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The Influence of Specimen Attachment and Dimension on Microtensile Strength

¹ Department of Dental Materials Science and
² Department of Functional Anatomy, Academic Center for Dentistry Amsterdam (ACTA), Louwesweg 1, 1066 EA Amsterdam, the Netherlands;

^* corresponding author, a.degee{at}acta.nl

	ABSTRACT

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The higher microtensile bond strength values found for specimens with a smaller cross-sectional area are often explained by the lower occurrence of internal defects and surface flaws. We hypothesized that this aberrant behavior is mainly caused by the lateral way of attachment of the specimens to the testing device, which makes the strength dependent on the thickness. This study showed that composite bars of 1x1x10, 1x2x10, and 1x3x10mm attached at their 1-mm-wide side (situation A) fractured at loads of the same magnitude, as a result of which the microtensile strength (µTS), calculated as F/A (force at fracture/cross-sectional area), significantly increased for specimens with decreasing thickness. Attachment at the 1-, 2-, or 3-mm-wide side (situation B) resulted in equal µTS values (P > 0.05). Finite element analysis showed different stress patterns for situation A, but comparable patterns for situation B. Both situations showed the same maximum stress at fracture.

KEY WORDS: finite element analysis • microtensile bond strength • microtensile strength • composite

	INTRODUCTION

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The bond strengths of restorative materials to dental hard tissues is usually reported as the load at failure divided by the cross-sectional area of the bonded interface (F/A). Strength values calculated in this way are referred to as the "nominal strength" values, but this is valid only if the applied load is equally distributed throughout the entire bonded interface. Therefore, a crucial factor in evaluation of the usefulness of a specific bond strength test is a thorough awareness of the stress patterns involved in bond failure.

Finite element analysis (FEA) studies have demonstrated that the manner in which loads are generally applied in shear test or tensile bond strength tests results in non-uniform stress patterns (Van Noort et al., 1989). With shear loading, severe stress concentrations arise near the loading site (DeHoff et al., 1995), as well as tensile stresses caused by a bending moment (Shiau et al., 1993). With the tensile bond strength test, where specimens are pulled away from a larger flat surface, there are pronounced stress concentrations at the periphery of the interface, due to the change in the geometry and material properties of the materials bonded together (Van Noort et al., 1989). These stress concentrations could explain the frequent cohesive failures within the substrate and the discrepancy between the actual nominal strength of the substrate and the apparent low stress measured (Øilo and Austrheim, 1993; Holtan et al., 1994; Versluis et al., 1997). Stress inhomogeneities due to geometry differences can be reduced significantly by bonding two-rod specimens of uniform cross-section together and by pulling them at the top and bottom surfaces (Della Bona and van Noort, 1995). The specimens used in the microtensile bond strength test (µTBS test) (Sano et al., 1994) have a uniform geometry at the bonding interface as well, but the tensile load in most investigations is not applied at top and bottom surfaces. Rectangular bar-shaped specimens are commonly attached by being stuck to by one of their flat lateral sides to the test set-up. Hourglass-shaped specimens, with either a cylindrical or a rectangular bonding area (Phrukkanon et al., 1998), are mounted by means of specially designed holders enclosing the specimens.

Some of these studies showed an inverse relationship between the µTBS and specimen size (Sano et al., 1994), and the higher values found for specimens with a smaller cross-sectional area were explained by a lower occurrence of internal defects and surface flaws. However, until now, the aspect of lateral attachment, as a possible cause for the inverse relationship, has not been taken into consideration. We hypothesized that this inverse relationship is mainly caused by the lateral way of attachment to the testing device, which makes the strength dependent on the thickness of the specimens. We tested the hypothesis by determining the microtensile strength (µTS) of rectangular composite bars by varying the width and thickness at the attachment site and using FEA to determine the stress patterns involved.

	MATERIALS & METHODS

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Specimen Preparation
Composite (Synergy, Coltène, Altstätten, Switzerland) was incrementally built-up in layers to produce blocks of approximately 15x10x10 mm. Each layer was light-cured for 40 sec by means of the Optilux 501 (Kerr, Danbury, CT, USA) at 700 mW/cm². Three blocks were prepared and stored in distilled water at 37°C for 1 day and subsequently cut into 7 slabs of 1 mm thickness by means of a low-speed water-cooled saw (Buehler Isomet 1000, Buehler Ltd., Lake Bluff, IL, USA). Each block was then rotated 90° (± 1°) and again sliced, but now at 3 different widths of 1, 2, and 3 mm. The bars were cut at a length of 10 mm to obtain 7 microbars of 1x1, 7 of 1x2, and 7 of 1x3 mm per block. Three or four microbars of each size were randomly collected from each cut block to a total of 10 microbars to make a group. Five groups were formed, one group with 1x1 microbars, 2 groups with 1x2 microbars, and two groups with 1x3 microbars.

Microtensile Strength Test
The µTS of the bars was determined in a universal testing machine (Instron, High Wycombe, Bucks, UK) at a crosshead speed of 1 mm/min. The specimens were attached with their lateral sides to the test set-up (Fig. 1) with a dental adhesive (Clearfil SE Bond, Kuraray Co., Osaka, Japan). We calculated the µTS of each composite bar by dividing the force at failure by its cross-sectional area. Due to the design of the test set-up, the force at failure was 80% of the measured force, since the latter was applied not directly along the axis of the microbar, but at a distance of 80% from the hinge (see Fig. 1). Two situations were evaluated. The first situation included groups with bars of 1x1x10, 1x2x10, and 1x3x10 mm, which were attached at their 1-mm-wide side, and the second included groups where the bars were attached at their 1-, 2-, or 3-mm-wide side. The 1x1 bars in the two situations were the same (Fig. 2).

View larger version (26K): [in this window] [in a new window]   Figure 1. Schematic illustration of the stainless steel testing device (left, 3D front view; right, rear view) showing lateral attachment of a 1x1x10 mm microbar with the middle 2 mm left free. The upside-down U-shaped part A encloses an exactly (frictionless) fitting bar B, which is connected to A through a 0.35-mm-thick brass sheet glued at the back side of A and B (see rear view). The brass sheet allows hinge movement of B when force (F) is applied to B via a rod and ball. The pitch distance from the ball to the hinge is 80% of the distance from the specimen to the hinge, and to obtain the forces exerted on the specimen, the measured forces had to be multiplied by a value of 0.80.

View larger version (16K): [in this window] [in a new window]   Figure 2. The five different ways of attaching the composite bars to the testing device. The upper and lower black surfaces indicate the sites that were bonded, each occupying 4 mm in length. The gauge length (middle) was 2 mm.

Finite Element Analysis (FEA)
To reveal the stress distribution in the composite bars, we carried out an FEA with FEMAP 8.10 (ESP, Maryland Heights, MO, USA) and CAEFEM 7.3 (CAC, West Hills, CA, USA). Three-dimensional models were created according to the different specimen dimensions as tested in the µTS test. The models were 10 mm long with cross-sectional areas of 1, 2, and 3 mm². In accordance with the way the specimens were attached to the test set-up, the stationary and moving parts of the stainless steel test set-up were at the lateral sides of the models, each occupying 4 mm of the length, with the middle 2 mm left free. The nodes of the lateral sides of the stainless steel parts of 1-mm thickness were fixed for the upper part (no translation or rotation in any direction) and pinned for the lower part (no translation in the X and Y directions, cross-sectional plane). The models with cross-sectional areas of 1, 2, and 3 mm² were composed of 2250, 3500, and 4750 elements, respectively. The elements, all equal in size, were solid brick elements with mid-side nodes that matched well to the three-dimensional analysis. Material properties were assumed to be isotropic, homogenous, and linear-elastic, and the attachment of the specimen to the stainless steel test set-up was assumed to be rigid. Typical values for the Young’s modulus and Poisson’s ratio of 16.6 GPa and 0.24, respectively, for the resin composite (Craig and Powers, 2002) and 190 GPa and 0.34 for the stainless steel (Shigley, 1980) were used in the FEA. For each model, the loads that were applied at the nodes at the lateral side of the lower stainless steel part were the corresponding loads at fracture (Table). As a control, an additional three-dimensional case for 1x1, 1x2, and 1x3 mm composite bars was run for attachments at the top and bottom surfaces, instead of at the lateral surface. The loads that were applied were those as found in the µTS test: 44.3 N for the 1x1 bars, 55.4 N and 77.4 N for the 1x2 bars, and 57.0 and 109.5 N for the 1x3 bars (Fig. 3).

View larger version (34K): [in this window] [in a new window]   Figure 3. Stress patterns in the middle 4 mm for the models with lateral attachment (models in top row) and top and bottom attachment (models in bottom row). For each of the models, the applied loads were the loads at fracture (Table). These loads were also applied for top and bottom attachment (bottom-row models). For lateral attachment, maximum major principle stresses were localized at approximately 0.2 mm from the fixed sites and were 70.8, 64.2, 56.0, 62.2, and 65.0 MPa (upper row from left to right). For top and bottom attachment, the major principle stresses were 44.3, 27.7, 19.0, 38.7, and 36.5 MPa (bottom row from left to right). The triangles and arrows indicate the stationary and moving sides of the models, respectively.

	RESULTS

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For attachments where the specimens had a constant width of 1 mm at the attachment site, but a variable thickness of 1, 2, or 3 mm, the µTS significantly decreased (P < 0.05). There was no difference among the groups (P > 0.05) when the attachment widths were varied (1, 2, and 3 mm) and the thickness was kept constant at 1 mm (Table).

The FEA models showed that stresses were localized at approximately 0.2 mm from the fixed sites, with an average value of the maximum major principle stress of approximately 64 MPa, and progressively decreased toward the opposite free surface to reach 32, 15, and 8 MPa for the 1x1, 1x2, and 1x3 bars attached at their 1-mm-wide side. The stress distribution patterns for bars attached at their 2- and 3-mm-wide sides were nearly identical to those of the 1x1 bars (Fig. 3).

The FEA for all groups with Young’s moduli of 5 and 120 GPa and a Poisson ratio of 0.24, and a Young’s modulus of 16.6 GPa and a Poisson ratio of 0.40 showed maximum stresses with values of 66, 56, and 67 MPa, respectively. The stress distribution patterns of these groups were not different from those found with material having a Young’s modulus of 16.6 GPa and a Poisson ratio of 0.24.

For the control groups, where the attachment was at the top and bottom of the bars, the stress distribution patterns were uniform for all models and nearly equal to the stresses induced by the applied loads (Fig. 3).

	DISCUSSION

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The results of this study demonstrated a clear dependence of µTS on the thickness of rectangular composite bars. The thinner the specimens became, the higher were the values for the µTS (Table). This inverse relationship arises since the loads at fracture for the 1x1, 1x2, and 1x3 bars attached at their 1-mm-wide side (Table) were of the same magnitude, while the cross-sectional area decreased (3 mm² 2 mm² 1 mm²); therefore, the µTS (F/A = fracture load/cross-sectional area) becomes higher. The rationale for this inverse relationship between the µTS and thickness can be obtained from the FEA models. These showed that, with lateral attachment, the resultant stresses were not uniformly distributed, and that stress concentration near the points of specimen fixation to the test set-up occurred with approximately the same magnitude (Fig. 3); the pattern of stress distribution improved when the thickness of the specimens decreased, i.e., when the distance between load path and free opposite surface became less eccentric. Increasing the width of specimen fixation with keeping the thickness constant at 1 mm had almost no effect on the stress distribution patterns. These stress patterns were quite similar to those of the 1x1 bars, and as a result the µTS of the specimens were similar.

The sensitivity of the µTS to changes in specimen thickness when specimens are attached at a lateral side to the test set-up will also be encountered with the microtensile bond strength (µTBS). Indeed, a similar dependence was found for the µTBS with hourglass-shaped specimens that were attached at the lateral side (Sano et al., 1994), and with cylindrical and rectangular hourglass-shaped specimens that were mounted in specially designed holders that provided the support and load application positioned at the shoulders of the hourglass (Phrukkanon et al., 1998). The lower maximum principle stress in specimens with the smallest cross-sectional area, as found in the latter study, is not contradictory to the present study, where, for these specimens, this stress was the highest. It should be noted that, in the FEA of the latter study, loads were applied that produced an average tensile stress which was the same (20 MPa) for all sizes of specimens. In the present study, the fracture loads were applied to the models to produce average tensile stresses which corresponded to the average µTS for each of the five groups.

The most effective way to avoid inhomogeneous stress distributions is by applying the loads and the support at the top and bottom surfaces of the specimens (Van Noort et al., 1989). The FEA results of the control models where this was done showed, for all models (1x1, 1x2, and 1x3 mm), that the generated stresses were uniform and equal to the applied stresses without any stress concentrations (Fig. 3). Yet an inverse relationship between strength and specimen size can exist as a result of differences in the quantity of flaws, which will be greater in number for specimens with a larger cross-section (Sano et al., 1994). The role of flaws could explain the differences in strength found between the 1, 2, and 3 mm² composite bars when the thickness was kept constant at 1 mm. Although the differences were not significant, the bars with larger cross-sectional areas tended to decrease in strength.

Important considerations in using a particular microtensile testing set-up are the ease of handling in producing the specimens and how they are attached. However, in the existing test set-ups, inhomogeneous stress distributions will always occur due to the way of mounting or attaching the specimens. Only with top and bottom attachment can stress concentrations be minimized or eliminated (Fig. 3). This way of attachment may be feasible for the hourglass-shaped specimens, but not for the straight bars, since they do not offer sufficient surface for adhesion to the test set-up to withstand the tensile forces applied during the test. The best option for straight bars for both the µTS and µTBS tests is still to attach them at their lateral side to the test set-up with the smallest possible thickness, since this brings the free opposite surface closer to the path of load application, which would contribute to further leveling of the stresses. The smallest dimension in thickness is limited by the cutting procedure, which should not cause premature fractures.

Although an inverse relationship between tensile strength and cross-sectional area was observed in the studies mentioned earlier (Sano et al., 1994; Phrukkanon et al., 1998), the present study has demonstrated that this is caused by lateral load application to the micro-specimens, and we are now able to better understand "the phenomenon of inverse relationship". The hypothesis that the µTS is dependent on the thickness of the specimens when the attachment is at the sides of the specimens was therefore accepted. In addition, the FEA results showed that, most probably, a wide range of materials is equally sensitive to these mounting conditions, although further tests are required for a sound proof.

	ACKNOWLEDGMENTS

 
This study was supported by the IOT, Research Foundation of the University of Amsterdam. The authors gratefully acknowledge Coltène, Inc. for supplying the composite used in this study.

Received April 29, 2003; Last revision February 27, 2004; Accepted March 2, 2004

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