Finite Element Analysis of Shear Versus Torsion Adhesive Strength Tests for Dental Resin Composites

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1 See discussions, stats, and author profiles for this publication at: Finite Element Analysis of Shear Versus Torsion Adhesive Strength Tests for Dental Resin Composites Article in Journal of Adhesion Science and Technology July 2009 Impact Factor: 0.96 DOI: / X CITATIONS 2 READS 39 5 authors, including: Tathy Aparecida Xavier University of São Paulo 27 PUBLICATIONS 206 CITATIONS SEE PROFILE Flávia Pires Rodrigues Universidade Paulista 20 PUBLICATIONS 221 CITATIONS SEE PROFILE Available from: Flávia Pires Rodrigues Retrieved on: 09 May 2016

2 Finite Element Analysis of Shear Versus Torsion Adhesive Strength Tests for Dental Resin Composites Tathy Aparecida Xavier a, Josete Barbosa Cruz Meira a, Flávia Pires Rodrigues b, Raul González Lima c, Rafael Yagüe Ballester a, a Department of Biomaterials and Oral Biochemistry, School of Dentistry, University of São Paulo, São Paulo, SP, Brazil b Department of Biomaterials, School of Dentistry, Bandeirante University of São Paulo UNIBAN, São Paulo, SP, Brazil c Department of Mechanical Engineering, Polytechnic School, University of São Paulo, São Paulo, SP, Brazil Abstract Stress distributions in torsion and wire-loop shear tests were compared using three-dimensional (3-D) linearelastic finite element method, in an attempt to predict the ideal conditions for testing adhesive strength of dental resin composites to dentin. The torsion test presented lower variability in stress concentration at the adhesive interface with changes in the proportion adhesive thickness/resin composite diameter, as well as lower variability with changes in the resin composite elastic modulus. Moreover, the torsion test eliminated variability from changes in loading distance, and reduced the cohesive fracture tendency in the dentin. The torsion test seems to be more appropriate than wire-loop shear test for testing the resin composite tooth interface strength. Koninklijke Brill NV, Leiden, 2009 Keywords Finite element stress analysis, stress distribution, interface, composite, torsion 1. Introduction Adhesive restorative materials have been widely used in dentistry, allowing a greater maintenance of the tooth structure as well as being more aesthetic. Even though the laboratory tests to evaluate the interface bond strength between the restorative material and the tooth are not as conclusive as clinical tests, they generate information for choosing and quickly developing techniques and also new adhesive materials. The use of a biological substrate like tooth imposes size and shape limits to the specimen standardization. Moreover, human tissues are scarce. * To whom correspondence should be addressed. Tel.: ; Fax: ; ryb@usp.br Koninklijke Brill NV, Leiden, 2009 DOI: / X433072

3 1576 T. A. Xavier et al. Due to these limitations, micro size specimens with several shapes were introduced: hourglasses, rectangular sticks and dumbbells for microtension testing [1] and small cylinders bonded to a flattened tooth for microshear [2]. Micro-specimens still present special characteristics such as the decrease in the probability of having larger critical size defects in the interface area [3], besides allowing a comparison of bonding resistances in different tooth regions. Conventional shear and microshear tests are commonly used in dentistry for quickly verifying the bond strength. For the specimens manufacturing, the tooth substrate (enamel or dentin) (Fig. 1(I-a)) is flattened (Fig. 1(I-b)) and embedded in an acrylic resin (Fig. 1(II)). After that, an adhesive system is applied to the flattened substrate (Fig. 1(III)) for bonding a resin composite cylinder (Fig. 1(IV)), with 3 to 4 mm in diameter for the shear test or 0.8 mm for the microshear test. For the microshear tests, a flowable resin composite is preferred since its greater flow facilitates mold filling; instead, for the shear tests, the cylinders are obtained using a packable or condensable paste of restorative resin composite, with greater elastic modulus and lower flow. A knife (Fig. 1(V-c)), or a steel wire (0.5 mm in diameter) (Fig. 1(V-a)), or a stainless steel ribbon (Fig. 1(V-b)) applies load parallel to the bonded interface, creating shear. The load is applied with a loop of metallic wire (0.2 mm in diameter) for the microshear test. A reasonable acceptance of these tests seems to be due to the relative simplicity of the specimens manufacturing, as there is no need for cutting or grinding processes after the bonding procedure, which has the advantages of avoiding the introduction of random defects in the specimens and not stressing mechanically the Figure 1. Shear and microshear specimens manufacturing (I IV) and loading application modes (V), adapted from [4].

4 T. A. Xavier et al interface before the test. This characteristic also makes shear tests especially suited for testing materials with low bond or cohesive strength and/or brittle ones. A critical aspect about shear and microshear bond strength tests is related to the poor standardization, which can cause important differences in stress distribution patterns. The main variables to be standardized are: As the adhesive thickness is constant (50 µm) because of the application technique recommended by the manufacturers, the adhesive is therefore proportionally thicker for microshear tests (which have smaller resin composite cylinders) than for conventional shear tests, although the thicknesses are the same [5, 6]; The elastic modulus of the resin composite cylinder [6]; The distance between the point of loading and the bonded interface, which varies, for example, with the diameter of metallic wire. As the loading point becomes closer to the dentin substrate a stress concentration develops at the interface due to the Saint-Venant effect [6], which is referred as the generalized stress concentration near the loading side. Increasing the distance up to an optimal point, an increase of stress concentration also occurs, caused by the bending moment [2, 6, 7], resulting in a predominance of tension stress, responsible for the fracture [5, 8]. Different stress distribution patterns will determine different preferential sites for the rupture initiation as well as different nominal stress values, which are calculated by dividing the load at failure by the area of the bonded interface. Thus, comparison between results from the same study, and specially, between different studies, cannot be done if attention is not paid to standardization of all the test configuration variables. Another critical aspect is the tension stress concentration in the dentin substrate due to the bending moment imposed on the specimen. This leads to a high frequency of cohesive failures in the dentin substrate, and then none or only a limited information is provided about the interface [5, 8, 9]. Cohesive failures were misinterpreted as indicative of a bond strength at the interface being higher than cohesive strength of substrate [10], without considering the analysis of the stress distribution. Push-out and pull-out tests were suggested as alternatives to the conventional shear tests as, apparently, the former generate preponderant shear stresses at the interface. However, in practice, they are sensitive to some variables that are difficult to control, such as the wall angle, mode of fixation of the specimen, rigidity of the material and even the operator, making the comparison of the results from different tests more difficult [9, 11, 12]. The fracture toughness test for the interface was also proposed for measuring the strength of the interface to an unstable fracture propagation. However, this is a very difficult test to execute [9]. Some authors [6, 13] suggested to apply the torsion test as an alternative for a pure shear test [13].

5 1578 T. A. Xavier et al. The aim of this study was to compare, using the Finite Element Method (FEM), the stress distributions in the shear bond strength tests (normal size diameter of 4 mm referred as macroshear and microshear size diameter of 0.8 mm), applied with a wire (Figs 1(V-a) and 3) to that of the torsion test. In addition, an attempt was made to predict which of these could offer some advantages, such as less sensitivity to variations in the test configuration details or less tendency to cohesive failures in the substrate. 2. Finite Element Modelling The software packages used to perform the finite element analysis were MSC Patran 2005r2 for the pre and post-processing and MSC Marc for the processing (MSC Software Corporation, Santa Ana, California, USA). Figure 2 shows a sectional view of the geometry of the 3-D-models of shear bond strength specimens: a restorative or a flowable resin composite cylinder bonded to a dentin cylinder substrate (with the largest diameter) by an adhesive layer. The torsion models are similar to the shear ones, with the addition of a metal cylinder over the resin composite (not shown in Fig. 2), which was used for torsion loading application. Notice that there is a surplus of adhesive layer in the z-direction for representing the region which is not covered by the resin composite cylinder as a result of the adhesive application technique on the entire substrate surface. The dental adhesive technique recommends adhesive photoactivation before applying the uncured resin composite (which bonds to the adhesive layer by residual carbon double bonds) to build a cylinder which will be photoactivated. This detail also avoids the stress concentration at the dentin/adhesive interface circumference formed by the 90 angle between the adhesive and the dentin, below the resin composite edge. Figure 2. Shear and microshear models with a mesh refinement in areas of interest.

6 T. A. Xavier et al In an attempt to simulate the geometry verified in real specimens, a rounded resin composite fillet (an excess of resin composite) at the confluence between the resin composite cylinder and the adhesive layer was simulated (Fig. 2) [7]. The profile of the fillet was obtained by measuring, with the aid of a profile projector, mean coordinates of three points (one in the centre and two at the ends) on five specimens produced in the laboratory. It was confirmed that some microshear specimens presented fillet and others did not; thus, both types of resin composite cylinder ends were simulated for this size of model. The dimensions for the macroshear test ( macro size) and the microshear test ( micro size) were based on the literature (Table 1) and they were proportional (factor of five), except for: (i) the resin composite-fillet; (ii) the adhesive layer thickness, which was always equal to 50 µm for both model sizes (this means that the adhesive layer was five times thicker in micro than in macro size models) [6]; and (iii) the adhesive layer diameter, since the simulation of its limits depended on the resin composite fillet size for each type of specimen. The dentin substrate had its base and lateral walls fixed in rotation as well as in translation in x-, y- and z-directions, simulating the tooth embedded in the acrylic resin. The dentin cylinder diameter was determined as the minimum value that does not contribute to stress concentration increase at the dentin/adhesive and dentin/resin composite interfaces. Perfect union was simulated at dentin/adhesive and adhesive/resin composite interfaces (the nodes were shared between materials of each interface, which represents finite element equivalence condition). All materials were considered isotropic, homogeneous and linear-elastic, with properties based on the literature [6, 7, 14], which are presented in Table 1. The mesh was performed with four-node tetragonal elements. The mesh refinement was greater in the areas of high stress concentration, which are at the periphery of the dentin/adhesive/resin composite interfaces and the neighbourhood (Fig. 2). The numbers of elements for the models were: macro elements for the torsion models and elements for the shear with wire models; micro Table 1. Specimen dimensions and material properties used in finite element analysis Materials Properties Dimensions (mm) diameter (z axis) x length (x axis) Elastic Poisson s Shear Microshear modulus (GPa) ratio ( macro ) ( micro ) Dentin Restorative resin composite Flowable resin composite Adhesive Metal (steel)

7 1580 T. A. Xavier et al elements for the torsion models and elements for the microshear with wire models (notice that torsion models, in which a metal cylinder was added, have more elements than wire-loop ones). The simulation of the loading in the shear and microshear models with an orthodontic wire-loop was done by the application of pressure (12.6 MPa for macro and 2.5 MPa for microshear) distributed throughout the half perimeter of the resin composite (where the wire-loop contacts the composite), resulting in an arbitrary 4 MPa nominal stress [6]. This way of simulating the loading seems to be the most realistic, considering the capacity of the metallic wire to be deformed and to compress the resin composite cylinder. The value of the pressure is deduced in Fig. 3 by the formula 2T = π 0 rn sin α dα N = T/r. In an attempt to isolate the influence of the relative adhesive layer thickness on stress distribution for one of the groups of macroshear and microshear models, the distance between the load application point and the interface was set as five times greater in macroshear models than in microshear ones. In another group, distances between load application and interface were modified in an attempt to simulate the cases reported in the literature ( real cases ), utilizing different diameters of orthodontic wire-loops: macroshear with restorative resin composite and loading at 0.25 mm from the interface; microshear models with flowable and with restorative resin composite and loading at 0.1 mm from the interface [6]. All distances between the wire and the dentin/adhesive interface are presented in Table 2. To facilitate the simulation of a distributed load for the entire resin composite cylinder perimeter in torsion models, a metal cylinder (steel) was connected to the Figure 3. Schematic representation of the wire-loop loading application (T ) according to the numerical deduction of the pressure value (N) in the text. Table 2. Distances from the load to the dentin/adhesive interface (in mm) for the wire-loop shear test Model Shear ( macro ) X X X X X X Microshear ( micro ) X X X X

8 T. A. Xavier et al top of the resin composite cylinder. The torsion load was applied to 4 diametrically opposed nodes at the top of the metal cylinder, also resulting in a 4 MPa nominal stress. The dentin/adhesive interface was the main target of this study due to its more critical bond strength, since the mechanical retention at this interface is weaker than the chemical adhesion between the resin composite and the adhesive. The failure of the dentin/adhesive interface allows microinfiltration of oral fluids and microorganisms, leading to a post-operative sensitivity, secondary caries and a marginal discoloration. Comparison parameters [6] were the following: Maximum principal (σ max ) and maximum shear (τ max ) stresses variations along a line of nodes through the diameter (median line) of the dentin/adhesive interface; Proportion between maximum principal and maximum shear stresses along the median line of the interface; Sites of maximum principal stress and maximum shear stress peaks; Maximum principal stress tensors. 3. Results and Discussion 3.1. Stress Distribution Patterns Stress Variations Along the Dentin/Adhesive Interface Figures 4 and 5 present the maximum shear and maximum principal stresses variations along a median line at the adhesive/dentin interface. The relative position at the interface allows comparison of the results of models with different diameters: this is given by the percentage of total length of the median line from the adhesive edge at the loading side 0%, where the wire contacts the resin composite to the opposite side 100%. In the graphs, the reference line of 4 MPa nominal stress is presented. Shear and torsion tests ( macro and micro ) present non-uniform stress distributions at the interface. The wire-loop tests (shear and microshear) produced shear peaks at the two ends of the interface (Fig. 4) due to the geometrical discontinuity, and the maximum principal stress produced greater values at the load application side (close to 0% of its total length) (Fig. 5), with peaks much higher than the nominal stress. At the opposite side of the load application, compressive stresses (negative values of maximum principal stress) were developed such as found in previous studies with Finite Element Analysis (FEA) [6, 7]. The tensile (positive values of maximum principal stress) and compressive stresses characterize a bending moment imposed on the specimen. In the torsion test, both maximum principal and maximum shear stresses presented higher values at the interface periphery following a concentric disposition, with the minimum at the circle center. Figures 6 and 7 show values of maximum

9 1582 T. A. Xavier et al. Figure 4. Maximum shear stress distribution along the median line at the dentin/adhesive interface of macro- and micro-size models (with proportional dimensions) with a flowable resin composite. Macro- and Icroshear models are identified by the distance from the loadingapplication point to the dentin/adhesive interface. Figure 5. Maximum principal stress distribution along the median line at dentin/adhesive interface of macro- and micro-size models (with proportional dimensions) with a flowable resin composite. Macro- and microshear models are identified by the distance from the loading application point to the dentin/adhesive interface.

10 T. A. Xavier et al Figure 6. Maximum principal stress and maximum shear stress peak values for different load application distances from the interface for shear and microshear models with flowable resin composite. Nominal stress as well as torsion and microtorsion values are also presented. Figure 7. Maximum principal and maximum shear stresses peak values for different load application distances from the interface for shear and microshear models with restorative resin composite. Nominal stress as well as torsion and microtorsion values are also presented.

11 1584 T. A. Xavier et al. principal and maximum shear peaks obtained from all models, for flowable and restorative resin composites, respectively, as a function of the distance between the load and the interface (mm), with the nominal stress as a reference. These figures show that the stress peaks from the torsion models (for both macro and micro) are lower and closer to the nominal stress than that from the wire-loop loading test Failure Risk under Tensile Stress Previous studies [2, 6, 7] also verified in the wire-loop test the tensile stress predominance when compared to the shear stress at the loading side, where a higher stress concentration was also found. Figure 8 shows the variation of maximum principal/maximum shear stress ratio along the median line at the adhesive/dentin interface. In this figure, it is possible to visualize that the shear surpasses the tension (ratio < 1) only in specific areas of low stress concentration (see in Fig. 5 the low stress from 50 to 100% of total length), which suggests that the fracture tends to initiate at the loading side caused by a tensile stress. On the other hand, in the case of the torsion test, the maximum principal stress values are much closer to the maximum shear stress ones, the stress ratio being approximately 1 along the whole interface. The fracture can be caused by a tensile stress or by a shear one, depending on the specimen strength under these loadings, i.e., it will fail by shear stress if the material is less resistant to shear stress than to tensile one. In a clinical situation, the interfaces are subjected to complex stresses. When an in vitro bond strength study is intended to characterize a material or a technique, including different test set-ups, it is important that all tests employed in the study can evaluate Figure 8. Maximum principal stress/maximum shear stress ratio along the median line at the adhesive/dentin interface. Notice the tensile stress predominance (ratio > 1) in areas of higher stress concentration (at the load application side). Graph lines indicate distances (in mm) from the load to the interface.

12 T. A. Xavier et al the bond strength under different loading conditions, with the predominance of a specific type of stress in each one. The bond strength under tensile stress will not guarantee good bond strength under shear stress, which makes the interpretation of the results very complicated. This hypothesis would explain different rankings related to the bond strength in tests which cause very different stress states [15]. Bond strength tests under tensile stress and under shear stress seem to be a good alternative to solve this problem. Although the wire-loop test applies a shear load, there is a predominance of tensile stress (factor of 3), while in the torsion test, the tensile stress/shear stress ratio is approximately 1 and, therefore, the influence of shear stress on failure increases Cohesive Failure Tendency Cohesive failure in the dentin substrate seems to occur due to stress concentration in the substrate (especially tensile stress) instead of failure at the interface [5, 8, 9]. A 2-D study [16] simulated shear loading with a wire in specimens with no fillet and with the same diameter for both the adhesive and the resin composite. The results showed that the peak in maximum principal stress was found at the sharp angle between the adhesive and the dentin (which suggests a sum of two stress concentration factors: a sharp angle and the proximity to the load application region), and the vector orientation of the maximum principal stress suggested fracture propagation in the dentin substrate. The geometry simulated for the 3-D-models in the present study is different because the sharp angle between the dentin and the adhesive was transferred from the region just below the line of load application to a further one (see Table 1), since the diameter of the adhesive is higher than that of the resin composite cylinder (see the excess adhesive layer in Fig. 2). In this case, the peak in tensile stress was not localized at the dentin in any model. In the present study for the torsion case, as for the wire-loop loading, the peak in tensile stress was found at the resin composite fillet [7], or at the sharp angle between the adhesive and the resin composite for the models with no fillet (Fig. 9). Figure 10 shows that Figure 9. Maximum principal stress contours (values of each scale are in MPa). (a) Stress concentration at the sharp angle between the adhesive and the resin composite; (b) stress concentration at the resin composite fillet (excess resin composite).

13 1586 T. A. Xavier et al. Figure 10. Maximum principal stress tensors (values of each scale are in MPa). Zoom view of cross-sections of the four models with flowable resin composite with fillet (left) and without fillet (right): (a) and (b) microtorsion (isometric view); (c) and (d) microshear (front view). the maximum principal stress tensors, for all models, make an angle of almost 45 with respect to the interface, which suggests the possibility of a crack propagation towards the dentin substrate. In the wire-loop test, this tendency seems to be higher because the tensile stress is several times greater than the shear one in areas with stress concentration (Fig. 8), and also the tensile stress peak is higher (Figs 6 and 7). On the other hand, in the torsion test, the specimen will fail due to a tensile stress only in case the tensile strength is lower than the shear one. The tensile stress peak is lower in torsion than that in wire-loop test (Figs 6 and 7). Even if the failure occurs due to a tensile stress, the crack tends to propagate along the interface (which is normally less resistant to fracture than the dentin), since the substrate is subjected to a smaller stress than in the shear test Area Subjected to the Maximum Stress Figure 11 shows a typical view of stress distribution patterns for wire-loop and torsion models. In the test with the wire-loop loading, the area subjected to the tensile and shear stress peaks is relatively smaller (only a semi-circle at the interface periphery) than that in the torsion test, where the maximum stresses are distributed over a larger circular area (all the perimeter of the interface), which can make the results more representative of the whole interface.

14 T. A. Xavier et al Figure 11. Stress distribution contours at the dentin/adhesive interface in the dentin. (a) Tensile stress in macroshear model; (b) tensile stress in macrotorsion model; (c) shear stress in macroshear model; (d) shear stress in macrotorsion model. Values of each scale are in MPa Influence of the Test Configuration Variables on Stress Distribution Relative Thickness of the Adhesive Layer As mentioned before, as the adhesive layer thickness is always 50 µm and the resin composite cylinder is five times smaller in micro than in macro-size models, the adhesive layer is proportionally five times thicker in micro than in macro specimens. In the wire-loop loading test, the stress distribution is similar, irrespective of specimen size, as can be visualized in Figs 4 and 5. However, it can be seen from Figs 6 and 7, which show the stress peak for all shear and torsion models, that there is a greater stress concentration when the relative thickness of the adhesive layer is lower ( macro size). About the real cases, higher stress concentration

15 1588 T. A. Xavier et al. was observed for the macroshear model (restorative resin composite and loading at 0.25 mm from the interface) than for the microshear model (flowable resin composite, loading at 0.1 mm from the interface). But in the torsion simulations, the stress distributions (Figs 4 and 5) and the maximum stress values (Figs 6 and 7) are similar for the two specimen sizes. This means that the stress distribution in the torsion test is less sensitive to the adhesive thickness variation than for the case of the wire-loop loading condition. Therefore, a lower variability in the results would be expected in the torsion test Distance between the Load Application Point and the Bonded Interface A wide variation of maximum shear stress and maximum principal stress as a function of the distance between the load application point and the interface can be seen in Figs 6 and 7. In the case of the wire-loop loading, a bending moment is applied on the resin composite cylinder creating a large tensile stress at the loading side which causes failure. An increase in the distance between the loading point and the interface increases the bending moment, as well as the tensile stress [2, 6, 7]. But another effect appears to be more influential: when the loading application point is close to the interface, a high stress concentration in terms of shear stress and tensile stress occurs, due to the so-called Saint-Venant effect [6]. In the torsion test, the standardization of the distance of the applied load is less critical than for the wire-loop one due to two reasons: there is no lever effect (and no bending moment, which is dependent on the distance between the loading point and the interface), and from a sufficiently long distance between the applied load and the interface, the Saint-Venant effect is expected to be negligible Elastic Modulus of Resin Composite Figures 6 and 7 show some important changes in maximum shear and maximum principal stresses as the stiffness varies from flowable to restorative resin composite. Most cases with the restorative resin composite, which has a higher elastic modulus than the flowable one, showed higher stress concentration at the interface than that with the flowable resin composite cylinder. However, if the relative adhesive thickness is lower (in macroshear models) and the distance of loading is lower than 0.4 mm, and a higher stress concentration occurs with the flowable resin composite cylinder. This characterizes in the cases of wire-loop tests two interactions between the following two factors: the effect of the elastic modulus of the resin composite is dependent on the relative adhesive layer thickness; and the effect of the elastic modulus of the resin composite is dependent on the distance of loading. On the other hand, for all models of torsion loading, a higher stress concentration occurred with the restorative resin composite. This should lead to less variability in results in the torsion test than in the wire-loop test. 4. Conclusion In comparison to the wire-loop loading test, the torsion test seems to be advantageous due to:

16 T. A. Xavier et al Higher influence of shear stress on the stress state at failure; The region of the stress concentration is closer to the interface region, which means that the load at failure is truly related to the interface bond strength; Higher extension of the bonded area is subjected to the maximum stress, which makes the results more representative of the interface; Easier standardization of the stress distribution due to the lower sensitivity to the relative adhesive thickness variation as well as to the lower influence of the elastic modulus of the resin composite cylinder. It also avoids the specific problem of wire-loop tests regarding the distance between the loading point and the adhesive interface. Acknowledgements The authors would like to thank the technical support given by Antonio Carlos Lascala and Sílvio Peixoto Soares, of the Department of Biomaterials and Oral Biochemistry, School of Dentistry, University of São Paulo. References 1. H. Sano, B. Ciucchi, W. G. Matthews and D. H. Pashley, J. Dental Res. 73, 1205 (1994). 2. W. G. McDonough, J. M. Antonucci, J. He, Y. Shimada, M. Y. Chiang, G. E. Schumacher and C. R. Schultheisz, Biomaterials 23, 3603 (2002). 3. A. A. Griffith, Phil. Trans. Roy. Soc. London A 221, (1920). 4. M. A. Sinhoreti, S. Consani, M. F. De Goes, L. C. Sobrinho and J. C. Knowles, J. Mater. Sci. Mater. Med. 12, (2001). 5. A. Versluis, D. Tantbirojn and W. H. Douglas, J. Dental Res. 76, 1298 (1997). 6. E. Placido, J. B. Meira, R. G. Lima, A. Muench, R. M. de Souza and R. Y. Ballester, Dental Mater. 23, 1086 (2007). 7. R. Van Noort, S. Noroozi, I. C. Howard and G. Cardew, J. Dentistry 17, 61 (1989). 8. A. Della Bona and R. van Noort, J. Dental Res. 74, 1591 (1995). 9. S. Sudsangiam and R. van Noort, J. Adhesive Dentistry 1, 57 (1999). 10. C. L. Davidson, A. I. Abdalla and A. J. De Gee, J. Oral Rehabil. 20, 291 (1993). 11. C. W. Wakefield, R. A. Draughn, W. D. Sneed and T. N. Davis, Operative Dentistry 23, 69 (1998). 12.W.J.Dhert,C.C.Verheyen,L.H.Braak,J.R.deWijn,C.P.Klein,K.deGrootandP.M.W.Rozing, J. Biomed. Mater. Res. 26, 119 (1992). 13. H. Pedrazzi, Análise da resistência ao cisalhamento pelo teste de torção de diferentes combinações resinas compostas/sistemas adesivos, MSc Thesis, University of São Paulo, Brazil (2004). Available at: P. H. DeHoff, K. J. Anusavice and Z. Wang, Dental Mater. 11, 126 (1995). 15. K. Moll, A. Fritzenschaft and B. Haller, Quintessence Int. 35, 845 (2004). 16. E. Placido, Distribuição de tensões em testes de cisalhamento e microcisalhamento mediante análise de elementos finitos, PhD Thesis, University of São Paulo, Brazil (2006). Available at: