Paul H. DeHoff

Three-dimensional finite element analysis of the shear bond test

OBJECTIVESnThe 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.nnnMETHODSnAll 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.nnnRESULTSnStress 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.nnnSIGNIFICANCEnMost 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.

Weibull analysis and flexural strength of hot-pressed core and veneered ceramic structures

OBJECTIVEnTo test the hypothesis that the Weibull moduli of single- and multilayer ceramics are controlled primarily by the structural reliability of the core ceramic.Methods. Seven groups of 20 bar specimens (25 x 4 x 1.2 mm) were made from the following materials: (1) IPS Empress--a hot-pressed (HP) leucite-based core ceramic; (2) IPS Empress2--a HP lithia-based core ceramic; (3 and 7) Evision--a HP lithia-based core ceramic (ES); (4) IPS Empress2 body--a glass veneer; (5) ES (1.1 mm thick) plus a glaze layer (0.1 mm); and (6) ES (0.8 mm thick) plus veneer (0.3 mm) and glaze (0.1 mm). Each specimen was subjected to four-point flexure loading at a cross-head speed of 0.5 mm/min while immersed in distilled water at 37 degrees C, except for Group 7 that was tested in a dry environment. Failure loads were recorded and the fracture surfaces were examined using SEM. ANOVA and Duncans multiple range test were used for statistical analysis.nnnRESULTSnNo significant differences were found between the mean flexural strength values of Groups 2, 3, 5, and 6 or between Groups 1 and 4 (p>0.05). However, significant differences were found for dry (Group 7) and wet (Groups 1-6) conditions. Glazing had no significant effect on the flexural strength or Weibull modulus. The strength and Weibull modulus of the ES ceramic were similar to those of Groups 5 and 6.nnnSIGNIFICANCEnThe structural reliability of veneered core ceramic is controlled primarily by that of the core ceramic.

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 (αO- αB) of +3.2, +0.7, 0.0, -0.9, and -1.5 ppm/°C. We fired the discs to the maturing temperature (982°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 (Δα = 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 μm (Δα = -1.5 ppm/°C) to 103.3 μm (Δα = + 3.2 ppm/C). The results of ANOVA indicate that significant differences in crack dimensions were controlled by cooling rate, contraction mismatch, and their combined effect (p<0.0001). Multiple contrast analysis (Tukeys HSD Test) revealed significantly lower (p < 0. 05) crack sizes for tempered specimens compared with those of fast-cooled and slow-cooled specimens. Compared with fast cooling, tempering reduced the mean crack diameter by 14.3 μm (13. 8%) for Δα = +3.2 ppm/°C, 20.5 μm (20.2%) for Δα = +0.7 ppml°C, 26.6 μm (26.3%) for Δα = 0, 16.9 μm (19.4%) for Δα = -0.9 ppm/°C, and 15.9 μm (17.3%) for Δα = - 1.5 ppm/°C. These results suggest that physical tempering can reduce the sizes of surface cracks (produced in feldspathic ceramics), which are associated with both positive and negative differences in contraction coefficients of the ceramic layers.

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°Clmin. 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 (αm - αp < 0) failed at significantly lower (p < 0.05) flexural loads than did specimens with a positive thermal contraction difference.

Viscoelastic stress analysis of thermally compatible and incompatible metal–ceramic systems

OBJECTIVEnThe 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.nnnMETHODSnCalculations 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.nnnRESULTSnWhile 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.nnnSIGNIFICANCEnCurrently 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 Tukeys multiple-contrast analyses indicated that the mean crack lengths of air-tempered specimens were significantly smaller (p ≤ 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.

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 × 10-6/°C or 2.2 × 10-6/°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.

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.

Creep functions of dental ceramics measured in a beam-bending viscometer

OBJECTIVEnTo characterize the high temperature viscoelastic properties of several dental ceramics by the determination of creep functions based on mid-span deflections measured in a beam-bending viscometer (BBV).nnnMETHODSnSix groups of beam specimens (58 x 5.5 x 2.5 mm) were made from the following materials: (1) IPS Empress2 body--a glass veneer ceramic (E2V); (2) an experimental glass veneer (EXV); (3) Vita VMK 68 feldspathic body porcelain--a low-expansion body porcelain (VB); (4) Will-Ceram feldspathic body porcelain--a high-expansion body porcelain (WCB); (5) Vita feldspathic opaque porcelain--a medium-expansion opaque porcelain (VO); and (6) Will-Ceram feldspathic opaque porcelain--a high-expansion opaque porcelain (WCO). Midpoint deflections for each specimen were measured in a BBV under isothermal conditions at furnace temperatures ranging from 450 to 675 degrees C. Non-linear regression and linear regression analyses were used to determine creep functions and shear viscosities, respectively, for each material at each temperature.nnnRESULTSnThe shear viscosities of each group of dental ceramics exhibited bilinear Arrhenius behavior with the slope ratios (x) ranging from 0.19 for WCB to 0.71 for EXV. At the higher temperature ranges, activation energies ranged from 363 kJ/mol for VO to 386 kJ/mol for E2V.nnnSIGNIFICANCEnThe viscoelastic properties of dental ceramics at high temperatures are important factors in understanding how residual stresses develop in all-ceramic and metal-ceramic dental restorations.

Application of the finite element analysis to determine forces and stresses in wound closing.

Abstract The finite element method of structural analysis was used to analyze the stresses and forces which develop during suturing of two types of defect configurations in skin. In one case, the maximum stress which develops during closing of an elliptical defect was calculated and compared with a modified tension field theory by Danielson and Natarajan. In the second case, the forces necessary to close the Z-plasty incision are calculated and compared qualitative with published experimental data.