Abstract
Objective
The aim of this study was to analyze the influence of polymerization shrinkage of the cement layer on stresses within feldspathic ceramic crowns, using experimentally validated FEA models for (1) increasing occlusal cement thickness; and, (2) bonded versus non-bonded ceramic-cement interfaces.
Methods
2-D axial symmetric models simulated stylized feldspathic crowns (1.5 mm occlusal thickness) cemented with resin-cement layers of 50–500 μm on dentin preparations, being loaded (500 N) or not. Ceramic–cement interface was either bonded or not. Cement was bonded to the dentin in all models. Maximum axial shrinkage of 0%, 1%, 2%, 3%, 4% and 4.65% were simulated. The first principal stresses developing in the cementation surface at the center and at the occluso-axial line-angle of the crown were registered.
Results
Polymerization shrinkage of the cement increased tensile stresses in the ceramic, especially in loaded non-bonded crowns for thicker cement layers. Stresses in loaded non-bonded crowns increased as much as 87% when cement shrinkage increased from 0% to 4.65% (100–187 MPa), for a 500 μm-thick cement. Increasing polymerization shrinkage strain raised the tensile stresses, especially at the internal occlusal-axial line-angle, for bonded crowns.
Significance
Changes in the polymerization shrinkage strain (from 0% to 4.65%) have little effect on the tensile stresses generated at the cementation surface of the ceramic crowns, when the occlusal cement thickness is thin (approx. 50 μm for bonded crowns). However, as the cement becomes thicker stresses within the ceramic become significant.
1
Introduction
Bonding between the ceramic surface and the cement has become a fundamental practice in restorative dentistry, largely due to two clinical studies of crowns and inlays . Some in vitro studies have suggested that adhesive composite cements can improve not only the bond strength but also the fracture strength of ceramic restorations .
One of the main concerns about composite cements is their volumetric shrinkage, which can lead to stress generation within restorative cavities, materials and can lead to bonding failures.
The volumetric shrinkage of four chemically cured resin cements dental cements has been reported to vary from 1.69% to 4.62% . For six dual resin cements, the shrinkage strain ranged from 1.77% to 5.28% when the cements were self-cured and from 4.10% to 5.29% when they were dual-cured .
Residual stress developing during polymerization is a multi-factorial phenomenon, determined by their volumetric shrinkage, visco-elastic behavior and by restrictions imposed to polymerization shrinkage . These factors are often described by the bonded/free surfaces ratio (c-factor) , bonding strength to the substrate walls and hardening vs. time-dependent viscosity of the composite .
High C-factor values (>25) may be of concern as shrinkage can cause the development of significant polymerization stresses and can lead to “spontaneous” cohesive failures . Small plastic deformations and low shrinkage stresses have been observed in very thin layers of resin cement. However, the cement mass also plays a dominant role in the shrinkage stresses within luting gaps . The greater mass of material (or the thicker the cement layer), the higher the polymerization stresses .
Recently, an study showed the importance of polymerization shrinkage being included in FEA models with increasing occlusal cement thickness; bonded and non-bonded ceramic–cement interface .
Based on the available literature it is hypothesized that the amount of cement shrinkage, depending on the percentage of contraction and on the cement mass, plays a role in the tensile stresses generated within ceramic crowns.
Therefore, the aim of this study was to analyze the influence increasing percentage of cement shrinkage on the stresses within feldspathic ceramic crowns, for a range of occlusal cement thickness (50–500 μm) having bonded and non-bonded ceramic-cement interfaces, using experimentally validated FEA models.
2
Materials and methods
Axial-symmetric drawings (dentin preparation, cement layer, crown and truncated-conical indenter) for cement thicknesses of 50 μm, 100 μm, 300 μm and 500 μm, were created ( Fig. 1 ), using Solidworks ® 2009 (Dassault Systèmes Solidworks Corp., Vélizy-Villacoublay, France). The *.dxf drawing files were imported as CAD files to COMSOL Multiphysics ® (Comsol Inc, Burlington, MA, USA). COMSOL Multiphysics ® was used for stress analyses of 2-D axial symmetric models simulating stylized feldspathic crowns (1.5 mm occlusal thickness) with different occlusal cement thickness, under 0 N or 500 N loading (2 mm diameter piston). Ceramic–cement interfaces were either bonded or not. Cement was bonded to the dentin in all models.
The cement–ceramic interface was considered either “bonded” (nodes coupled for displacement) or “non-bonded” (independent nodes at the interface). Contact pairs were created for piston-ceramic and “non-bonded” ceramic–cement interface boundaries, with no gap and no friction. The constraints of displacement were: the bottom boundary of the dentin preparation was set to “fixed” in the three axis of displacement; boundaries in r = 0 (central axis) were set to “axial symmetry”; compressive distributed loading was applied on the top boundary of the indenter (500 N), for loaded models. The other object boundaries had free displacement. The material properties were defined according to Table 1 .
| Material | Elastic modulus, E (GPa) | Poisson’s ratio, ν |
|---|---|---|
| Piston/preparation | 14.9 a | 0.31 * |
| Resin cement | 6.3 b | 0.35 * |
| Feldspathic ceramic | 64 c | 0.25 * |
For shrinkage, the sub-domain “cement” was set to include thermal expansion, in which the final and initial temperature resulted in a negative temperature gradient (Δ T ). Maximum axial shrinkage-strain of 4.65%, observed for the resin cement Multilink Automix ® , was used as a reference for finding the Δ T necessary to shrink the cement. A disk with the same dimensions used for this study (∅ = 8 mm; h = 1 mm) and the same elastic properties of the cement layer ( Table 1 ) were modeled in COMSOL Multiphysics ® . The maximum shrinkage of 1%, 2%, 3%, 4% and 4.65% (in the center of the cement disk) was obtained by Δ T of −72 K, −144 K, −214 K, −280 K, and −327 K, for a thermal expansion coefficient, α , set at 70 × 10 −6 ). Then, the different Δ T , necessary for obtaining the different shrinkages, where applied to the cement layer under crowns (see above described models). For those models without cement shrinkage, the thermal expansion option was not included.
Triangular second order elements were used. Maximum element sizes for the cement varied from 0.025 mm to 0.20 mm, in order to obtain 3 layers of elements for each cement thickness. Meshing was controlled through free mesh parameters and the final mesh size was determined by convergence testing, testing gradually finer meshes. Maximum element size of 0.1 mm for ceramic was chosen since FEA presented reasonable solution times and all analyzed models had reached convergence (less than 3% solution change for a maximum element size of 0.05 mm).
The first principal stresses were analyzed in the cementation surface of the ceramic crowns (at the central site, where the crowns are expected to fail from, when axially loaded, and at the internal occlusal axial angle, where the stresses concentrate due to shrinkage polymerization). Fig. 2 illustrates two FEA solutions.
FEA models used in this study were experimentally validated in a former study , using the cement Multilink Automix ® (Ivoclar Vivadent, Liechtenstein) (4.65% of maximum shrinkage) for bonded and non-bonded crowns and cement thickness range of 50 μm to 500 μm, as it is shown in Fig. 3 .
Stress data were analyzed by linear regression (Minitab ® , State College, PA, USA) and tensile stresses vs. shrinkage slopes for bonded and non-bonded crowns were compared by the F -test.
2
Materials and methods
Axial-symmetric drawings (dentin preparation, cement layer, crown and truncated-conical indenter) for cement thicknesses of 50 μm, 100 μm, 300 μm and 500 μm, were created ( Fig. 1 ), using Solidworks ® 2009 (Dassault Systèmes Solidworks Corp., Vélizy-Villacoublay, France). The *.dxf drawing files were imported as CAD files to COMSOL Multiphysics ® (Comsol Inc, Burlington, MA, USA). COMSOL Multiphysics ® was used for stress analyses of 2-D axial symmetric models simulating stylized feldspathic crowns (1.5 mm occlusal thickness) with different occlusal cement thickness, under 0 N or 500 N loading (2 mm diameter piston). Ceramic–cement interfaces were either bonded or not. Cement was bonded to the dentin in all models.
The cement–ceramic interface was considered either “bonded” (nodes coupled for displacement) or “non-bonded” (independent nodes at the interface). Contact pairs were created for piston-ceramic and “non-bonded” ceramic–cement interface boundaries, with no gap and no friction. The constraints of displacement were: the bottom boundary of the dentin preparation was set to “fixed” in the three axis of displacement; boundaries in r = 0 (central axis) were set to “axial symmetry”; compressive distributed loading was applied on the top boundary of the indenter (500 N), for loaded models. The other object boundaries had free displacement. The material properties were defined according to Table 1 .
| Material | Elastic modulus, E (GPa) | Poisson’s ratio, ν |
|---|---|---|
| Piston/preparation | 14.9 a | 0.31 * |
| Resin cement | 6.3 b | 0.35 * |
| Feldspathic ceramic | 64 c | 0.25 * |
For shrinkage, the sub-domain “cement” was set to include thermal expansion, in which the final and initial temperature resulted in a negative temperature gradient (Δ T ). Maximum axial shrinkage-strain of 4.65%, observed for the resin cement Multilink Automix ® , was used as a reference for finding the Δ T necessary to shrink the cement. A disk with the same dimensions used for this study (∅ = 8 mm; h = 1 mm) and the same elastic properties of the cement layer ( Table 1 ) were modeled in COMSOL Multiphysics ® . The maximum shrinkage of 1%, 2%, 3%, 4% and 4.65% (in the center of the cement disk) was obtained by Δ T of −72 K, −144 K, −214 K, −280 K, and −327 K, for a thermal expansion coefficient, α , set at 70 × 10 −6 ). Then, the different Δ T , necessary for obtaining the different shrinkages, where applied to the cement layer under crowns (see above described models). For those models without cement shrinkage, the thermal expansion option was not included.
Triangular second order elements were used. Maximum element sizes for the cement varied from 0.025 mm to 0.20 mm, in order to obtain 3 layers of elements for each cement thickness. Meshing was controlled through free mesh parameters and the final mesh size was determined by convergence testing, testing gradually finer meshes. Maximum element size of 0.1 mm for ceramic was chosen since FEA presented reasonable solution times and all analyzed models had reached convergence (less than 3% solution change for a maximum element size of 0.05 mm).
The first principal stresses were analyzed in the cementation surface of the ceramic crowns (at the central site, where the crowns are expected to fail from, when axially loaded, and at the internal occlusal axial angle, where the stresses concentrate due to shrinkage polymerization). Fig. 2 illustrates two FEA solutions.
FEA models used in this study were experimentally validated in a former study , using the cement Multilink Automix ® (Ivoclar Vivadent, Liechtenstein) (4.65% of maximum shrinkage) for bonded and non-bonded crowns and cement thickness range of 50 μm to 500 μm, as it is shown in Fig. 3 .
