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Evaluation of sources of uncertainties in microtensile bond strength of dental adhesive system for different specimen geometries
d e n t a l m a t e r i a l s 2 4 ( 2 0 0 8 ) 536–547
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Evaluation of sources of uncertainties in microtensile bond strength of dental adhesive system for different specimen geometries Elaheh Ghassemieh ∗ Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objective. The aim of this research is to use finite element analysis (FEA) to quantify the effect
Received 6 June 2006
of the sample shape and the imperfections induced during the manufacturing process of
Received in revised form
samples on the bond strength and modes of failure of dental adhesive systems through
20 March 2007
microtensile test. Using the FEA prediction for individual parameters effect, estimation of
Accepted 18 June 2007
expected variation and spread of the microtensile bond strength results for different sample geometries is made. Methods. The estimated stress distributions for three different sample shapes, hourglass,
Keywords:
stick and dumbbell predicted by FEA are used to predict the strength for different frac-
Microtensile bond strength
ture modes. Parameters such as the adhesive thickness, uneven interface of the adhesive
Finite element analysis
and composite and dentin, misalignment of axis of loading, the existence of flaws such
ANOVA
as induced cracks during shaping the samples or bubbles created during application of
Failure modes
the adhesive are considered. Microtensile experiments are performed simultaneously to
Dental adhesive
measure bond strength and modes of failure. These are compared with the FEA results.
Dental composite
Results. The relative bonding strength and its standard deviation for the specimens with
Sample geometry
different geometries measured through the microtensile tests confirm the findings of the FEA. The hourglass shape samples show lower tensile bond strength and standard deviation compared to the stick and dumbbell shape samples. ANOVA analysis confirms no significant difference between dumbbell and stick geometry results, and major differences of these two geometries compared to hourglass shape measured values. Induced flaws in the adhesive and misalignment of the angle of application of load have significant effect on the microtensile bond strength. Using adhesive with higher modulus the differences between the bond strength of the three sample geometries increase. Significance. The result of the research clarifies the importance of the sample geometry chosen in measuring the bond strength. It quantifies the effect of the imperfections on the bond strength for each of the sample geometries through a systematic and all embracing study. The results explain the reasons of the large spread of the microtensile test results reported by various researchers working in different labs and the need for standardization of the test method and sample shape used in evaluation of the dentin–adhesive bonding system. © 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
∗
Tel.: +44 114 2227868. E-mail address: E.Ghassemieh@sheffield.ac.uk. 0109-5641/$ – see front matter © 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.dental.2007.06.022
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1.
Introduction
To date no standard test has been approved for measuring the bond strength of dentin and composite using dental adhesive system. Different test methods and parameters used have resulted in discrepancy of the data reported by different researchers on the same adhesive system. The factors affecting the bond strength have been addressed by few researchers before. Pashley et al. [1] have listed these factors in a review paper under the broad categories of substrate variables, etching variables, priming variables, bonding variables, storage variables and testing variables. Most of this review has focused on the issues relating to the differences induced by the material properties or the process used in sample preparation. The substrate and adhesive variables induce inherent differences in the material properties. Data reported on the dentin and bovine strength can be up to 50% different depending on the source and part of the dentin or bovine used. The same sort of data spread is reported for demineralized dentin, with some data on the strength being almost one-third of the other test data. The process used in the preparation of the sample as well such as etching and priming have effect on the interface properties and therefore on the bond strength. Van noort et al. [2] have analyzed the effect of the test method in the bond strength results. They have made a comparison between the microtensile test and shear test in measuring bond strength. Applying FEA they have concluded that the shear test results in unfavorable stresses in the specimen. Consequently, they have recommended the tensile test as a preferred test method for measuring bond strength. While the advantages of the microtensile test were proved, many researchers applied the method to measure the bond strength of dental adhesive [3–6]. Nakabayahsi et al. [3] apply the method to detect defects in the specimen. They study the effect of defects in the failure characteristics of the miniaturized samples. Capel Cordoso et al. [4] use the microtensile bond strength to compare the bond strength of three adhesive systems with the cohesive strength of dentin and composite. In all three systems they find the adhesive bond strength to be much lower than the strength of composite or dentin. Yoshiyama et al. [5] apply the microtensile test to measure the bond strength to different regions of dentin. They have reported higher bond strength on the coronal and apical dentin compared to the bond strength to the cervical root dentin. The effect of specimen size and geometry in the results of the bond strength is studied partly by other researchers [7–9]. Phrukkanon et al. [7] have investigated specimens with round and rectangular cross sections. For four different adhesive systems they have reported higher bond strength for the circular cross section compared to the rectangular cross section. The second parameter they have considered is the cross sectional area of the samples. For three different cross sections, lower bond strength is estimated for larger cross sections. The results have been explained using FEA to estimate the stress distribution. They have attributed this result to higher stress values for the samples with larger cross section. Other researchers have used Griffith theory to explain the same results. They have reasoned that smaller samples
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will have smaller flaw size and therefore higher strength. In Phrukkanon’s research they have increased the surface area without changing any other part of the sample. If they scale up all parts of the sample with the surface area the FE results would not indicate any changes for different surface areas. Whereas experimental tests still indicate smaller strength for the samples with larger cross sectional area. This shows a second parameter having role in reducing the bond strength for the larger size specimens which is recommended by Griffith’s theory. Although the researchers have highlighted the parameters affecting the result of the bond strength in the previous studies, there is little indication of quantifying each effect and systematic study. At the same time most of the previous researches on the factors affecting the result of the bond strength have identified only one or two parameters, ignoring the other parameters. In the current research we have considered broad range of factors affecting the bond strength and modes of failure. Using finite element analysis we have investigated the effect of each parameter on the general stress distribution in different regions of adhesive, at the interface of the adhesive and composite and at the interface of adhesive and dentin. We have quantified the effect of each variable on the bond strength and modes of failure for the most commonly used geometries of stick, dumbbell and hourglass. The advantage of using finite element analysis in this respect is that it makes separation of the parameters and its effect possible. This possibility does not exist with the experimental test while interaction of the variables is normally unavoidable. The final FEA predictions of bond strength, its variations and modes of failure are derived from bringing together the results of analysis for all the identified individual parameters. Microtensile bond strength experiments are performed in order to validate the FEA estimation of the mode of failure, bond strength and its standard deviation for the mentioned geometries. The experimental measurements of these parameters and the ranking of different geometries in bond strength approve the collective predictions of FEA. This confirms the reliability of the FEA in its estimation of other individual effects as well.
2.
Methodology
2.1.
Finite element analysis
The main approach used in this research is finite element analysis which is validated by experiments. All the variables affecting the bond strength measured during microtensile test are identified. The first variable considered is the effect of the geometry of the specimen on the bond strength. Three most commonly used geometries in the experimental tests have been considered. This includes stick, dumbbell and hourglass geometries. Another set of parameters considered is induced as a result of the inaccuracies and errors during making the samples or performing the tests. In this category, variables such as adhesive thickness, uneven spread of adhesive, and misalignment of the axis of the applied load are examined for all three specimen geometries. Finally, the effect of the presence of flaw at the edge of adhesive and at the middle sections
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analysis clarifies the similarities and differences between the test sets with various sample geometries.
2.2.1.
Fig. 1 – Finite element mesh for the (a) stick; (b) dumbbell; (c) hourglass geometries.
of the adhesive is considered. These flaws might occur during application of the adhesive or manufacturing of the specimen. The effect of each parameter on the bond strength is evaluated and an estimation of data spread as a result of these parameters has been made.
2.1.1.
Finite element model and materials properties input
Finite element model: Geometric models are developed for stick, dumbbell and hourglass specimens. Typical finite element meshes of these geometries are shown in Fig. 1a–c. The samples are of 26 mm length. The areas of the adhesive section in all the samples are equal to about 1.08 mm2 [width 1.2 mm × thickness 0.9 mm). Load of 10 N is applied to all the samples in y direction. The thickness of the adhesive is about 0.26 mm. The thickness is chosen on the basis of measuring the adhesive thickness following the manufacturer’s guidance in application of the adhesive. The properties of the adhesive, composite and dentin used in this model are summarized in Table 1.
2.2.
Microtensile bond strength experiments
Experimental tests have been carried out to validate FEA results and to broaden and enhance the perspective of the study. An adhesive and composite system has been chosen. Microtensile test is used to measure bond strength for three different sample geometries. The bond strength and its standard deviation and modes of failure have been identified. The results of the experiment show similar trend in the bond strength and its variation compared to the FEA results. ANOVA
Table 1 – Material properties used in the FEA Material Adhesive Composite Dentin
Modulus (MPa) 3.3 8.0 14.0
Strength (MPa)
Poisson ratio
27.0 85.0 110.0
0.30 0.30 0.23
Test materials and sample preparation
In this research, caries-free human molars are used for sample preparation. Self-etching primer adhesive system (Opti-Bond Solo Plus, Kerr Corporation, CA, Lot: 408737) is selected as bonding agent and Herculite XRV composite material (Kerr Corporation, CA, Lot: 4-1286) is used to form a flat-topped crown. The human molars are stored in a 0.9% sodium chloride solution (normal saline) and 0.2% sodium azide at room temperature for not more than 1 month before use. Just prior to the preparation, a tooth is thoroughly rinsed in running water. The surface is gently scraped by penknife in order to remove any excess tissue. The tooth is then steadied on a metal table (Fig. 2a) with araldite structural adhesive before attempting the cutting procedure. The occlusal enamel is removed perpendicular to its long axis, using low speed diamond disc (LECO Corporation VC-50 Japan) under water-cooling (Fig. 2b). The crown portion is then removed. The remaining exposed section is inspected to ensure the surface is flat. The surface is then ground with 600-grit sand paper under running water for 1 min to create a uniform smear layer. The dentin surface is thoroughly washed with water, and gently air-dried by using air spray. Manufacturer’s instruction is used in application of the adhesive and composite. Self-etch primer is applied to the prepared dentin surface with a light brushing motion for 15 s. Then it is air sprayed for 3 s. Optibond solo plus is applied with light brush motion for 15 s and air sprayed for 3 s. Optibond solo plus is reapplied in the same manner. Then the adhesive is light cured for 20 s. After the application of adhesive system on the dentin surface, resin composite is placed on the adhesive surface in equal increments of about 2 mm to form the crown. Each layer of composite is light cured for not less then 20 s. The procedure was repeated until a 6 mm flat-topped resin composite crown with adhesive was formed on the dentin. After 24 h, 15 teeth are randomly separated into three groups and then steadied on a metal table using araldite structural adhesive. One of the groups is approximately sectioned (Fig. 2d–e) in 1.2 mm × 0.9 mm square shape by low speed diamond disc for stick shape preparation. The other two groups are sectioned to 3.5 mm × 0.9 mm rectangular shape for dumbbell and hourglass shape samples preparation. For these two former groups, the region of adhesive and interfaces is then formed using a round diamond bur for hourglass shape samples and a cylindrical diamond bur for dumbbell shape samples. In both cases high-speed hand piece is applied in shaping process. All samples are tested using a microtester (Micro material Limited, WREXHAM, UK). Bonding area of each sample is measured using vernier and is inputted into the computer before performing the tensile test. The sample is placed on the top of two metal plates. Both plates are placed horizontally with a 5 mm gap apart so that the bonding section between dentin and composite is in the gap between the plates. The end section of dentin and composite are stabilized on the metal plates. The two ends
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Fig. 2 – (a) Tooth stabilized to metal table; (b) cutting the occlusal crown; (c) flat top composite crown; (d) sectioning final specimen; (d) sectioned specimen.
of the samples, dentin and composite end sections are fixed to the metal plates using very strong adhesive. Enough time is given for the adhesive to dry completely. Sample with supporting plates is then carefully placed on the testing bench. The load is applied at the rate of 2 mm/min and the test is stopped automatically once fracture occurred. The results of the microtensile bond strength for each of the samples are recorded. Twenty samples for each of the geometries are tested. The mean values and standard deviations are calculated. After the microtensile bond strength test, the failed sample is studied under optical microscope to determine the mode of failure.
3.
Results and discussion
3.1.
Finite element results
In order to evaluate the bond strength for different sample geometries, we first study the overall stress distribution produced by application of the load in a tensile bond strength test. As the stresses in the adhesive and interfaces are more deterministic in the bond strength, we more specifically focus on these stresses. Finally, we consider variations and imperfections that are likely to occur during the sample preparation and the effect that these imperfections can induce in the result of the bond strength.
3.1.1. Stress distribution in different geometries 3.1.1.1. Direct stress distribution. The contour plots of the direct stress in the direction of application of tensile load for the three geometries are shown in Fig. 3a–c. Equal range of maximum and minimum is chosen for all the plots in order to make a fair comparison between the three geometries. The
maximum stresses for the dumbbell shape sample occur at the curved corners of the dentin and composite. Maximum stress in the adhesive region is in the centre of the adhesive (Fig. 3a). In the hourglass specimen the maximum stress is concentrated in the adhesive edges. This maximum stress extends from the adhesive region into the dentin and composite sections adjacent to the adhesive (Fig. 3b). In the stick specimen the maximum stress is observed in the middle of the adhesive (Fig. 3c). Regarding the stress distribution and rate of changes the dumbbell geometry induce relatively high stresses all over the straight centre region of the dumbbell, in the hourglass the high stress is more than any other geometry concentrated in the adhesive region only and in the stick the stress concentration is less localized than other two geometries.
3.1.1.2. Stress in the adhesive and at the interface. Fig. 4a shows the Von Mises stresses in the middle of the adhesive for the three geometries. The stress distribution in the dumbbell and stick are very similar. However, the hourglass sample shows completely different stress profile. For the dumbbell and stick the stress along the width of the adhesive is almost the same. Therefore, in the dumbbell and stick samples there is no preferred point of failure. In the case of the hourglass sample the concentration of the stress is very close to the edges indicating that the initiation of failure is likely to be at the edges of the specimen. These different patterns of stress will cause different types of failures for the hourglass sample compared to the other two geometries. Especially as we investigate in later sections, the effect of a crack or failure induced at the edges of the sample is fatal, whereas a flaw or crack in the middle of the sample can be much better tolerated. The stress profiles at the interface of the composite and adhesive are indicated in Fig. 4b. The maximum stress for the dumbbell and stick shape samples is found in the mid-
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Fig. 3 – Contour plots for the direct stress distribution in the (a) dumbbell; (b) hourglass; (c) stick samples.
dle of the sample with almost no point of preference. In the hourglass sample the trend is different with maximum stress occurring at the edges of the interface. The stress for the hourglass sample is higher than dumbbell/stick samples. However, stress profiles at the interface of the dentin and adhesive indicate that for all the samples the maximum stress occurs at the edge (Fig. 4c). The stress in the hourglass specimen seems to be slightly higher than the other two samples. These results fully support the experimental results reported in later sections that more mode B failure (combined adhesive and dentin failure) is observed for all the samples compared to the mode C failure (combined adhesive and resin failure). Predictions of FEA for the failure stresses of various samples for different modes of failure along with the possible location of initiation of failure for each mode are reported in
Table 2. The failure stress for the adhesive failure is the highest for the stick sample with the value of 32.2. The dumbbell sample shows slightly lower value of 31.1. The hourglass has the lowest failure stress of 27.1 for the adhesive mode of failure. In order to predict the stresses of failure at interface, we need to have the values of the strength for the interface. However, no previous research has reported any quantitative data on the interface strengths. There is only qualitative research available on the strength of the interface and its characteristics. The fracture toughness of the interface is highly dependent on the process of surface preparation before applying the adhesive. The type of adhesive used and its compatibility with the composite or dentin is a determining factor in the interface bond strength. Schulze et al. [10] have studied the differences of the resin–substrate interface
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Table 2 – Maximum stress values (MPa), its location and predicted failure stresses (MPa) for different modes of failure in three types of samples (Mid-Uni, middle-uniform) Stick Max Adhesive Adhesive–dentin Average Dentin Composite
Location
8.50E+06 1.16E+07
Mid-Uni Edge
1.05E+07 8.50E+06
Edge Mid-Edge
Dumbbell Failure
Max
32.2 23.6 28 10E+0 102
8.80E+06 1.05E+07
Mid-Uni Edge
1.10E+07 8.80E+06
Edge Mid-Edge
layer of the dental restoration under different surface processing condition of self-etching versus acid etching. They have reported different interface properties for the two cases as a result of moisture condition. Clark et al. [11] have studied the effect of the surface preparation of enamel on the bond strength and mode of failure. They have considered two types of surface preparation processes: sand-blasting and acid etching. Major differences have been observed for the bond strength of the right on adhesive through these two surface preparation processes. While this difference is decreased for a composite added adhesive, the modes of failure are still affected by the surface preparation. The main reason is different interface strength for the samples prepared through different processes. For the sand-blasted bonding with right on adhesive the mode of failure is shifted toward the interface between the enamel and the adhesive and reduced values of bond strength. Clark’s study is on the effect of surface preparation for enamel on the interface properties. However, it is expected that the surface preparation and manufacturing process to cause different interface properties for dentin which we are studying here as well. Since these parameters are known to affect the interface strength in most bonding process applications. Leforestier et al. [12] have also indicated the complexity of the interface layer and its dependence on the dentin superficial parameters, physico-chemical and rheologic behavior of the resin and composite. The failure stresses predicted by FEA for the failure at the interface of the adhesive/composite and adhesive/dentin is on the basis of the assumption that the strengths of the interfaces are equal to the strength of the adhesive. The assumption is made in order to obtain some relative failure stress values for the three specimens which should be adequate enough for comparison purposes. More accurate failure stress predictions for the interfaces can only be obtained if the strengths of the interfaces are known. Pashley et al. [1] have estimated the strength of the interphase of dentin–resin as strong as dentin material. However, there has been no experimental work to support this. The assumption of taking the strength of the interface equal to the adhesive provides a range of the lowest stresses (underestimate) for the failure stresses at the interface. On the contrary, taking the strength of the interface equal to dentin, there will be overestimation of the failure stresses at the interface. On the basis of our assumption the failure stress of the dentin–adhesive interface is the smallest for all the samples. It is expected for the failure to start at the edges. Obviously, this can only be valid if the samples are all perfectly made and are free from flaws that are considered in the next sections.
Location
HourGlass Failure 31.1 26 28.4 95.5 98.3
Max
Location
Failure
1.00E+07 1.28E+07
Edge Edge
1.20E+07 1.00E+07
Edge Edge
27.4 21.4 24.7 87.5 86.5
The location of initiation of the cohesive failure of adhesive or adhesive/composite interface debonding is in the middle with no preference point for both stick and dumbbell shape samples. However, for the hourglass the location of initiation of cohesive failure is at the edge. The position of initiation of debonding of the interface of dentin/adhesive is at the edge for all the shape samples. The failure stress predicted by FEA is smaller for the hourglass sample compared to the dumbbell and stick. The second weak sample is the stick and the dumbbell is supposed to provide the highest failure stress value. Goracci et al. [9] have done microtensile test on specimens with hourglass or stick geometry for different cross sectional area and they consistently have obtained lower bond strength data for hourglass compared to the stick shape samples with the same cross sectional area. This confirms the results of our FEA prediction on the effect of the specimen geometry on the bond strength values. Our experimental results reported in later sections approves these findings as well.
3.1.2. Different imperfections and design variations and their effect on the stresses Different types of imperfections and variations that might occur in the samples are considered as follows.
3.1.2.1. Thickness of the adhesive. Fig. 5a indicates the Von Mises stress in the middle of the adhesive for the samples with three different shapes with thin and thick layer of adhesive. The thickness of the adhesive is 0.2 mm for the samples with thin adhesive and 0.4 mm for the samples with thick adhesive. If the thickness of the adhesive is increased two times, the maximum Von Mises in the adhesive is increased for all the samples. However, the percentage of increase of the stress for the thick adhesive is lower for hourglass sample compared to the dumbbell and stick shape samples. The percentage of changes in the maximum stresses in the adhesive, at the interface of the adhesive/composite and interface of the adhesive/dentin for the three shapes are summarized in the first set of rows of Table 3. In the dumbbell and stick samples with thick adhesive the maximum stress at the interface of the adhesive/composite and adhesive/dentin increases more compared to the stresses in the adhesive. However, the stresses at both interfaces show slight decrease for the hourglass sample. FE prediction indicates that the thicker the adhesive the more likely the failure to be shifted to the adhesive–composite interface for the stick and dumbbell samples. Thicker adhesive in hourglass samples would not cause major effect and it is likely to increase the bond strength.
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Fig. 5 – Von Mises stress distribution in the thin and thick adhesive (DB, dumbbell; S, stick; HG, hourglass).
Table 3 – Percentage of change in maximum stresses in the adhesive, interface of adhesive/composite and interface of adhesive/dentin Geometry
Adhesive
Thickness Stick Dumbbell Hourglass
5.7 6.8 2.2
14.3 14.1 −0.9
10.3 11.4 −3.1
Uneven adhesive Stick Dumbbell Hourglass
3.9 4.2 4.2
5.9 0.2 2.8
14.7 9.5 1.6
32.4 42.5 42.7
23.3 26.0 41.7
37.1 47.6 43.0
Angled axis Stick Dumbbell Hourglass
Adhesive/ composite
Adhesive/ dentin
increase of the failure for the thicker adhesive. The percentage of increase of the stresses at the interfaces for thick adhesive samples is much higher than the percentage of increase of the stresses at the interface of the samples with thin layer of adhesive. Therefore, more failure at the interfaces is predicted by our FE results for the sample with thicker adhesive, confirming the Arici’s test outcomes. Fig. 4 – (a) Von Mises stress in the adhesive; (b) direct stress at the interface of composite-adhesive; (c) direct stress at the interface of dentin–adhesive.
Experimental study on the effect of the adhesive thickness on the strength by Arici et al. [14] shows that increasing the adhesive thickness two times will cause reduction in the bond strength (8% for the CO which is the light cured composite). The mode of failure is shifted toward more failure with no adhesive on the tooth (ARI) and all adhesive on the tooth, which are the cases of failure at the interfaces. Our finite element model results reported here accurately predict the
3.1.2.2. Uneven adhesive layer. During the procedure of application of the adhesive, it is likely that the adhesive thickness spread over surfaces is not the same all over the interface. This will cause different stresses at different parts of the adhesive. Simulation has been obtained for the samples with the adhesive thickness which is linearly increasing to double the thickness from one edge to the other edge. The stresses in the adhesive in the thicker part are higher than the thinner section. This is clearly indicated in Fig. 6, where zero point on the x axis indicate the thicker side of the adhesive layer and point 12 on the x axis shows the thin side of the adhesive layer. This will result in failure of the sample at lower stresses from the location of thicker adhesive especially for the dumbbell and
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Fig. 6 – Von Mises stress profile in the middle of the adhesive for three different geometries as a result of uneven adhesive layer (DB, dumbbell; S, stick; HG, hourglass).
stick samples. The Hourglass shape sample shows less sensitivity to uneven adhesive (Fig. 6). There is hardly any change of the maximum stress of hourglass sample with uneven adhesive compared to the flawless sample. This result is consistent with the results reported in Section 1 for the samples with different adhesive thickness. The percentage of change in the maximum stress induced in the adhesive, adhesive/composite and adhesive/dentin is shown in second set of rows of Table 3. The increase in the maximum stress is more significant for the dumbbell and stick sample especially at the dentin–adhesive interface compared to the hourglass shaped sample.
3.1.2.3. Angle of application of load. During the process of fixing specimens in the microtensile machine, there is the possibility of lack of alignment of the axis of the application of load and the axis of the sample. Even one degree angle between the axis of the application of load and the axis of the sample, causes significant change in the stress pattern in the adhesive. This will result in the concentration of the stress on one edge of the sample. Apart from reducing the stress for the initiation of the failure, the pattern of progress of any failure will be different from the aligned sample. This is shown in Fig. 7a for the hourglass sample. Similar change of stress pattern is observed for the dumbbell and stick samples. The misalignment of the axis of loading with sample can change the pattern of progression of failure. Especially in dumbbell and stick samples it could change the failure progression lines from inside the adhesive layer toward the interfaces with the dentin or composite. This is indicated by the arrows in Fig. 7a. In the hourglass sample the increase of the stress in the adhesive layer and at the interfaces of adhesive/dentin or adhesive/composite are almost equal (third set of rows of Table 3). Therefore, although failure occurs at lower stress, but the initiation of failure might remain at the site similar to the sample with axis of loading well adjusted. For all the samples the progression could be toward the interfaces in the direction of loading rather than in the horizontal direction.
Fig. 7 – (a) Contour plot of Von Mises stress for angled axis of loading for hourglass sample; (b) Von Mises stress in the adhesive for samples with angled axis of loading for all the geometries (DB, dumbbell; S, stick; HG, hourglass).
The Von Mises stress profiles induced within the adhesive for the three sample geometries are reported in Fig. 7b. It shows the shift of the maximum stresses toward one side of the sample and changing the symmetric condition across the adhesive layer. The results indicate that the effect of angled axis of application of force in the load for initiation of failure and in the failure mode is significant even if the angle of misalignment is very small. Other types of defects such as variation of thickness of adhesive and uneven adhesive application are important, but their effect is not as significant as the angled axis of the loading.
3.1.2.4. Flaw in the adhesive (air bubble or crack) at the edge or in the middle. Air bubble trapped in the adhesive resulting in the flaw sites in the adhesive, is one of the other causes of defects occurring during manufacturing of the samples. At the same time inducing a crack at the edge of the sample dur-
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Table 5 – Standard deviation for the bond strength predicted by FEA Stick 5.7
Dumbbell
Hourglass
5.2
4.6
of the adhesive and composite and interface of adhesive and dentin which results in progression of the crack and mixed failure mode. In the case of the flaw in the middle of the adhesive, the stress concentration area surrounds all around the flaw without a location of preference for progression of flaw. The area of high-stress concentration is surrounded by lower stress and this reduces the possibility of propagation of the flaw. In the dumbbell and stick sample the increase in the stress level for both types of edge or middle flaw is almost similar. Whereas in the hourglass sample the edge flaw will cause much higher stress concentration compared to the flaw in the middle of the adhesive which increase the sensitivity of the sample to the edge flaw. Since the hourglass sample is in need of bur diamond shaping at the edges the possibility of creating such a flaw at the edge of the sample is higher.
3.1.3. Estimation of the standard deviation of the bond strength using FEA
Fig. 8 – Von Mises stress profile in the adhesive for samples with (a) centred flaw; (b) edge flaw (DB, dumbbell; S, stick; HG, hourglass).
ing the shaping and manufacturing process is possible. Both of these will affect the stress distribution in and around the adhesive. We have simulated the flaw both at the edge and in the middle of the adhesive for all three shapes. The Von Mises stress distributions in the samples with flaws in the centre and at the edge of the adhesive are shown in Fig. 8a–b, respectively. The percentages of changes introduced by the edge and centred flaws on the maximum stresses are reported in Table 4. In all the sample geometries with the flaw at the edge the stress is concentrated at the tip of the flaw. The high-stress areas at the tip of the crack is oriented toward the interface
Table 4 – Percentage of change in maximum stresses in the adhesive for sample with middle/edge flaw in the adhesive Geometry Stick Dumbbell Hourglass
Middle flaw
Edge flaw
46.9 49.2 41.0
27.5 28.9 35.6
We have simulated most of the imperfections that might occur in the samples. Now in order to estimate the standard deviation that these imperfections and variations can induce in the results of the bond strength, we consider all the imperfections simulate and assume that the possibility of occurrence of all the imperfections is the same. On this basis we estimate the standard deviation of bond strength for each of the specimen geometries. It is worth mentioning that the standard deviations calculated on this basis can only be used as indicators of possible spread of results. It is not expected for these values to match the results of the experiments. As the standard deviations during the test results are influenced by other factors such as the experience and skill of researchers in producing the samples. Our estimation using the FEA prediction for bond strength indicates that the stick sample is expected to show highest standard deviation. The standard deviation of the bond strength of hourglass shows the lowest value and that of the dumbbell sample is between hourglass and stick specimen (Table 5). Goracci et al. have studied both hourglass and stick shape samples. They have tested the bond strength of these specimens using microtensile test. They have calculated the standard deviation of the bond strength. They have reported lower standard deviation for hourglass samples compared to the stick samples. This is in agreement with the FEA prediction. Although the process of manufacturing of the samples could significantly affect the standard deviation, it is expected if the same standard is taken in making both samples it is likely that the stick sample show higher standard deviation compared to the hourglass samples. Our experimental results reported in following parts of this paper as well confirm the FEA results prediction for the standard deviations.
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Table 7 – Percentage of samples failed at different failure modes and the mean strength for each mode of failure Failure modes
Fig. 9 – Von Mises stress in the adhesive for the three geometries for system with low modulus adhesive.
3.1.4. The effect of the modulus in the differences between the three sample geometries Two different elastic moduli for the adhesive have been used to see the effect of adhesive modulus in the maximum stresses induced in the samples of hourglass, stick and dumbbell and the differences between different geometries in these maximum stresses. The result for the adhesive with modulus of 3 MPa is shown in Fig. 1a. The Von Mises stress in the adhesive with the modulus of 1 MPa modulus is shown in Fig. 9. The comparison of the results indicates that for the higher modulus adhesive the differences between the maximum stresses of the hourglass sample and the dumbbell and stick samples is 14% while this value reduces to 10% for the low modulus adhesive. The dumbbell and stick samples show very similar stress pattern in the straight region. The dumbbell sample shows some stress concentration at the edge of the curved parts of the sample both in composite and dentin sections. It is expected as the adhesive with higher modulus is used for bonding the differences between the test results of the bond strength to increase.
3.2. Microtensile bond strength test results and its statistical analysis The results of the microtensile bond strength for each of the sample geometries are collected and the mean values and standard deviations are calculated. The outcomes are shown in Table 6. The mean values obtained for dumbbell and stick sample are very close. The hourglass sample has slightly lower bond
A
B
C
D
E
F
Stick Percentage Mean strength
50.0 29.0
27.8 30.0
16.7 38.7
0.0 –
0.0 –
5.6 17.03
Dumbbell Percentage Mean strength
55.6 29.5
27.8 32.4
11.1 36.2
5.6 31.7
5.6 9.5
5.6 12.1
Hourglass Percentage Mean strength
55.6 28.1
22.2 27.4
11.1 28.9
11.1 29.1
0.0 –
0.0 –
strength. The relative placement of the bond strength for the three different geometries obtained by the tests is in agreement with the FEA results (Table 6). The standard deviations obtained from the experimental results confirm the FEA predictions for the deviations on the basis of different types of variations considered in the samples. In both cases the hourglass sample shows lower standard deviation with dumbbell and stick being in the next orders (Table 6). At the same time the Weibull plots were produced for all three geometries and Weibull moduli were extracted from the plots and reported in Table 6. The Weibull moduli of the stick and dumbbell samples are very close and both lower than hourglass samples. The Weibull analysis confirms both FEA and other test results. Indicating that the failure data for the hourglass sample is expected to fit in smaller range. Different stress distribution for the hourglass sample has been predicted by FEA compared of the other two. After the fracture, the failure mode of the sample is identified by Optical Microscope. Possible failure modes are classified as follows:
(A) Adhesive failure between the bonding resin and dentin. (B) Partial adhesive failure between the bonding resin composite and dentin, and partial cohesive failure in dentin. (C) Partial adhesive failure between the bonding resin composite and dentin, and partial cohesive failure in resin composite. (D) Partial adhesive failure between the bonding resin and dentin, and partial cohesive failure in dentin and resin composite. (E) Cohesive failure in dentin. (F) Cohesive failure in resin composite.
Table 6 – Comparison of the Microtensile test and FEA results predictions for the mean strength and standard deviations Microtensile bond tests
Stick Dumbbell Hourglass
FEA
Mean strength
Standard deviation
Weibull modulus
31.01 31.18 28.13
5.11 4.04 3.28
6.5 6.8 9.6
Mean strength 28 28.4 24.7
Standard deviation 5.7 5.2 4.6
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Table 8 – ANOVA analysis results for each two-sample geometries and for all the three types of samples Samples Stick–dumbbell Stick–hourglass Dumbbell–hourglass Stick–dumbbell–hourglass
SS
d.f.
MS
F
P-value
F critical
0.28 72.25 83.93 104.91
1 1 1 2
0.28 72.25 83.93 52.45
0.013 3.96 6.19 2.98
0.90 0.05 0.02 0.059
4.13 4.13 4.13 3.18
For each of the sample geometries, the number of samples within each mode of failure along with the percentage of the failures in that mode is calculated. At the same time mean value of the bond strength with certain mode of failure is obtained. The results of the percentage for each failure mode and relevant mean strengths are reported in Table 7. These results indicate that most of the samples fail within the adhesive layer. The second dominant mode of failure is failure in adhesive combined with fracture in dentin. Considering the brittle nature of the dentin and the complicated interaction of dentin and adhesive in order to achieve a good interphase, this is expected. The third mode of failure observed mostly is the failure in adhesive combined with the resin fracture. The other types of failures are less likely to occur. The results reported in Table 7 also indicate that for the stick and dumbbell samples modes B and C of failure occur at higher stress values compared to mode A which is pure adhesive failure. Whereas for the hourglass samples the failure stresses for modes A–C are very similar. In all the samples the mode F of failure in the dentin occurs at very low stress, indicating that this type of failure is only present when the sample has considerable damage or defect on the dentin side. Therefore, the results of this type of failure are not a true indication of the adhesive bond strength and they should not be considered in the evaluation of the bond strength. The bond strength values are analyzed using the statistical method one-way analysis of variance (ANOVA). The tests involved fracture of dentin (F mode) and resin (E mode) with low failure stresses are not included in this analysis. The result of the ANOVA analysis is shown in Table 8. The first three rows indicate the comparison of each two sample shape. The last row in the table shows the ANOVA analysis for the three sets. The ANOVA for stick and dumbbell shape samples indicates that the F-value is much smaller than the F critical and the P-value as well is larger than 0.05, indicating that the two sets are not statistically different and the null hypothesis cannot be rejected. Analysis for the hourglass with stick/dumbbell on the other hand shows F is higher or very close to the critical F- and the P-values are smaller or very close to 0.05. Therefore, significant difference exists between hourglass and the other two sample shapes and the null hypothesis can be rejected. ANOVA for the three sets indicates that F is fairly close to F critical and P is close to 0.05 showing that the three sets are not similar. The result of the ANOVA once again confirms the outcomes of the FE analysis in classification of the samples on the basis of their geometries.
4.
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Conclusions (9)
(1) The stress concentration and distribution inside the stick and dumbbell samples are very similar in the straight
region of the samples. There are some stress concentration areas at the curved parts of the sample which occur in the composite and dentin sections. If the samples were free from flaws it was expected that the two shapes offer the same failure stresses. However, since the dumbbell samples involve shaping of the curved and dumbbell parts there will be increased risk of inducing flaws in the areas to be shaped which might increase the risk of failure in this regions. The stress concentration and pattern in the hourglass sample is very different from the dumbbell and stick sample. It is expected that the hourglass sample fail at lower stress compared to the other two samples, since the stresses induced in the adhesive is larger for the hourglass sample. The hourglass sample is more sensitive to the flaws induced in the sample at the edge during shaping process compared to dumbbell sample. The thickness of the adhesive and the even distribution of the adhesive affect the stress concentration level and the bond strength. However the effect of misalignment of the sample in the tensile machine is much more significant in the strength values predicted. The modulus of the adhesive affects the differences between the hourglass and dumbbell–stick samples in the bond strength values. As the modulus of the adhesive is increased the differences between the maximum stresses in the adhesive for the hourglass and other two stick and dumbbell shape samples increases. Apart from the inherent differences between the stress distributions that different sample shapes offer which can affect the bond strength measured, the manufacturing of the samples in some cases is more prune to inducing flaws at the edges of the sample. The flaws induced during manufacturing are specifically important in the hourglass sample. Finite element analysis is capable of quantifying the effect of each parameter on the bond strength. The prediction of FEA is in agreement with the experimental results in relative bond strength in three different geometries. Experimental results confirm the FE analysis results in ranking of the sample geometries in the bond strengths with the hourglass sample showing the lowest bond strength and almost similar results for the dumbbell and stick geometries. Standard deviations calculated on the basis of the experimental results confirm the FE prediction for these values, indicating the highest standard deviation for stick geometry and dumbbell and hourglass in next orders. Most of the samples for all three geometries fail either in the simple or combined adhesive failure modes. The dentin or resin fracture results in very low failure stresses
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indicating these types of failure only can be present in seriously damaged samples that need to be omitted from final estimation of the bond strengths. In stick and dumbbell samples combined adhesive failures are accompanied with higher stress values compared to the simple adhesive failure. These differences are not present between the stresses of the combined and simple adhesive modes of failure in the hourglass samples. (10) ANOVA analysis shows that the hourglass sample results are significantly different from the dumbbell and stick samples statistically. For the dumbbell and stick samples on the other hand the null hypothesis cannot be rejected. These once again confirm FE predictions in grouping the three geometries.
Acknowledgements The author would like to thank Mr. Z. Ou for performing the microtensile tests, Kerr Company for providing the adhesive and composite materials for the tests and Professor Van Noort and Ms. Betamer from dental school of University of Sheffield for providing dentin materials, facilities and assistance in shaping the samples.
references
[1] Pashley DH, Sano H, Ciucchi B, Yoshiyama M, Carvalho RM. Adhesion testing of dentine bonding agents: a review. Dent Mater 1995;11(March):117–25. [2] Van noort R, Della Bona A. Shear vs. tensile bond strength of resin composite bonded ceramics. J Dent Res 1995;74(9):1591–6. [3] Nakabayashi N, Watanabe A, Arao T. A tensile test to facilitate the identification of defects in dentine bonded specimen. J Dent 1998;26(4):379–85.
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[4] Capel Cardoso PE, Sadek FT, Placido E, Santos JFF. Microtensile bond strength of current adhesive systems when compared to cohesive strength of sound dentin and a resin-based composite. Mater Res 2004;7(4): 575–81. [5] Yoshiyama M, Carvalho RM, Sano H, Hornerg JA, Brewer PD, Pashley DH. Regional bond strength of resins to human root dentine. J Dent 1996;24(6):435–42. [6] Burrow MF, Nopnakeepong U, Phrukkanon S. A comparison of microtensile bond strengths of several dentine bonding systems to primary and permanent dentine. Dental Mater 2002;18:239–45. [7] Phrukannon S, Burrow MF, Tyas MJ. The influence of cross sectional shape and surface area on the microtensile bond test. Dent Mater 1998;14(June):212–21. [8] Loguercio AD, Uceda-Gomez N, Carrilho MRdO, Reis A. Influence of specimen size and regional variation on long-term resin–dentin bond strength. Dental Mater 2005;21:224–31. [9] Goracci C, Sadek FT, Monticelli F, Cardoso PEC, Ferrari M. Influence of substrate, shape, and thickness on microtensile specimens’ structural integrity and their measured bond strengths. Dental Mater 2004;20:643–54. [10] Schulze KA, Oliveira SA, Wilson RS, Gansky SA, Marshall GW, Marshall SJ. Effect of hydration variability on hybrid layer properties of a self-etching versus an acid-etching system. Biomaterials 2005;26:1011–8. [11] Clarke SA, Gordon PH, McCabe JF. An ex vivo investigation to compare orthodontic bonding using a 4-META-based adhesive or composite adhesive to acid-etched and sand blasted enamel. J Orthodont 2003;30:51–8. [12] Leforestiera E, Darque-Ceretti E, Costini JM, Muller M, Bolla M. Adaptation of a standard adherence test to dentistry: the peeling test. Study of the interface between dentine and a one step dentine adhesive system. Int J Adhes Adhes 2002;22:23–35. [14] Arici S, Arici N. Adhesive thickness effects on the bond strength of a light cured resin-modified glass ionomer cement. Angle Orthodont 2005;75(2):250–5.
available at www.sciencedirect.com
journal homepage: www.intl.elsevierhealth.com/journals/dema
Evaluation of sources of uncertainties in microtensile bond strength of dental adhesive system for different specimen geometries Elaheh Ghassemieh ∗ Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objective. The aim of this research is to use finite element analysis (FEA) to quantify the effect
Received 6 June 2006
of the sample shape and the imperfections induced during the manufacturing process of
Received in revised form
samples on the bond strength and modes of failure of dental adhesive systems through
20 March 2007
microtensile test. Using the FEA prediction for individual parameters effect, estimation of
Accepted 18 June 2007
expected variation and spread of the microtensile bond strength results for different sample geometries is made. Methods. The estimated stress distributions for three different sample shapes, hourglass,
Keywords:
stick and dumbbell predicted by FEA are used to predict the strength for different frac-
Microtensile bond strength
ture modes. Parameters such as the adhesive thickness, uneven interface of the adhesive
Finite element analysis
and composite and dentin, misalignment of axis of loading, the existence of flaws such
ANOVA
as induced cracks during shaping the samples or bubbles created during application of
Failure modes
the adhesive are considered. Microtensile experiments are performed simultaneously to
Dental adhesive
measure bond strength and modes of failure. These are compared with the FEA results.
Dental composite
Results. The relative bonding strength and its standard deviation for the specimens with
Sample geometry
different geometries measured through the microtensile tests confirm the findings of the FEA. The hourglass shape samples show lower tensile bond strength and standard deviation compared to the stick and dumbbell shape samples. ANOVA analysis confirms no significant difference between dumbbell and stick geometry results, and major differences of these two geometries compared to hourglass shape measured values. Induced flaws in the adhesive and misalignment of the angle of application of load have significant effect on the microtensile bond strength. Using adhesive with higher modulus the differences between the bond strength of the three sample geometries increase. Significance. The result of the research clarifies the importance of the sample geometry chosen in measuring the bond strength. It quantifies the effect of the imperfections on the bond strength for each of the sample geometries through a systematic and all embracing study. The results explain the reasons of the large spread of the microtensile test results reported by various researchers working in different labs and the need for standardization of the test method and sample shape used in evaluation of the dentin–adhesive bonding system. © 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
∗
Tel.: +44 114 2227868. E-mail address: E.Ghassemieh@sheffield.ac.uk. 0109-5641/$ – see front matter © 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.dental.2007.06.022
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1.
Introduction
To date no standard test has been approved for measuring the bond strength of dentin and composite using dental adhesive system. Different test methods and parameters used have resulted in discrepancy of the data reported by different researchers on the same adhesive system. The factors affecting the bond strength have been addressed by few researchers before. Pashley et al. [1] have listed these factors in a review paper under the broad categories of substrate variables, etching variables, priming variables, bonding variables, storage variables and testing variables. Most of this review has focused on the issues relating to the differences induced by the material properties or the process used in sample preparation. The substrate and adhesive variables induce inherent differences in the material properties. Data reported on the dentin and bovine strength can be up to 50% different depending on the source and part of the dentin or bovine used. The same sort of data spread is reported for demineralized dentin, with some data on the strength being almost one-third of the other test data. The process used in the preparation of the sample as well such as etching and priming have effect on the interface properties and therefore on the bond strength. Van noort et al. [2] have analyzed the effect of the test method in the bond strength results. They have made a comparison between the microtensile test and shear test in measuring bond strength. Applying FEA they have concluded that the shear test results in unfavorable stresses in the specimen. Consequently, they have recommended the tensile test as a preferred test method for measuring bond strength. While the advantages of the microtensile test were proved, many researchers applied the method to measure the bond strength of dental adhesive [3–6]. Nakabayahsi et al. [3] apply the method to detect defects in the specimen. They study the effect of defects in the failure characteristics of the miniaturized samples. Capel Cordoso et al. [4] use the microtensile bond strength to compare the bond strength of three adhesive systems with the cohesive strength of dentin and composite. In all three systems they find the adhesive bond strength to be much lower than the strength of composite or dentin. Yoshiyama et al. [5] apply the microtensile test to measure the bond strength to different regions of dentin. They have reported higher bond strength on the coronal and apical dentin compared to the bond strength to the cervical root dentin. The effect of specimen size and geometry in the results of the bond strength is studied partly by other researchers [7–9]. Phrukkanon et al. [7] have investigated specimens with round and rectangular cross sections. For four different adhesive systems they have reported higher bond strength for the circular cross section compared to the rectangular cross section. The second parameter they have considered is the cross sectional area of the samples. For three different cross sections, lower bond strength is estimated for larger cross sections. The results have been explained using FEA to estimate the stress distribution. They have attributed this result to higher stress values for the samples with larger cross section. Other researchers have used Griffith theory to explain the same results. They have reasoned that smaller samples
537
will have smaller flaw size and therefore higher strength. In Phrukkanon’s research they have increased the surface area without changing any other part of the sample. If they scale up all parts of the sample with the surface area the FE results would not indicate any changes for different surface areas. Whereas experimental tests still indicate smaller strength for the samples with larger cross sectional area. This shows a second parameter having role in reducing the bond strength for the larger size specimens which is recommended by Griffith’s theory. Although the researchers have highlighted the parameters affecting the result of the bond strength in the previous studies, there is little indication of quantifying each effect and systematic study. At the same time most of the previous researches on the factors affecting the result of the bond strength have identified only one or two parameters, ignoring the other parameters. In the current research we have considered broad range of factors affecting the bond strength and modes of failure. Using finite element analysis we have investigated the effect of each parameter on the general stress distribution in different regions of adhesive, at the interface of the adhesive and composite and at the interface of adhesive and dentin. We have quantified the effect of each variable on the bond strength and modes of failure for the most commonly used geometries of stick, dumbbell and hourglass. The advantage of using finite element analysis in this respect is that it makes separation of the parameters and its effect possible. This possibility does not exist with the experimental test while interaction of the variables is normally unavoidable. The final FEA predictions of bond strength, its variations and modes of failure are derived from bringing together the results of analysis for all the identified individual parameters. Microtensile bond strength experiments are performed in order to validate the FEA estimation of the mode of failure, bond strength and its standard deviation for the mentioned geometries. The experimental measurements of these parameters and the ranking of different geometries in bond strength approve the collective predictions of FEA. This confirms the reliability of the FEA in its estimation of other individual effects as well.
2.
Methodology
2.1.
Finite element analysis
The main approach used in this research is finite element analysis which is validated by experiments. All the variables affecting the bond strength measured during microtensile test are identified. The first variable considered is the effect of the geometry of the specimen on the bond strength. Three most commonly used geometries in the experimental tests have been considered. This includes stick, dumbbell and hourglass geometries. Another set of parameters considered is induced as a result of the inaccuracies and errors during making the samples or performing the tests. In this category, variables such as adhesive thickness, uneven spread of adhesive, and misalignment of the axis of the applied load are examined for all three specimen geometries. Finally, the effect of the presence of flaw at the edge of adhesive and at the middle sections
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analysis clarifies the similarities and differences between the test sets with various sample geometries.
2.2.1.
Fig. 1 – Finite element mesh for the (a) stick; (b) dumbbell; (c) hourglass geometries.
of the adhesive is considered. These flaws might occur during application of the adhesive or manufacturing of the specimen. The effect of each parameter on the bond strength is evaluated and an estimation of data spread as a result of these parameters has been made.
2.1.1.
Finite element model and materials properties input
Finite element model: Geometric models are developed for stick, dumbbell and hourglass specimens. Typical finite element meshes of these geometries are shown in Fig. 1a–c. The samples are of 26 mm length. The areas of the adhesive section in all the samples are equal to about 1.08 mm2 [width 1.2 mm × thickness 0.9 mm). Load of 10 N is applied to all the samples in y direction. The thickness of the adhesive is about 0.26 mm. The thickness is chosen on the basis of measuring the adhesive thickness following the manufacturer’s guidance in application of the adhesive. The properties of the adhesive, composite and dentin used in this model are summarized in Table 1.
2.2.
Microtensile bond strength experiments
Experimental tests have been carried out to validate FEA results and to broaden and enhance the perspective of the study. An adhesive and composite system has been chosen. Microtensile test is used to measure bond strength for three different sample geometries. The bond strength and its standard deviation and modes of failure have been identified. The results of the experiment show similar trend in the bond strength and its variation compared to the FEA results. ANOVA
Table 1 – Material properties used in the FEA Material Adhesive Composite Dentin
Modulus (MPa) 3.3 8.0 14.0
Strength (MPa)
Poisson ratio
27.0 85.0 110.0
0.30 0.30 0.23
Test materials and sample preparation
In this research, caries-free human molars are used for sample preparation. Self-etching primer adhesive system (Opti-Bond Solo Plus, Kerr Corporation, CA, Lot: 408737) is selected as bonding agent and Herculite XRV composite material (Kerr Corporation, CA, Lot: 4-1286) is used to form a flat-topped crown. The human molars are stored in a 0.9% sodium chloride solution (normal saline) and 0.2% sodium azide at room temperature for not more than 1 month before use. Just prior to the preparation, a tooth is thoroughly rinsed in running water. The surface is gently scraped by penknife in order to remove any excess tissue. The tooth is then steadied on a metal table (Fig. 2a) with araldite structural adhesive before attempting the cutting procedure. The occlusal enamel is removed perpendicular to its long axis, using low speed diamond disc (LECO Corporation VC-50 Japan) under water-cooling (Fig. 2b). The crown portion is then removed. The remaining exposed section is inspected to ensure the surface is flat. The surface is then ground with 600-grit sand paper under running water for 1 min to create a uniform smear layer. The dentin surface is thoroughly washed with water, and gently air-dried by using air spray. Manufacturer’s instruction is used in application of the adhesive and composite. Self-etch primer is applied to the prepared dentin surface with a light brushing motion for 15 s. Then it is air sprayed for 3 s. Optibond solo plus is applied with light brush motion for 15 s and air sprayed for 3 s. Optibond solo plus is reapplied in the same manner. Then the adhesive is light cured for 20 s. After the application of adhesive system on the dentin surface, resin composite is placed on the adhesive surface in equal increments of about 2 mm to form the crown. Each layer of composite is light cured for not less then 20 s. The procedure was repeated until a 6 mm flat-topped resin composite crown with adhesive was formed on the dentin. After 24 h, 15 teeth are randomly separated into three groups and then steadied on a metal table using araldite structural adhesive. One of the groups is approximately sectioned (Fig. 2d–e) in 1.2 mm × 0.9 mm square shape by low speed diamond disc for stick shape preparation. The other two groups are sectioned to 3.5 mm × 0.9 mm rectangular shape for dumbbell and hourglass shape samples preparation. For these two former groups, the region of adhesive and interfaces is then formed using a round diamond bur for hourglass shape samples and a cylindrical diamond bur for dumbbell shape samples. In both cases high-speed hand piece is applied in shaping process. All samples are tested using a microtester (Micro material Limited, WREXHAM, UK). Bonding area of each sample is measured using vernier and is inputted into the computer before performing the tensile test. The sample is placed on the top of two metal plates. Both plates are placed horizontally with a 5 mm gap apart so that the bonding section between dentin and composite is in the gap between the plates. The end section of dentin and composite are stabilized on the metal plates. The two ends
d e n t a l m a t e r i a l s 2 4 ( 2 0 0 8 ) 536–547
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Fig. 2 – (a) Tooth stabilized to metal table; (b) cutting the occlusal crown; (c) flat top composite crown; (d) sectioning final specimen; (d) sectioned specimen.
of the samples, dentin and composite end sections are fixed to the metal plates using very strong adhesive. Enough time is given for the adhesive to dry completely. Sample with supporting plates is then carefully placed on the testing bench. The load is applied at the rate of 2 mm/min and the test is stopped automatically once fracture occurred. The results of the microtensile bond strength for each of the samples are recorded. Twenty samples for each of the geometries are tested. The mean values and standard deviations are calculated. After the microtensile bond strength test, the failed sample is studied under optical microscope to determine the mode of failure.
3.
Results and discussion
3.1.
Finite element results
In order to evaluate the bond strength for different sample geometries, we first study the overall stress distribution produced by application of the load in a tensile bond strength test. As the stresses in the adhesive and interfaces are more deterministic in the bond strength, we more specifically focus on these stresses. Finally, we consider variations and imperfections that are likely to occur during the sample preparation and the effect that these imperfections can induce in the result of the bond strength.
3.1.1. Stress distribution in different geometries 3.1.1.1. Direct stress distribution. The contour plots of the direct stress in the direction of application of tensile load for the three geometries are shown in Fig. 3a–c. Equal range of maximum and minimum is chosen for all the plots in order to make a fair comparison between the three geometries. The
maximum stresses for the dumbbell shape sample occur at the curved corners of the dentin and composite. Maximum stress in the adhesive region is in the centre of the adhesive (Fig. 3a). In the hourglass specimen the maximum stress is concentrated in the adhesive edges. This maximum stress extends from the adhesive region into the dentin and composite sections adjacent to the adhesive (Fig. 3b). In the stick specimen the maximum stress is observed in the middle of the adhesive (Fig. 3c). Regarding the stress distribution and rate of changes the dumbbell geometry induce relatively high stresses all over the straight centre region of the dumbbell, in the hourglass the high stress is more than any other geometry concentrated in the adhesive region only and in the stick the stress concentration is less localized than other two geometries.
3.1.1.2. Stress in the adhesive and at the interface. Fig. 4a shows the Von Mises stresses in the middle of the adhesive for the three geometries. The stress distribution in the dumbbell and stick are very similar. However, the hourglass sample shows completely different stress profile. For the dumbbell and stick the stress along the width of the adhesive is almost the same. Therefore, in the dumbbell and stick samples there is no preferred point of failure. In the case of the hourglass sample the concentration of the stress is very close to the edges indicating that the initiation of failure is likely to be at the edges of the specimen. These different patterns of stress will cause different types of failures for the hourglass sample compared to the other two geometries. Especially as we investigate in later sections, the effect of a crack or failure induced at the edges of the sample is fatal, whereas a flaw or crack in the middle of the sample can be much better tolerated. The stress profiles at the interface of the composite and adhesive are indicated in Fig. 4b. The maximum stress for the dumbbell and stick shape samples is found in the mid-
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Fig. 3 – Contour plots for the direct stress distribution in the (a) dumbbell; (b) hourglass; (c) stick samples.
dle of the sample with almost no point of preference. In the hourglass sample the trend is different with maximum stress occurring at the edges of the interface. The stress for the hourglass sample is higher than dumbbell/stick samples. However, stress profiles at the interface of the dentin and adhesive indicate that for all the samples the maximum stress occurs at the edge (Fig. 4c). The stress in the hourglass specimen seems to be slightly higher than the other two samples. These results fully support the experimental results reported in later sections that more mode B failure (combined adhesive and dentin failure) is observed for all the samples compared to the mode C failure (combined adhesive and resin failure). Predictions of FEA for the failure stresses of various samples for different modes of failure along with the possible location of initiation of failure for each mode are reported in
Table 2. The failure stress for the adhesive failure is the highest for the stick sample with the value of 32.2. The dumbbell sample shows slightly lower value of 31.1. The hourglass has the lowest failure stress of 27.1 for the adhesive mode of failure. In order to predict the stresses of failure at interface, we need to have the values of the strength for the interface. However, no previous research has reported any quantitative data on the interface strengths. There is only qualitative research available on the strength of the interface and its characteristics. The fracture toughness of the interface is highly dependent on the process of surface preparation before applying the adhesive. The type of adhesive used and its compatibility with the composite or dentin is a determining factor in the interface bond strength. Schulze et al. [10] have studied the differences of the resin–substrate interface
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Table 2 – Maximum stress values (MPa), its location and predicted failure stresses (MPa) for different modes of failure in three types of samples (Mid-Uni, middle-uniform) Stick Max Adhesive Adhesive–dentin Average Dentin Composite
Location
8.50E+06 1.16E+07
Mid-Uni Edge
1.05E+07 8.50E+06
Edge Mid-Edge
Dumbbell Failure
Max
32.2 23.6 28 10E+0 102
8.80E+06 1.05E+07
Mid-Uni Edge
1.10E+07 8.80E+06
Edge Mid-Edge
layer of the dental restoration under different surface processing condition of self-etching versus acid etching. They have reported different interface properties for the two cases as a result of moisture condition. Clark et al. [11] have studied the effect of the surface preparation of enamel on the bond strength and mode of failure. They have considered two types of surface preparation processes: sand-blasting and acid etching. Major differences have been observed for the bond strength of the right on adhesive through these two surface preparation processes. While this difference is decreased for a composite added adhesive, the modes of failure are still affected by the surface preparation. The main reason is different interface strength for the samples prepared through different processes. For the sand-blasted bonding with right on adhesive the mode of failure is shifted toward the interface between the enamel and the adhesive and reduced values of bond strength. Clark’s study is on the effect of surface preparation for enamel on the interface properties. However, it is expected that the surface preparation and manufacturing process to cause different interface properties for dentin which we are studying here as well. Since these parameters are known to affect the interface strength in most bonding process applications. Leforestier et al. [12] have also indicated the complexity of the interface layer and its dependence on the dentin superficial parameters, physico-chemical and rheologic behavior of the resin and composite. The failure stresses predicted by FEA for the failure at the interface of the adhesive/composite and adhesive/dentin is on the basis of the assumption that the strengths of the interfaces are equal to the strength of the adhesive. The assumption is made in order to obtain some relative failure stress values for the three specimens which should be adequate enough for comparison purposes. More accurate failure stress predictions for the interfaces can only be obtained if the strengths of the interfaces are known. Pashley et al. [1] have estimated the strength of the interphase of dentin–resin as strong as dentin material. However, there has been no experimental work to support this. The assumption of taking the strength of the interface equal to the adhesive provides a range of the lowest stresses (underestimate) for the failure stresses at the interface. On the contrary, taking the strength of the interface equal to dentin, there will be overestimation of the failure stresses at the interface. On the basis of our assumption the failure stress of the dentin–adhesive interface is the smallest for all the samples. It is expected for the failure to start at the edges. Obviously, this can only be valid if the samples are all perfectly made and are free from flaws that are considered in the next sections.
Location
HourGlass Failure 31.1 26 28.4 95.5 98.3
Max
Location
Failure
1.00E+07 1.28E+07
Edge Edge
1.20E+07 1.00E+07
Edge Edge
27.4 21.4 24.7 87.5 86.5
The location of initiation of the cohesive failure of adhesive or adhesive/composite interface debonding is in the middle with no preference point for both stick and dumbbell shape samples. However, for the hourglass the location of initiation of cohesive failure is at the edge. The position of initiation of debonding of the interface of dentin/adhesive is at the edge for all the shape samples. The failure stress predicted by FEA is smaller for the hourglass sample compared to the dumbbell and stick. The second weak sample is the stick and the dumbbell is supposed to provide the highest failure stress value. Goracci et al. [9] have done microtensile test on specimens with hourglass or stick geometry for different cross sectional area and they consistently have obtained lower bond strength data for hourglass compared to the stick shape samples with the same cross sectional area. This confirms the results of our FEA prediction on the effect of the specimen geometry on the bond strength values. Our experimental results reported in later sections approves these findings as well.
3.1.2. Different imperfections and design variations and their effect on the stresses Different types of imperfections and variations that might occur in the samples are considered as follows.
3.1.2.1. Thickness of the adhesive. Fig. 5a indicates the Von Mises stress in the middle of the adhesive for the samples with three different shapes with thin and thick layer of adhesive. The thickness of the adhesive is 0.2 mm for the samples with thin adhesive and 0.4 mm for the samples with thick adhesive. If the thickness of the adhesive is increased two times, the maximum Von Mises in the adhesive is increased for all the samples. However, the percentage of increase of the stress for the thick adhesive is lower for hourglass sample compared to the dumbbell and stick shape samples. The percentage of changes in the maximum stresses in the adhesive, at the interface of the adhesive/composite and interface of the adhesive/dentin for the three shapes are summarized in the first set of rows of Table 3. In the dumbbell and stick samples with thick adhesive the maximum stress at the interface of the adhesive/composite and adhesive/dentin increases more compared to the stresses in the adhesive. However, the stresses at both interfaces show slight decrease for the hourglass sample. FE prediction indicates that the thicker the adhesive the more likely the failure to be shifted to the adhesive–composite interface for the stick and dumbbell samples. Thicker adhesive in hourglass samples would not cause major effect and it is likely to increase the bond strength.
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Fig. 5 – Von Mises stress distribution in the thin and thick adhesive (DB, dumbbell; S, stick; HG, hourglass).
Table 3 – Percentage of change in maximum stresses in the adhesive, interface of adhesive/composite and interface of adhesive/dentin Geometry
Adhesive
Thickness Stick Dumbbell Hourglass
5.7 6.8 2.2
14.3 14.1 −0.9
10.3 11.4 −3.1
Uneven adhesive Stick Dumbbell Hourglass
3.9 4.2 4.2
5.9 0.2 2.8
14.7 9.5 1.6
32.4 42.5 42.7
23.3 26.0 41.7
37.1 47.6 43.0
Angled axis Stick Dumbbell Hourglass
Adhesive/ composite
Adhesive/ dentin
increase of the failure for the thicker adhesive. The percentage of increase of the stresses at the interfaces for thick adhesive samples is much higher than the percentage of increase of the stresses at the interface of the samples with thin layer of adhesive. Therefore, more failure at the interfaces is predicted by our FE results for the sample with thicker adhesive, confirming the Arici’s test outcomes. Fig. 4 – (a) Von Mises stress in the adhesive; (b) direct stress at the interface of composite-adhesive; (c) direct stress at the interface of dentin–adhesive.
Experimental study on the effect of the adhesive thickness on the strength by Arici et al. [14] shows that increasing the adhesive thickness two times will cause reduction in the bond strength (8% for the CO which is the light cured composite). The mode of failure is shifted toward more failure with no adhesive on the tooth (ARI) and all adhesive on the tooth, which are the cases of failure at the interfaces. Our finite element model results reported here accurately predict the
3.1.2.2. Uneven adhesive layer. During the procedure of application of the adhesive, it is likely that the adhesive thickness spread over surfaces is not the same all over the interface. This will cause different stresses at different parts of the adhesive. Simulation has been obtained for the samples with the adhesive thickness which is linearly increasing to double the thickness from one edge to the other edge. The stresses in the adhesive in the thicker part are higher than the thinner section. This is clearly indicated in Fig. 6, where zero point on the x axis indicate the thicker side of the adhesive layer and point 12 on the x axis shows the thin side of the adhesive layer. This will result in failure of the sample at lower stresses from the location of thicker adhesive especially for the dumbbell and
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Fig. 6 – Von Mises stress profile in the middle of the adhesive for three different geometries as a result of uneven adhesive layer (DB, dumbbell; S, stick; HG, hourglass).
stick samples. The Hourglass shape sample shows less sensitivity to uneven adhesive (Fig. 6). There is hardly any change of the maximum stress of hourglass sample with uneven adhesive compared to the flawless sample. This result is consistent with the results reported in Section 1 for the samples with different adhesive thickness. The percentage of change in the maximum stress induced in the adhesive, adhesive/composite and adhesive/dentin is shown in second set of rows of Table 3. The increase in the maximum stress is more significant for the dumbbell and stick sample especially at the dentin–adhesive interface compared to the hourglass shaped sample.
3.1.2.3. Angle of application of load. During the process of fixing specimens in the microtensile machine, there is the possibility of lack of alignment of the axis of the application of load and the axis of the sample. Even one degree angle between the axis of the application of load and the axis of the sample, causes significant change in the stress pattern in the adhesive. This will result in the concentration of the stress on one edge of the sample. Apart from reducing the stress for the initiation of the failure, the pattern of progress of any failure will be different from the aligned sample. This is shown in Fig. 7a for the hourglass sample. Similar change of stress pattern is observed for the dumbbell and stick samples. The misalignment of the axis of loading with sample can change the pattern of progression of failure. Especially in dumbbell and stick samples it could change the failure progression lines from inside the adhesive layer toward the interfaces with the dentin or composite. This is indicated by the arrows in Fig. 7a. In the hourglass sample the increase of the stress in the adhesive layer and at the interfaces of adhesive/dentin or adhesive/composite are almost equal (third set of rows of Table 3). Therefore, although failure occurs at lower stress, but the initiation of failure might remain at the site similar to the sample with axis of loading well adjusted. For all the samples the progression could be toward the interfaces in the direction of loading rather than in the horizontal direction.
Fig. 7 – (a) Contour plot of Von Mises stress for angled axis of loading for hourglass sample; (b) Von Mises stress in the adhesive for samples with angled axis of loading for all the geometries (DB, dumbbell; S, stick; HG, hourglass).
The Von Mises stress profiles induced within the adhesive for the three sample geometries are reported in Fig. 7b. It shows the shift of the maximum stresses toward one side of the sample and changing the symmetric condition across the adhesive layer. The results indicate that the effect of angled axis of application of force in the load for initiation of failure and in the failure mode is significant even if the angle of misalignment is very small. Other types of defects such as variation of thickness of adhesive and uneven adhesive application are important, but their effect is not as significant as the angled axis of the loading.
3.1.2.4. Flaw in the adhesive (air bubble or crack) at the edge or in the middle. Air bubble trapped in the adhesive resulting in the flaw sites in the adhesive, is one of the other causes of defects occurring during manufacturing of the samples. At the same time inducing a crack at the edge of the sample dur-
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Table 5 – Standard deviation for the bond strength predicted by FEA Stick 5.7
Dumbbell
Hourglass
5.2
4.6
of the adhesive and composite and interface of adhesive and dentin which results in progression of the crack and mixed failure mode. In the case of the flaw in the middle of the adhesive, the stress concentration area surrounds all around the flaw without a location of preference for progression of flaw. The area of high-stress concentration is surrounded by lower stress and this reduces the possibility of propagation of the flaw. In the dumbbell and stick sample the increase in the stress level for both types of edge or middle flaw is almost similar. Whereas in the hourglass sample the edge flaw will cause much higher stress concentration compared to the flaw in the middle of the adhesive which increase the sensitivity of the sample to the edge flaw. Since the hourglass sample is in need of bur diamond shaping at the edges the possibility of creating such a flaw at the edge of the sample is higher.
3.1.3. Estimation of the standard deviation of the bond strength using FEA
Fig. 8 – Von Mises stress profile in the adhesive for samples with (a) centred flaw; (b) edge flaw (DB, dumbbell; S, stick; HG, hourglass).
ing the shaping and manufacturing process is possible. Both of these will affect the stress distribution in and around the adhesive. We have simulated the flaw both at the edge and in the middle of the adhesive for all three shapes. The Von Mises stress distributions in the samples with flaws in the centre and at the edge of the adhesive are shown in Fig. 8a–b, respectively. The percentages of changes introduced by the edge and centred flaws on the maximum stresses are reported in Table 4. In all the sample geometries with the flaw at the edge the stress is concentrated at the tip of the flaw. The high-stress areas at the tip of the crack is oriented toward the interface
Table 4 – Percentage of change in maximum stresses in the adhesive for sample with middle/edge flaw in the adhesive Geometry Stick Dumbbell Hourglass
Middle flaw
Edge flaw
46.9 49.2 41.0
27.5 28.9 35.6
We have simulated most of the imperfections that might occur in the samples. Now in order to estimate the standard deviation that these imperfections and variations can induce in the results of the bond strength, we consider all the imperfections simulate and assume that the possibility of occurrence of all the imperfections is the same. On this basis we estimate the standard deviation of bond strength for each of the specimen geometries. It is worth mentioning that the standard deviations calculated on this basis can only be used as indicators of possible spread of results. It is not expected for these values to match the results of the experiments. As the standard deviations during the test results are influenced by other factors such as the experience and skill of researchers in producing the samples. Our estimation using the FEA prediction for bond strength indicates that the stick sample is expected to show highest standard deviation. The standard deviation of the bond strength of hourglass shows the lowest value and that of the dumbbell sample is between hourglass and stick specimen (Table 5). Goracci et al. have studied both hourglass and stick shape samples. They have tested the bond strength of these specimens using microtensile test. They have calculated the standard deviation of the bond strength. They have reported lower standard deviation for hourglass samples compared to the stick samples. This is in agreement with the FEA prediction. Although the process of manufacturing of the samples could significantly affect the standard deviation, it is expected if the same standard is taken in making both samples it is likely that the stick sample show higher standard deviation compared to the hourglass samples. Our experimental results reported in following parts of this paper as well confirm the FEA results prediction for the standard deviations.
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Table 7 – Percentage of samples failed at different failure modes and the mean strength for each mode of failure Failure modes
Fig. 9 – Von Mises stress in the adhesive for the three geometries for system with low modulus adhesive.
3.1.4. The effect of the modulus in the differences between the three sample geometries Two different elastic moduli for the adhesive have been used to see the effect of adhesive modulus in the maximum stresses induced in the samples of hourglass, stick and dumbbell and the differences between different geometries in these maximum stresses. The result for the adhesive with modulus of 3 MPa is shown in Fig. 1a. The Von Mises stress in the adhesive with the modulus of 1 MPa modulus is shown in Fig. 9. The comparison of the results indicates that for the higher modulus adhesive the differences between the maximum stresses of the hourglass sample and the dumbbell and stick samples is 14% while this value reduces to 10% for the low modulus adhesive. The dumbbell and stick samples show very similar stress pattern in the straight region. The dumbbell sample shows some stress concentration at the edge of the curved parts of the sample both in composite and dentin sections. It is expected as the adhesive with higher modulus is used for bonding the differences between the test results of the bond strength to increase.
3.2. Microtensile bond strength test results and its statistical analysis The results of the microtensile bond strength for each of the sample geometries are collected and the mean values and standard deviations are calculated. The outcomes are shown in Table 6. The mean values obtained for dumbbell and stick sample are very close. The hourglass sample has slightly lower bond
A
B
C
D
E
F
Stick Percentage Mean strength
50.0 29.0
27.8 30.0
16.7 38.7
0.0 –
0.0 –
5.6 17.03
Dumbbell Percentage Mean strength
55.6 29.5
27.8 32.4
11.1 36.2
5.6 31.7
5.6 9.5
5.6 12.1
Hourglass Percentage Mean strength
55.6 28.1
22.2 27.4
11.1 28.9
11.1 29.1
0.0 –
0.0 –
strength. The relative placement of the bond strength for the three different geometries obtained by the tests is in agreement with the FEA results (Table 6). The standard deviations obtained from the experimental results confirm the FEA predictions for the deviations on the basis of different types of variations considered in the samples. In both cases the hourglass sample shows lower standard deviation with dumbbell and stick being in the next orders (Table 6). At the same time the Weibull plots were produced for all three geometries and Weibull moduli were extracted from the plots and reported in Table 6. The Weibull moduli of the stick and dumbbell samples are very close and both lower than hourglass samples. The Weibull analysis confirms both FEA and other test results. Indicating that the failure data for the hourglass sample is expected to fit in smaller range. Different stress distribution for the hourglass sample has been predicted by FEA compared of the other two. After the fracture, the failure mode of the sample is identified by Optical Microscope. Possible failure modes are classified as follows:
(A) Adhesive failure between the bonding resin and dentin. (B) Partial adhesive failure between the bonding resin composite and dentin, and partial cohesive failure in dentin. (C) Partial adhesive failure between the bonding resin composite and dentin, and partial cohesive failure in resin composite. (D) Partial adhesive failure between the bonding resin and dentin, and partial cohesive failure in dentin and resin composite. (E) Cohesive failure in dentin. (F) Cohesive failure in resin composite.
Table 6 – Comparison of the Microtensile test and FEA results predictions for the mean strength and standard deviations Microtensile bond tests
Stick Dumbbell Hourglass
FEA
Mean strength
Standard deviation
Weibull modulus
31.01 31.18 28.13
5.11 4.04 3.28
6.5 6.8 9.6
Mean strength 28 28.4 24.7
Standard deviation 5.7 5.2 4.6
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Table 8 – ANOVA analysis results for each two-sample geometries and for all the three types of samples Samples Stick–dumbbell Stick–hourglass Dumbbell–hourglass Stick–dumbbell–hourglass
SS
d.f.
MS
F
P-value
F critical
0.28 72.25 83.93 104.91
1 1 1 2
0.28 72.25 83.93 52.45
0.013 3.96 6.19 2.98
0.90 0.05 0.02 0.059
4.13 4.13 4.13 3.18
For each of the sample geometries, the number of samples within each mode of failure along with the percentage of the failures in that mode is calculated. At the same time mean value of the bond strength with certain mode of failure is obtained. The results of the percentage for each failure mode and relevant mean strengths are reported in Table 7. These results indicate that most of the samples fail within the adhesive layer. The second dominant mode of failure is failure in adhesive combined with fracture in dentin. Considering the brittle nature of the dentin and the complicated interaction of dentin and adhesive in order to achieve a good interphase, this is expected. The third mode of failure observed mostly is the failure in adhesive combined with the resin fracture. The other types of failures are less likely to occur. The results reported in Table 7 also indicate that for the stick and dumbbell samples modes B and C of failure occur at higher stress values compared to mode A which is pure adhesive failure. Whereas for the hourglass samples the failure stresses for modes A–C are very similar. In all the samples the mode F of failure in the dentin occurs at very low stress, indicating that this type of failure is only present when the sample has considerable damage or defect on the dentin side. Therefore, the results of this type of failure are not a true indication of the adhesive bond strength and they should not be considered in the evaluation of the bond strength. The bond strength values are analyzed using the statistical method one-way analysis of variance (ANOVA). The tests involved fracture of dentin (F mode) and resin (E mode) with low failure stresses are not included in this analysis. The result of the ANOVA analysis is shown in Table 8. The first three rows indicate the comparison of each two sample shape. The last row in the table shows the ANOVA analysis for the three sets. The ANOVA for stick and dumbbell shape samples indicates that the F-value is much smaller than the F critical and the P-value as well is larger than 0.05, indicating that the two sets are not statistically different and the null hypothesis cannot be rejected. Analysis for the hourglass with stick/dumbbell on the other hand shows F is higher or very close to the critical F- and the P-values are smaller or very close to 0.05. Therefore, significant difference exists between hourglass and the other two sample shapes and the null hypothesis can be rejected. ANOVA for the three sets indicates that F is fairly close to F critical and P is close to 0.05 showing that the three sets are not similar. The result of the ANOVA once again confirms the outcomes of the FE analysis in classification of the samples on the basis of their geometries.
4.
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Conclusions (9)
(1) The stress concentration and distribution inside the stick and dumbbell samples are very similar in the straight
region of the samples. There are some stress concentration areas at the curved parts of the sample which occur in the composite and dentin sections. If the samples were free from flaws it was expected that the two shapes offer the same failure stresses. However, since the dumbbell samples involve shaping of the curved and dumbbell parts there will be increased risk of inducing flaws in the areas to be shaped which might increase the risk of failure in this regions. The stress concentration and pattern in the hourglass sample is very different from the dumbbell and stick sample. It is expected that the hourglass sample fail at lower stress compared to the other two samples, since the stresses induced in the adhesive is larger for the hourglass sample. The hourglass sample is more sensitive to the flaws induced in the sample at the edge during shaping process compared to dumbbell sample. The thickness of the adhesive and the even distribution of the adhesive affect the stress concentration level and the bond strength. However the effect of misalignment of the sample in the tensile machine is much more significant in the strength values predicted. The modulus of the adhesive affects the differences between the hourglass and dumbbell–stick samples in the bond strength values. As the modulus of the adhesive is increased the differences between the maximum stresses in the adhesive for the hourglass and other two stick and dumbbell shape samples increases. Apart from the inherent differences between the stress distributions that different sample shapes offer which can affect the bond strength measured, the manufacturing of the samples in some cases is more prune to inducing flaws at the edges of the sample. The flaws induced during manufacturing are specifically important in the hourglass sample. Finite element analysis is capable of quantifying the effect of each parameter on the bond strength. The prediction of FEA is in agreement with the experimental results in relative bond strength in three different geometries. Experimental results confirm the FE analysis results in ranking of the sample geometries in the bond strengths with the hourglass sample showing the lowest bond strength and almost similar results for the dumbbell and stick geometries. Standard deviations calculated on the basis of the experimental results confirm the FE prediction for these values, indicating the highest standard deviation for stick geometry and dumbbell and hourglass in next orders. Most of the samples for all three geometries fail either in the simple or combined adhesive failure modes. The dentin or resin fracture results in very low failure stresses
d e n t a l m a t e r i a l s 2 4 ( 2 0 0 8 ) 536–547
indicating these types of failure only can be present in seriously damaged samples that need to be omitted from final estimation of the bond strengths. In stick and dumbbell samples combined adhesive failures are accompanied with higher stress values compared to the simple adhesive failure. These differences are not present between the stresses of the combined and simple adhesive modes of failure in the hourglass samples. (10) ANOVA analysis shows that the hourglass sample results are significantly different from the dumbbell and stick samples statistically. For the dumbbell and stick samples on the other hand the null hypothesis cannot be rejected. These once again confirm FE predictions in grouping the three geometries.
Acknowledgements The author would like to thank Mr. Z. Ou for performing the microtensile tests, Kerr Company for providing the adhesive and composite materials for the tests and Professor Van Noort and Ms. Betamer from dental school of University of Sheffield for providing dentin materials, facilities and assistance in shaping the samples.
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