Thermal incompatibility analysis of metal-ceramic systems based on flexural displacement data.

The feasibility of simple tests or analytical methods for prediction of residual stress states in metal-ceramic (MC) prostheses has not been demonstrated. Biomaterial metal-ceramic strips have been proposed to provide sensitive measures of transient and residual stress states through the measurement of midpoint deflection after cooling from the ceramic sintering temperature. The objective of this study was to apply the elastic-viscoelastic analogy to calculate transient and residual midpoint deflections in MC biomaterial strips and to compare these values with deflections measured with a beam-bending viscometer (BBV). Calculations and measurements were made for five MC systems that were found from a clinical study to be "thermally compatible" systems. Metal strips, 64 mm in length, 3 mm wide, and either 0.5 mm, 1.0 mm, or 2.0 mm in thickness, were veneered with four 0.25-mm thick layers of opaque porcelain. Midpoint deflection of the MC strips (ceramic oriented in the posterior position) was measured during cooling from an initial temperature of 700 degrees C. In general, the directions of the measured residual deflections did not agree with the "textbook" convention that negative deflections are associated with positive thermal contraction mismatch (alpha(M) - alpha(c) > 0) regardless of metal thickness. For a metal thickness of 0.5 mm, the residual midpoint deflection for all thermal contraction mismatch cases, except one, was positive (upward deflection) whereas the residual midpoint deflections were all negative when the metal thickness was increased to 1 or 2 mm, independent of the thermal contraction mismatch. The best agreement between calculated and measured values of residual midpoint deflection (+16 microns vs. +14 +/- 2.3 microns, respectively was obtained for MC biomaterial strips with a Ni-Cr alloy (0.5 mm thick) while the largest difference (+346 microns vs. +61 +/- 43.8 microns) was obtained for MC bimaterial strips with a Au-Pd allow (0.5 mm thick). In all but one case, changes in deflection direction as a function of metal thickness were correctly predicted by the viscoelastic analysis. The results of this study indicate that a viscoelastic model is useful for estimating thermal compatibility conditions of MC systems.

Viscoelastic stress analysis of thermally compatible and incompatible metal-ceramic systems.

OBJECTIVE: The purpose of this study was to analyze transient and residual midpoint deflections and stresses in metal-opaque porcelain-body porcelain systems with matched and mismatched thermal contraction coefficients. METHODS: Calculations and measurements were made for seven trimaterial strips that covered a wide range of thermal contraction mismatches among constituent materials. Midpoint deflections were measured in a beam-bending viscometer during slow cooling from an initial temperature of 700 degrees C. Linear regression analysis with a correlation coefficient of 0.950 was used to compare measured and calculated residual midpoint deflections. Stress relaxation data were fit to a three-term exponential series by nonlinear regression analyses with correlation ratios ranging from 0.9972 to 0.9999. RESULTS: While finite element analyses correctly predicted the general shape of the deflection behavior as a function of temperature for all combinations, the best agreement between measured mean residual midpoint deflections and calculated values (+250 microns vs. +268 microns) was obtained for strips composed of a Au-Pd alloy (alpha m = 13.5 ppm/ degree C) with a medium expansion opaque porcelain (alpha o = 13.3 ppm/degree C) and a high expansion body porcelain (alpha B = 14.4 ppm/degree C). The highest calculated residual tensile stress of +26 MPa at the surface of body porcelain was associated with the 0.5-mm-thick Ni-Cr-Be alloy strip (alpha m = 15.1 ppm/degree C) with medium expansion porcelains (alpha o = 13.5 ppm/degree C and alpha B = 13.9 ppm/degree C). The smallest measured residual deflection (+10 microns) was also associated with this combination. The results of this study indicated that metal-ceramic strips are sensitive indicators of stress development caused by a thermal contraction mismatch; however, the magnitudes of the residual deflections do not necessarily correlate with the stress magnitudes in the ceramic. SIGNIFICANCE: Currently there are no U.S. or international standards that define the maximum difference in thermal contraction coefficients that can exist between a metal and its ceramic veneer without causing transient failures of ceramic during cooling or delayed failures in ceramic because of high residual tensile stresses. The present research represents a major step in understanding the various factors that influence the development of transient and residual stresses. A knowledge of the effects of process variables on stress development is necessary for selection of potentially successful metal-ceramic systems and for optimizing the design of dental prostheses.

Analysis of tempering stresses in metal-ceramic disks.

Previous studies showed that residual compressive stresses induced by thermal tempering retarded the growth of surface cracks in bilayered porcelain disks. The objectives of the present study were: (1) to determine whether thermal tempering by air blasting reduces the length of cracks induced by microhardness indentation in metal-ceramic disks, and (2) to use visco-elastic finite element analyses to calculate transient and residual stresses in metal-ceramic disks. Ni-Cr-Be disks, 16 mm in diameter and 0.3 mm in thickness, were prepared with a 0.5-mm-thick layer of opaque porcelain and a 1.5-mm-thick layer of body porcelain. Metal-porcelain combinations were selected to provide a range of thermal contraction mismatch values. The disks were fired to the maturing temperature of body porcelain and then were subjected to three cooling procedures: (1) slow cooling in a furnace (SC), (2) cooling in air (FC), and (3) air tempering (T) by blasting the surface of the body porcelain with compressed air. The lengths of cracks induced in the surface of the body porcelain by a microhardness indenter were measured immediately after indentation at 20 points along diametral lines. The results of Tukey's multiple-contrast analyses indicated that the mean crack lengths of air-tempered specimens were significantly smaller (p < or = 0.05) than the crack lengths of the fast-cooled and slow-cooled groups. Except for one case, there were no statistically significant differences in the mean crack lengths between FC and SC specimens independent of thermal contraction mismatch. Residual tensile stresses were calculated for SC and FC specimens for all thermal contraction mismatch cases, with the largest values being associated with combinations containing the body porcelain with the smaller contraction coefficient. Calculations by use of the model confirmed that tempering induces large residual compressive stresses in the surface of body porcelain for all of the thermal contraction mismatch cases included in this study.

Three-dimensional finite element analysis of the shear bond test.

OBJECTIVES: The purpose of this study was to use finite element analyses to model the planar shear bond test and to evaluate the effects of modulus values, bonding agent thickness, and loading conditions on the stress distribution in the dentin adjacent to the bonding agent-dentin interface. METHODS: All calculations were performed with the ANSYS finite element program. The planar shear bond test was modeled as a cylinder of resin-based composite bonded to a cylindrical dentin substrate. The effects of material, geometry and loading variables were determined primarily by use of a three-dimensional structural element. Several runs were also made using an axisymmetric element with harmonic loading and a plane strain element to determine whether two-dimensional analyses yield valid results. RESULTS: Stress calculations using three-dimensional finite element analyses confirmed the presence of large stress concentration effects for all stress components at the bonding agent-dentin interface near the application of the load. The maximum vertical shear stress generally occurs approximately 0.3 mm below the loading site and then decreases sharply in all directions. The stresses reach relatively uniform conditions within about 0.5 mm of the loading site and then increase again as the lower region of the interface is approached. Calculations using various loading conditions indicated that a wire-loop method of loading leads to smaller stress concentration effects, but a shear bond strength determined by dividing a failure load by the cross-sectional area grossly underestimates the true interfacial bond strength. SIGNIFICANCE: Most dental researchers are using tensile and shear bond tests to predict the effects of process and material variables on the clinical performance of bonding systems but no evidence has yet shown that bond strength is relevant to clinical performance. A critical factor in assessing the usefulness of bond tests is a thorough understanding of the stress states that cause failure in the bond test and then to assess whether these stress states also exist in the clinical situation. Finite element analyses can help to answer this question but much additional work is needed to identify the failure modes in service and to relate these failures to particular loading conditions. The present study represents only a first step in understanding the stress states in the planar shear bond test.

Stress relaxation behavior of dental porcelains at high temperatures.

OBJECTIVES: The purpose of this study was to measure the stress relaxation behavior at elevated temperatures of three experimental opaque porcelains and three experimental body porcelains. METHODS: Feldspathic porcelain formulations covering a range of thermal contraction coefficients were supplied by a dental ceramics manufacturer. Six specimens, 11 mm in diameter by 22 mm long, were fabricated for each porcelain. The specimens were tested in compression at five temperatures controlled to +/- 1 degree C in a hot stage furnace attached to a screw-type uni-axial testing machine. RESULTS: Mean values of relaxation time, tau u, and the b function were determined by a regression fit to the relation: psi (t) = exp [-(t/tau u)b]. Values of b ranged from 0.23 to 0.53 for opaque porcelain and 0.47 to 0.64 for body porcelain. Relaxation times ranged from 2.6 s to 4 x 10(4) s for the opaque porcelains and 1.5 s to 5.5 x 10(2) s for the body porcelains. A statistically significant variation of b with temperature for three of the experimental porcelains is an indication that these porcelains do not satisfy the theoretical requirements for the porcelains to be classified as thermorheologically simple. SIGNIFICANCE: A knowledge of the relaxation behavior of dental porcelains is necessary so that dental researchers can identify metal/porcelain combinations that will result in low stress values and, therefore, reduce the potential for failure from thermally induced stresses. These properties can be used in the optimization of prosthesis design to reduce the destruction of healthy tissue to accommodate the placement of the dental prosthesis.

Analysis of tempering stresses in bilayered porcelain discs.

Previous studies of opaque-porcelain/body-porcelain discs have shown that compressive stresses which develop in the porcelain surface by being tempered in air can inhibit the sizes of cracks induced within the surface. The objective of this study was to develop a theoretical model for analysis of transient and residual stresses in opaque-porcelain/body-porcelain discs which were produced under variable cooling conditions. The model incorporates the effects of stress and structural relaxation. Transient and residual stresses were calculated for bilayered porcelain discs 16 mm in diameter and 2 mm in thickness for three opaque-porcelain/body-porcelain combinations. Transient temperature distributions in the discs for simulated convective cooling were calculated by finite-element analysis. Data from microhardness indentations reported by Anusavice et al. (1989) indicate that crack lengths measured for bilayered porcelain discs subjected to slow cooling conditions, for which the model predicted residual tensile stresses, were greater than those combinations for which residual compressive stresses were calculated. Calculated values of residual compressive stress for tempered specimens were considerably higher than those for specimens that were slowly cooled and those that were cooled by free convection. In general, residual stress levels calculated by use of the analytical model were in fairly good agreement with the trends observed for crack lengths and bi-axial flexural strengths reported by Anusavice and Hojjatie (1991). The results of the present study indicate that a visco-elastic model is a viable approach for determination of transient and residual stresses in opaque-porcelain/body-porcelain discs.

Effectiveness of cast-joined Ni-Cr-Be structures.

This study tested the load transfer effectiveness of cast-joined structures under flexural loading conditions. Bars of Rexillium III alloy (Ni-Cr-Be) were tested under four-point bending conditions in an Instron testing machine. Six specimens were prepared for each of five interlocking designs. After wax elimination of the investment mold, new metal was cast into the central interlock area. Strain gauges were bonded across the interfaces between the as-cast and secondary cast structures on the bottom surface, and the specimens were loaded to failure in a four-point-bending fixture. Failure was assumed at a strain level of 0.1%, which corresponds to the tensile failure strain of feldspathic porcelain. Three as-cast bars were tested as controls. The average failure load of an interlock design used by Weiss and Munyon was significantly higher (P less than 0.05) than that of the remaining four designs but was significantly lower (P less than 0.05) than that of the solid bar. At the critical strain level of 0.1%, the load-transfer effectiveness of the Weiss and Munyon design was less than 22%. The results suggest that the cast-joining technique may increase the risk of failure in clinical situations where high flexural stresses exist.

Tempering as a means to strengthen porcelain-fused-to-metal restorations.

Structural failures of porcelain-fused-to-metal (PFM) dental restorations still occur despite the known success of specific products and reliable techniques. The possible causes of these failures are varied but the actual fractures usually originate at a surface flaw. Although it is difficult to produce a porcelain that is free of surface flaws, it is possible to inhibit the growth of these flaws by inducing compressive stresses in the surface of the porcelain by a tempering process. The objectives of the present study were: 1) to develop an analytical model to calculate incompatibility stresses in metal-porcelain discs due to thermal contraction mismatch between metal and porcelain, and 2) to determine whether tempering stresses can retard the growth of induced cracks in the porcelain surface of metal-porcelain discs. Ni-Cr-Be alloy discs, 16mm in diameter and 0.3mm thick, were prepared with a 0.5mm thick layer of opaque porcelain and a 1.5mm-thick layer of body porcelain. The materials were selected to provide a range of thermal contraction mismatches. The discs were fired to the maturing temperature of body porcelain (982 degrees C) and then were subjected to three cooling procedures: slow cooling in a furnace (SC), fast cooling in air (FC) and tempering (T) by blasting the surface of the body porcelain with compressed air. The lengths of cracks induced in the surface of the body porcelain by a microhardness indenter were measured immediately after indentation at 30 points along diametral lines.(ABSTRACT TRUNCATED AT 250 WORDS)

Effect of visco-elastic behavior on stress development in a metal-ceramic system.

We developed an analytical model to calculate transient stress and gap displacement during cooling of a porcelainized semicircular arch with a gapped diametral segment. Constant cooling rates were assumed after the specimens were slowly cooled (with power terminated to the furnace) from the porcelain firing temperature. The analytical model incorporates linear visco-elasticity and structural relaxation effects. We calculated transient and residual gap displacements and stresses for a semicircular arch specimen (composed of an experimental opaque porcelain and a Ni-Cr-Be alloy) for six thickness ratios at a cooling rate of 3 degrees C/min. Residual gap displacements were measured for metal-porcelain arch specimens of six thickness ratios. Compared with measured values, calculations based on the visco-elastic theory overestimated gap closure for porcelain/metal thickness ratios below 1.5, and underestimated gap closure at thickness ratios above 1.5.

Influence of tempering and contraction mismatch on crack development in ceramic surfaces.

Tempering of glass produces a state of compressive stress in surface regions which can enhance the resistance to crack initiation and growth. The objective of this study was to determine the influence of tempering on the sizes of surface cracks induced within the tempered surfaces of opaque porcelain-body porcelain discs, with contraction coefficient differences (alpha O-alpha B) of +3.2, +0.7, 0.0, -0.9, and -1.5 ppm/degrees C. We fired the discs to the maturing temperature (982 degrees C) of body porcelain and then subjected them to three cooling procedures: slow cooling in a furnace (SC), fast cooling in air (FC), and tempering (T) by blasting the body porcelain surface with compressed air for 90 s. We used body porcelain discs as the thermally compatible (delta alpha = 0) control specimens. We measured the diameters of cracks induced by a microhardness indenter at an applied load of 4.9 N at 80 points along diametral lines within the surface of body porcelain. The mean values of the crack diameters varied from 75.9 microns (delta alpha = -1.5 ppm/degrees C) to 103.3 microns (delta alpha = +3.2 ppm/degrees C). The results of ANOVA indicate that significant differences in crack dimensions were controlled by cooling rate, contraction mismatch, and their combined effect (p less than 0.0001). Multiple contrast analysis (Tukey's HSD Test) revealed significantly lower (p less than 0.05) crack sizes for tempered specimens compared with those of fast-cooled and slow-cooled specimens.(ABSTRACT TRUNCATED AT 250 WORDS)

Tempering stresses in feldspathic porcelain.

The objective of this study was to develop an analytical model to calculate transient and residual (tempering) stresses in dental porcelain plates subjected to cooling rates used by commercial laboratories. The model incorporates linear viscoelasticity and structural relaxation effects. The viscosities of three experimental body porcelains and three experimental opaque porcelains as a function of temperature were calculated from creep rates measured in a bending beam viscometer. Measurements were made under thermal equilibrium conditions for temperatures ranging from 550 degrees C to 625 degrees C. Thermal expansion data measured in a differential dilatometer at slow heating rates were supplied by the manufacturer. Temperature distribution in the plates as a function of convective heat transfer coefficient, initial plate temperature, and plate thickness was calculated by use of standard numerical techniques. Calculations of transient and residual stress were performed for one body porcelain, for two plate thicknesses, and for three variable cooling rates. Calculated surface residual stresses were strongly dependent on plate thickness, cooling rate, and initial soak temperature. For the cases studied, the maximum residual surface compressive stress was 26.4 MPa.

Delayed crack development in porcelain due to incompatibility stress.

Delayed failure of metal-ceramic restorations due to static fatigue can occur when residual tensile stress is present in porcelain, even in the absence of intra-oral forces. Fixed-partial-denture (FPD) specimens and semicircular arch specimens with gapped cross-arch segments were employed to characterize the potential of two incompatible metal-ceramic systems for producing delayed crack development and to determine the relative sensitivity of these test designs as monitors of incompatibility stresses which resulted from thermal contraction differences between a nickel-chromium alloy and three experimental porcelains. The arch specimens were judged to be more suitable for analysis of residual stresses because of the larger magnitude of gap changes at each procedural change. However, the FPD specimens exhibited earlier evidence of delayed crack growth in porcelain when the thermal contraction coefficient of the metal exceeded that of the porcelain by either 1.7 X 10(-6)/degrees C or 2.2 X 10(-6)/degrees C. For these two states of incompatibility, the agreement between experimental gap values for the arch specimens and the gap values predicted from composite strip equations was excellent.

Influence of contraction mismatch and cooling rate on flexural failure of PFM systems.

The interactive influence of cooling rate and the sign and magnitude of thermal contraction difference between metals and ceramic veneers on bond strength have not been extensively analyzed, although numerous bond-test studies have been reported during the past two decades. A previous analytical study of residual incompatibility stress in bond-test specimens indicated that bond strength values may be of relatively little value if the residual stress state of the metal-ceramic specimens is not considered. The objective of this study was to determine the influence of cooling rate and contraction mismatch on the flexural failure resistance of metal opaque-porcelain strips. Specimens were subjected to four-point loading in an Instron testing machine until crack initiation occurred at the metal-ceramic interface. The residual stress states in the ceramic region were estimated from finite element stress analyses of the bond-test specimens by use of dilatometry data obtained at the cooling rate of 3 degrees C/min. The total stress induced from the residual stress and the applied flexural load was also determined for these specimens. Statistical analyses of the experimental data revealed that the slowly cooled specimens exhibited a significantly lower (p < 0.05) flexural strength compared with rapidly cooled specimens. Regardless of the cooling technique, metal-ceramic specimens with a negative thermal contraction difference (alpha m - alpha p < 0) failed at significantly lower (p < 0.05) flexural loads than did specimens with a positive thermal contraction difference.

Influence of metal thickness on stress distribution in metal-ceramic crowns.

The objective of this study was to calculate the stress distribution induced in anterior metal-ceramic crowns fabricated with either gold-alloy or nickel-alloy copings of reduced thickness using plane stress analyses. Two-dimensional finite element models of three crown designs were subjected to a simulated biting force of 200 N which was distributed over porcelain near the lingual metal-ceramic junction. Based on plane stress analyses, the maximum tensile and compressive stresses in porcelain for the three cases were 29.5 MPa and 123.1 MPa, respectively. The highest tensile strains in porcelain for veneered Ni-Cr and Au-Pd copings with conventional dimensions were 0.016% and 0.014%, respectively. The maximum stresses and strains in porcelain for the crowns with a conventional coping thickness (0.3 mm) and a reduced coping thickness (0.1 mm) were not significantly different. All values were below the critical failure values of porcelain.

An analytical model to predict the effects of heating rate and applied load on glass transition temperatures of dental porcelain.

An analytical model was developed to predict the effects of heating rate and load on the glass transition temperature (Tg) of dental porcelain. An equation similar to the Moynihan equation relating heating rate to Tg was found for midspan load. The validity of the analytical model was demonstrated by using viscosity data from one published study to predict Tg behavior in an independent study. Values of Tg calculated with the analytical model for a dilatometer specimen were found to be higher than Tg values calculated for a bending beam viscometer.

Analysis of alloy-porcelain compatibility using a multi-component material strip equation.

An analytical model has been developed to calculate residual stresses and curvature changes due to thermal contraction differences in metal-porcelain strips consisting of any number (n) of component materials. This model was also used to analyze transient and residual stresses due to solidification of a semicircular arch casting. Results obtained from this model were in close agreement with those obtained from finite element calculations for the cases studied. Some experimental evidence exists to suggest that thermal contraction coefficients of certain body porcelains progressively increase with the number of firing cycles. Therefore, a parametric study was conducted to determine the effects of variations in the thermal contraction coefficient of each porcelain layer on residual stresses and gap changes produced in porcelainized semicircular arch specimens. Based on the analytical model developed in this study, we found that calculated residual stresses near interfacial areas of adjacent layers of porcelain are most sensitive to variations in thermal contraction coefficients of the material layers.

Effect of metal design on marginal distortion of metal-ceramic crowns.

An analysis of residual stress and marginal distortion due to thermal contraction mismatch between metal and ceramic is presented for metal-ceramic crowns. Using dilatometric data, finite element stress analyses were performed on pre-molar crowns designed with chamfer-knife edge, chamfer with collar, shoulder with collar, and shoulder-bevel with collar geometries and a maxillary central incisor crown with a chamfer-knife edge geometry. Calculations were made using combinations of a Ni-Cr alloy or a Au-Pd alloy with each of three porcelain products. Calculated marginal distortions due to crown design and metal-porcelain thermal contraction incompatibility were found to be well below experimental values found in the literature. For the cases studied, the calculated marginal distortions due to metal-porcelain thermal contraction mismatch depend primarily on the metal-porcelain combination and are insensitive to the coping design. However, this study excluded copings which have been extensively ground to thicknesses of 0.1 mm or less, and such copings may be more susceptible to localized or generalized distortion.

Thermal shock resistance of porcelain discs.

Thermal shock testing of opaque porcelain-body porcelain discs and body porcelain discs was performed on three porcelain products. Significant differences exist between the mean failure temperature differentials, delta T, for the composite opaque-body porcelain discs. The residual tensile stress and the transient tensile stress distribution are more severe for one of the three porcelains tested.

Analysis of thermally-induced stresses in porcelain-metal systems.

An analysis of the stresses which develop during air cooling and shock testing of a simulated porcelain-metal crown is presented. Strain gauges were used to experimentally determine porcelain surface stresses during shock testing. The finite element method was used to calculate stress patterns throughout the simulated crown. This study indicates that the previously reported high degree of correlation between dilatometry-derived compatibility index values and delta T values may be related to porcelain tensile strengths and defect density.

An evaluation of the four-point flexural test for metal-ceramic bond strength.

An experimental and analytical stress analysis of the four-point flexural test for metal-ceramic bond strength is presented. Specimen geometry dictates whether failure occurs at the porcelain surface or at the interface under a line of force magnification. Finite element stress analysis indicates that bond separation, if it occurs, is probably due to normal tensile stresses.