This paper studied in vitro the effect of the C -factor on interfacial debonding during curing of composite restorations using the acoustic emission (AE) technique. Finite element (FE) analyzes were also carried out to evaluate the interfacial stresses caused by shrinkage of the composite resin in restorations with different C -factors.
Materials and methods
Twenty extracted third molars were divided into 4 groups of 5. They were cut to form Class-I (Groups 1 and 2) and Class-II (Groups 3 and 4) cavities with different C -factors. The average C -factors of the four groups were 3.37, 2.88, 2.00, and 1.79, respectively. The cavities were then applied with an adhesive and restored with a composite, which was cured by a halogen light for 40 s. A 2-channel AE system was used to monitor the interfacial debonding, caused by shrinkage stress, between the tooth and restoration through an AE sensor attached to the surface of the specimen. Recording of the AE started at the same time as curing of the composite and lasted 10 min. Simplified FE models were used to evaluate the interfacial stresses in restorations with different C -factors, with a thermal load (temperature decrease) being applied to the composite resin to simulate its shrinkage.
The mean and standard deviation of the total number of AE events for the four groups were 29.6 ± 15.7, 10.0 ± 5.8, 2.6 ± 1.5, and 2.2 ± 1.3, i.e. the number of AE events increased with an increase in the C -factor. The FE results also showed that, the higher the C -factor of the restoration, the higher the interfacial tensile stress between the tooth and restoration.
From the results of the AE tests and FE simulations, it can be concluded that, the higher the C -factor, the higher the shrinkage stress and the more likely is interfacial debonding.
The polymerization shrinkage of composite resins presents one of the biggest challenges in their application to dental restoration. It is ascribed to the shortening of distance between molecules in the cross-linked polymer networks following polymerization . During curing of the composite, because of restriction due to bonding to the tooth cavity walls, shrinkage stresses are built up within the tooth structure and restoration which may cause tooth deflection and post-operative sensitivity. When the shrinkage stresses along the interface exceed the bond strength, debonding will take place. The latter, as demonstrated by both in vivo and in vitro experiments, may lead to microleakage, marginal staining and even secondary caries .
The magnitude of the shrinkage stress is affected by several factors, for example, material properties, the restorative technique and configuration of the cavity . The latter is often characterized by the so-called C -factor ( C ) of the restoration, which is defined as the ratio of the bonded areas to the unbonded areas . Feilzer et al. investigated the effect of the C -factor on the shrinkage stress using a simulated cavity where the composite resin was bonded to two opposing rigid parallel discs. They found that, after curing of the composite, all specimens with C > 2 had fractured cohesively, while only some of the specimens with 1 < C < 2 had failed. Further, all specimens with C ≤ 1 had remained intact. Although the tests were carried out in laboratory conditions, the results indicated that increasing the C -factor would increase the incidence of interfacial failure, probably as a result of an increased shrinkage stress. Similarly, Nikolaenko et al. investigated the influence of the C -factor on the bond strength of resin-dentin specimens prepared from composite-restored teeth. The results showed that the higher the C -factor, the lower the bond strength. Again, the reduced bond strength of the specimens was attributed to the higher shrinkage stress in restorations with a high C -factor that had caused more interfacial debonding. Some studies indicated that volume of the restoration also influenced the relationships between the C -factor, the shrinkage stress and the amount of interfacial debonding .
There are many methods to assess the level of interfacial debonding between the tooth and composite resin. The most common method is dye penetration, which needs the sample to be immersed into a dye solution, sectioned into slices and inspected under a profilometer or microscope . Although this method is widely used, its procedure is destructive and laborious, while the information provided by the 2D sectional view is limited. Therefore, 3D non-destructive methods, such as X-ray microcomputed tomography (μCT), have been used to evaluate the interfacial condition of composite restorations . However, because of its lower resolution, μCT cannot detect debonding at a submicron level. Further, none of the techniques mentioned above can be used to monitor debonding as it happens; they can only be used to examine the restoration at the end of the polymerization process.
Recently, another non-destructive method, based on measurement of acoustic emission (AE), was used to detect and monitor in situ the interfacial debonding of composite restorations during polymerization of the composite resin . The AE technique uses transducers or sensors to detect the high-frequency sound waves produced as a result of the strain energy released within a material following fracture. It is a real-time, in situ, non-destructive and highly sensitive method for structural integrity monitoring. It has been widely used in research and industry to monitor the development of crack growth and fracture behavior in different structures. In dentistry, AE has been used since the 1990s to monitor the fracture of restorations made of composite, ceramic or fiber reinforced composite . The experiments conducted by Li et al. demonstrated the effectiveness of the AE technique for detecting interfacial debonding of restorations during polymerization of the composite resin. Their results showed clearly a relationship between the number of AE events and interfacial debonding of the tooth restoration: the more interfacial debonding there is, the higher the number of AE events.
In the current study, AE would be used to evaluate the interfacial debonding in composite restorations with different C -factors during curing of the composite resin. Simple finite element analyzes (FEA) would also be carried out to estimate the shrinkage stresses due to polymerization so as to better understand the effect of the C -factor on interfacial debonding in such restorations. The hypothesis to be tested was that the higher the C -factor of the restoration, the greater the shrinkage stress and the more interfacial debonding there would be between tooth tissue and composite resin.
Materials and methods
Twenty sound human third molars, which had been extracted and stored in saturated thymol solution at 4 °C for one month, were used to prepare the specimens. The teeth were washed in running tap water and then kept in de-ionized water at room temperature for 24 h. Then they were randomly divided into four groups ( n = 5): Group 1 with large Class-I cavities, Group 2 with small Class-I, Group 3 with small Class-II and Group 4 with large Class-II. All cavities were prepared by the same operator following standard clinical procedures with a high-speed handpiece and conically shaped carbide burs. Fig. 1 shows schematically the Class-I and Class-II cavities prepared and the dimensions of interest. The dimensions of each specimen were measured with a micrometer (Mitutoyo, Japan) whereby the C -factor was calculated. At least 3 measurements were made for each aspect of the cavity and the average value used for calculation. The average C -factors of the four groups were 3.37, 2.90, 2.00 and 1.79, respectively, as shown in Table 1 .
|Cavity type||Group||Length (mm)||Width (mm)||Depth (mm)||C -factor||Bond area (mm 2 )||Volume (mm 3 )|
After preparing the cavity, the new surfaces were cleaned using ethanol pads, washed under running tap water thoroughly and then dried with compressed air. With the total-etch adhesive Adper™ Single Bond Plus (3 M ESPE, St Paul, USA) used as the bonding agent, the cavity was restored with the composite Z100 (3 M ESPE, St Paul, USA) which was bulk cured using a blue curing light (ESPE Elipar ® Trilight) for 40 s. The intensity of the halogen light curing unit was measured at 550 mW/cm 2 by the built-in radiometer prior to testing. For ease of dimensional measurement, the top surface of the composite restoration was flattened prior to curing.
A two-channel AE system (PCI-2, Physical Acoustic Corporation, USA) was used to monitor the interfacial debonding between the tooth structure and composite resin during curing. The AE operational settings were: 40 dB pre-amplification, 100 kHz–2 MHz band pass and 32 dB threshold. Before curing the composite resin, an AE sensor (S9225, Physical Acoustic Corporation, USA) was adhered to the outer surface of the tooth with cyanoacrylate adhesive (Super Bond, Staples Inc, USA). The recording of AE started simultaneously with the curing and lasted for 10 min. During the test, the outer surface of the tooth was wrapped with a piece of wet paper to keep it moist so that it would not crack from drying and generate spurious AE signals.
Six FE models were built to study the effect of the C -factor on the interfacial shrinkage stress. Four Class-I and two Class-II restorations were analyzed with axisymmetric and plane-strain models, respectively. The commercial software Abaqus (version 6.9, Dassault Systèmes Simulia Corp., USA) was used for this FE study. All the models were constructed with the same basic 2D rectangular mesh, which was 6 mm in width, 10 mm in height and included three materials (enamel, dentin and composite restoration), as shown in Fig. 2 (a) . Depending on the type of elements selected, the model could represent an axisymmetric cylinder (Class-I) or a plane-strain rectangular (Class-II) block; see Fig. 2 (c and d), respectively. Thus, CAX4 elements were used for the axisymmetric analysis and CPE4 elements were used for the plane-strain analysis. Thickness of the plane-strain models was set at 9 mm. By changing the dimensions of the restoration, different C -factors were achieved, i.e. 7, 5, 3 and 2 for the Class-I models and 1.04 and 0.46 for the Class-II models.
The interfacial bond between the tooth structure and the composite resin was modeled by a contact pair which tied the two surfaces together. This allowed stresses normal and tangential to the interface to be evaluated. For the axisymmetric models, the bottom of the tooth structure was fixed by constraining both the horizontal and vertical displacements. For the plane-strain models, besides fixing the bottom surface, the horizontal movement along the axis of symmetry was also constrained.
Being simple but effective, the Maxwell model was used to simulate the viscoelastic behavior of the composite during polymerization, i.e.