Ol), and all axial stresses have negative values and hence were compressive in nature (Table 3). At the cement-dentin interface, the radial tensile stresses of the chamfer were significantly higher (P< .01) than those of the rounded-shoulder; no difference was found between bevelled-shoulder and either of the other two designs (P> .01). At the metal-cement interface, all designs display similar
21
September 1992, Volume 1;Number 1
Table 3. Mean Axial Stresses (ma)Along Three Interfaces Cementdentin Metalcement Porcelain-metal
RounddShoulder
Beaelled-Shoulder
Chamfer
-61.19
-66.25 f 55.67 (n = 31) -101.0 f 42.75 (n = 31) - 117.8 f 50.24 (n = 28)
-70.30 5 54.47 (n = 29) - 108.1t 35.64 (n = 29) -122.6 15.81 (n = 29)
5
51.17
(n = 32) -98.64 t 30.20 (n = 32) - 124.3 5 33.74 (n = 29)
*
Values exprcsscd as mean f SD. Negative values denote compression; positive values denote tension. n is the number of calculation points along an interface.
radial stresses (P> .01). At the porcelain-metal interface, the radial tensile stresses of both the shoulder and the bevelled-shoulder were higher than those of the chamfer (P< .01) (Table 4). The mean thickness of the cement layers at the rounded-shoulder and the bevelled-shoulder margin decreased whereas that of the chamfer margin increased (Table 5). The change ofcement thickness of the chamfer margin is significantlygreater than that of either the rounded-shoulder or the bevelledshoulder margin (P< .O 1).
Discussion Comparison of the equivalent Mises tensile stresses gives an impression of the likelihood of materials to yield in response to stress. The only significant finding is between rounded-shoulder (154.2 MPa) and chamfer (139.4 MPa) at the porcelain-metal interface. It appears that failure of porcelain-metal interface is more likely at the rounded-shoulder margin than the chamfer margin. The presence of a 0.5-mm wide metal margin in the form of a 45" bevel decreases the equivalent Mises tensile stress at the porcelain-metal interface (150.8 MPa) to the statistical equivalent of that of the chamfer. The advantage of the bevel could be attributed to the provision of extra bulk of metal at the margin.
Mean axial stress at the three interfaces of all margins did not differ statistically. Some significant differences between the mean radial stresses along the cement-dentin and porcelain-metal interfaces were observed, their values were too low to be of clinical significance. Calculation of the change of cement thickness at the margins showed that the mean cement thicknesses of the shoulder and the bevelled shoulder margin decreased whereas that of the chamfer increased. There is a statistically significant difference between the change of cement thickness of the chamfer when compared with that of the shoulder. Calculation of the actual change in thickness at the chamfer margin, under the parameters of this study, showed that an increase of about 0.056 p m (0.223% X 25 pm = 0.056 pm) had taken place (Table 5). Although a change of this magnitude does not seem to be significant, one should consider the mode of failure of the cement layer. Dental cement is a brittle material that fails by propagation of cracks. Strain or a change in the thickness of the cement in practice would be expressed as opening of inherent microcracks. The mechanism is such that the stress field is concentrated in the material in front of the crack; propagation of the crack occurs when the equivalent von Mises tensile stress exceeds that of yield stress of the material. Also important in the
Table 4. Mean Radial Stresses (MPa) Along Three Interfaces Cement-dentin
Rounded-Shoulder
Bevelled-Shoulder
-1.950
5.638 f 15.44
5
20.41*
Metalcement
(n = 32) 1.209 t 16.19
Porcelain-metal
(n = 32) 1.799t 7.181* (n = 29)
(n = 31) 5.966 f 15.10 (n = 31) 3.812 t 5.995** (n = 28)
Chamfer
17.72 f 11.87* (n = 29) 0.331 ? 6.993 (n = 29) -5.980 t 9.276** (n = 29)
Values expressed as mean t- SD. Negative values denote compression; positive values denote tension. n is the number of calculation points along an interface. * o r **Significant diffcrcncc bctween groups (P< .01).
Table 5. Mean Strain of C e m e n t Thickness Rounded-Shoulder
Becelled-Shoulder
Chnmfm ~~
-0.00292 f 0.00557 (n = 32)
-0.00514 2 0.0106* (n = 31)
0.00223 t 0.00620* (n = 29)
Values expressed as mean 2 SD. Negative values denote decrease in cement thickness, positive values denote increase in cement thickness. n is the number of calculation points along an interface *Significant difference betwcen groups (P< .Ol).
discussion of materials failure is the effect of fatigue and the size of a crack. The magnitude of repeated loads necessary to induce failure in a materid is lower than a static load. According to the Griffith’s Law, the critical stress for crack propagation is proportional to the reciprocal of the square root of the crack length.33 In other words, the larger the crack, the lower the stress required to initiate crack propagation. Thus, the clinical significance of the change in cement thicknesses of the margins requires further investigation. Other than the chamfer margin showing significantly lower mean equivalent von Mises tensile stress at the porcelain-metal interface than the shoulder margin, there is no conclusive evidence, using the parameters of this study, to show that one margin design is superior to any other. The choice of a margin is dependent on other factors that are as important as the effects of the margin on stress distribution. Examples are the provision of adequate thickness of porcelain for esthetics, conservation of tooth structure, accuracy of fabrication, location of the restoration in the arch, and depth of the gingival sulcus. All of these factors should be considered in the clinical selection of a margin design.
Conclusion In comparing the rounded-shoulder, bevelled-shoulder, and chamfer, the following can be concluded. (1) Mean equivalent Mises tensile stress at the cementdentin and metal-cements interfaces of the three margins did not differ. The mean equivalent Mises tensile stress at the porcelain-metal interface was found to he significantlyhigher for rounded-shoulder when compared with the chamfer. (2) Mean axial stresses along the three interfaces of the three margin designs were all compressive in nature and did not differ statistically. (3) Mean radial stresses along the cement-dentin and porcelain-metal interfaces of the three margin designs differed statistically. However, the clinical significance of the differences is unknown. (4) Statistically significant difference in the change of cement thickness be-
tween the chamfer and the shoulder was found. This finding requires further investigation.
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