Abstract
Objectives
To purpose a method for predicting the shrinkage stress development in the adhesive layer of resin-composite cylinders that shrink bonded to a single flat surface, by measuring the deflection of a glass coverslip caused by the shrinkage of the bonded cylinders. The correlation between the volume of the bonded resin-composite and the stress-peak was also investigated.
Methods
A glass coverslip deflection caused by the shrinkage of a bonded resin-composite cylinder (diameter: d = 8 mm, 4 mm, or 2 mm, height: h = 4 mm, 2 mm, 1 mm, or 0.5 mm) was measured, and the same set-up was simulated by finite element analysis (3D-FEA). Stresses generated in the adhesive layer were plotted versus two geometric variables of the resin-composite cylinder (C-Factor and volume) to verify the existence of correlations between them and stresses.
Results
The FEA models were validated. A significant correlation ( p < 0.01, Pearson’s test) between the stress-peak and the coverslip deflection when the resin-composites were grouped by diameter was found for diameters of 2 and 4 mm. The stress-peak of the whole set of data showed a logarithmic correlation with the bonded resin-composite volume ( p < 0.001, Pearson’s test), but did not correlate with the C-Factor.
Significance
The described method should be considered for standardizing the stress generated by the shrinkage of resin-composite blocks bonded to a single flat surface.
1
Introduction
A significant factor in the adhesion quality of a resin-composite to the tooth is the polymerization shrinkage. When a resin-composite shrinks bonded to rigid surfaces that cannot passively follow the deformation, stresses in the bonding interface and into these two materials are generated. If the shrinkage stress exceeds the tooth/restoration bond strength, debonding may occur , which will result in microleakage and subsequent caries and marginal discoloration. Thus, sealing the interface between the tooth and the restorative material influences the restoration longevity.
The quality of the tooth/restoration interface is often verified by microtensile bond strength testing . To obtain micro-specimens, the tooth is flattened, and a resin-composite block is bonded to its flat surface. If the shrinkage stress was not uniform throughout the interface, or varies because of the shape of the bonded resin-composite, it could contribute to the variability attributed to the test. Thus, it is important to know the geometric variables of the resin-composite block that could influence the shrinkage stress when it is bonded to a flat surface, helping also on the development of new microtensile tests designs for standardized shrinkage stress incident at the interface.
Shrinkage stress of resin-composites has been evaluated by various methods such as finite element analysis (FEA) , photoelastic analysis , and mechanical testing . The mechanical tests are generally conducted in an experimental setting using a tensilometer . Through studies performed with experimental setting with a tensilometer of low compliance, a correlation between the magnitude of the shrinkage stress and the C-Factor was established. This correlation was extrapolated to predict the stress in several types of dental cavities, regardless of their shape or location. But this method has limitations in simulating the resin-composite bonded to the dental cavities: (1) it represents the cavities as spaces between two opposite parallel walls, providing only an average value of stress, which is assigned to the entire “cavity”; (2) the tensilometer compliance may be very different from those in clinical situations ; (3) the tensilometer can only measure stress developed in the direction of its long axis. From these limitations, the C-Factor should be considered a simplified summary of the factors that would influence the stress developed for resin-composites bonded to cavities, since different adjoining cavity walls present different shrinkage stress-peaks . Furthermore, in the case of specimens’ preparation for microtensile tests, the “cavity” is very special, since adhesion occurs on a single flat surface: although in this case the C-Factor can decrease indefinitely as the height of the bonded cylinder increases, it does not seem to be reasonable to expect that increasing height would decrease the stress developed at the interface indefinitely. Thus, since the C-factor does not seem to be an acceptable index to predict the stress of resin-composite that shrinks when bonded to a single flat surface, it is necessary to look for a better stress predictor.
Considering the lack of information about stress development at interfaces of resin-composites bonded to flat surfaces, this study proposes a method to assess them by combining an experimental test with a finite element analysis. The first hypothesis is that it would be possible to evaluate the stress produced by a resin-composite that polymerizes when bonded to a single flat surface, analyzing the deflection of a coverslip that occurs due to polymerization shrinkage of the bonded resin-composite. Based on the possible acceptance of the first hypothesis, a second and a third hypothesis was addressed: the stress-peak varies in accordance with the volume of the bonded resin-composite and that the magnitude of the stress-peak was not correlated with the C-Factor.
2
Materials and methods
The proposed method for predicting the shrinkage stress consisted of measuring the deflection of a glass coverslip caused by the shrinkage of a bonded resin-composite cylinder. The resin-composite cylinders (Aelite LS, Bisco, Inc., Schaumburg, IL, USA) were made in a single increment with the aid of a polyacetal mould ( n = 5 for each group). They were bonded on the center of a glass coverslip (24 mm × 24 mm × 0.13 mm code 4357, Biosystems, Curitiba, PR, Brazil) previously treated with silane (Rely X Ceramic Primer, 3 M ESPE, St Paul, MN, USA) and adhesive (Adper Scotchbond Multi-Purpose, 3 M ESPE, St Paul, MN, USA). The dimensions of the resin-composite cylinders differed in diameter (2, 4, or 8 mm) and height (0.5, 1, 2, or 4 mm). For the resin-composite curing, the tip of the quartz tungsten halogen curing light (Demetron LC, Kerr Corp. Orange, CA, USA) was positioned firstly for 60 s at the base of the resin-composite (starting the polymerization of the resin-composite in the side bonded to the coverslip and for curing the resin-composite concurrently with the adhesive), and then during 60 s at the top in all groups.
The measurement of the experimental deflection of the coverslip was performed with an optical microscope of microhardness equipment (HMV-2, Shimadzu, Kyoto, Japan) with 100× magnification and extra illumination with a transversal fluorescent lamp. The XY table was equipped with two digital micrometers with accuracy of 0.001 mm (Mitutoyo Corporation, Kanagawa, Japan). Before resin-composite curing, the ocular reference of the microhardness tester was moved to coincide with a reference point marked with black ink at one of the corners of the coverslip. Three minutes after curing, the coverslip reference was replaced to fit back to the ocular’s by the displacement of the microscope stage in X and Y axis. Thus, the experimental deflection of the coverslip was recorded as the triangle hypotenuse of X and Y displacement. The experimental set-up described is illustrated in Fig. 1 . Fig. 2 shows the procedure of measure, as seeing at the optical microscope.
To verify the possibility of a correlation between coverslip deflection and resin-composite shrinkage stress, the stresses and deflections were also analyzed by simulating the experimental sets by FEA using MSC.Patran 2005r2 ® for the pre-and post-processing and MSC.Marc ® for processing (MSC.Software Corporation, Santa Ana, CA, USA). In this step, three-dimensional models that represented half of the experimental set were constructed (the model displacement was restricted in Z axis direction because a symmetry condition was assumed ( Fig. 3 , Part A)). To simulate the adhesive in the experimental stage, this layer was built with a larger diameter than the resin-composite cylinder to simulate the experimental condition in which the adhesive was brushed in a central area of the coverslip, which was significantly greater than that in contact with the resin-composite. Then, the FEA models presented adhesive layer with 15 mm in diameter and 0.05 mm thickness. All materials were considered homogeneous, isotropic, and linear-elastic, and their properties are presented in Table 1 .
| Properties | Materials | ||
|---|---|---|---|
| Resin-composite | Glass | Adhesive | |
| Elastic modulus (GPa) | 20 | 60 | 4 |
| Poisson’s ratio | 0.3 | 0.25 | 0.35 |
| Thermal-linear expansion coefficient | 3.33 × 10 −3 °C −1 | – | – |
The three-dimensional mesh was generated from two-dimensional quadrilateral elements with four nodes that were extruded. In the adhesive interfaces (coverslip/adhesive and adhesive/cylinder), a “glue type contact” (which indicates that there is no relative tangential motion between the different materials) was established to simulate a condition of flawless adhesion.
The polymerization shrinkage of the resin-composite was modeled by thermal analogy with thermal-linear expansion coefficient attributed to the resin-composite equal to 3.33 × 10 −3 °C −1 associated with a temperature reduction of 1.11 °C, to produce a volumetric shrinkage of 1.11%. The coverslip was fixed by one of its corners at the nodes of the hypotenuse of a 7 mm side triangle in all directions ( Fig. 3 , Part B), and its deflection was measured based on the displacement in X direction of the corner diametrically opposite to the constrained corner. The maximum principal stress and maximum shear stress-peaks in the adhesive layer were recorded.
To ensure that FEA models accurately represented the experimental models, the average deflection measured experimentally should agree significantly with the deflection values obtained by FEA. Consequently, the experimental values were plotted against the values obtained by the FEA and, subsequently, the corresponding linear regression line was built. To verify the validity of the models, the regression line should not be significantly different from the expression y = x with significant R 2 value to ensure that the points were represented significantly. It would be sufficient that the confidence interval (5%) of the terms of the linear regression of these points ( a and b in general formula y = a + bx ) include the zero value for the term “ a ” and the one value for “ b .”
The maximum principal stress was plotted versus the FEA deflection to verify if it is possible to associate the coverslip deflection with the magnitude of the stresses generated by resin-composite shrinkage. The stresses and deflections were also plotted versus the resin-composite geometric variables: C-Factor and volume, in an attempt to understand how they influence the stress development by resin-composites shrinkage when they are bonded to flat surfaces. The Pearson’s correlation test was applied to the correlation between stress-peak and volume at a significance level of 0.1% and to the correlation between stress-peak and deflection obtained by FEA at a significance level of 1%.
2
Materials and methods
The proposed method for predicting the shrinkage stress consisted of measuring the deflection of a glass coverslip caused by the shrinkage of a bonded resin-composite cylinder. The resin-composite cylinders (Aelite LS, Bisco, Inc., Schaumburg, IL, USA) were made in a single increment with the aid of a polyacetal mould ( n = 5 for each group). They were bonded on the center of a glass coverslip (24 mm × 24 mm × 0.13 mm code 4357, Biosystems, Curitiba, PR, Brazil) previously treated with silane (Rely X Ceramic Primer, 3 M ESPE, St Paul, MN, USA) and adhesive (Adper Scotchbond Multi-Purpose, 3 M ESPE, St Paul, MN, USA). The dimensions of the resin-composite cylinders differed in diameter (2, 4, or 8 mm) and height (0.5, 1, 2, or 4 mm). For the resin-composite curing, the tip of the quartz tungsten halogen curing light (Demetron LC, Kerr Corp. Orange, CA, USA) was positioned firstly for 60 s at the base of the resin-composite (starting the polymerization of the resin-composite in the side bonded to the coverslip and for curing the resin-composite concurrently with the adhesive), and then during 60 s at the top in all groups.
The measurement of the experimental deflection of the coverslip was performed with an optical microscope of microhardness equipment (HMV-2, Shimadzu, Kyoto, Japan) with 100× magnification and extra illumination with a transversal fluorescent lamp. The XY table was equipped with two digital micrometers with accuracy of 0.001 mm (Mitutoyo Corporation, Kanagawa, Japan). Before resin-composite curing, the ocular reference of the microhardness tester was moved to coincide with a reference point marked with black ink at one of the corners of the coverslip. Three minutes after curing, the coverslip reference was replaced to fit back to the ocular’s by the displacement of the microscope stage in X and Y axis. Thus, the experimental deflection of the coverslip was recorded as the triangle hypotenuse of X and Y displacement. The experimental set-up described is illustrated in Fig. 1 . Fig. 2 shows the procedure of measure, as seeing at the optical microscope.
To verify the possibility of a correlation between coverslip deflection and resin-composite shrinkage stress, the stresses and deflections were also analyzed by simulating the experimental sets by FEA using MSC.Patran 2005r2 ® for the pre-and post-processing and MSC.Marc ® for processing (MSC.Software Corporation, Santa Ana, CA, USA). In this step, three-dimensional models that represented half of the experimental set were constructed (the model displacement was restricted in Z axis direction because a symmetry condition was assumed ( Fig. 3 , Part A)). To simulate the adhesive in the experimental stage, this layer was built with a larger diameter than the resin-composite cylinder to simulate the experimental condition in which the adhesive was brushed in a central area of the coverslip, which was significantly greater than that in contact with the resin-composite. Then, the FEA models presented adhesive layer with 15 mm in diameter and 0.05 mm thickness. All materials were considered homogeneous, isotropic, and linear-elastic, and their properties are presented in Table 1 .
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