d e n t a l m a t e r i a l s 3 1 ( 2 0 1 5 ) 807–813
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Investigating failure behavior and origins under supposed “shear bond” loading Hassam Sultan, J. Robert Kelly ∗ , Reza B. Kazemi School of Dental Medicine University of Connecticut Health Center, 263 Farmington Avenue, Farmington, CT 06030-1615, United States
a r t i c l e
i n f o
a b s t r a c t
Article history:
Purpose. This study evaluated failure behavior when resin-composite cylinders bonded to
Received 15 January 2015
dentin fractured under traditional “shear” testing. Failure was assessed by scaling of failure
Received in revised form
loads to changes in cylinder radii and fracture surface analysis. Three stress models were
17 March 2015
examined including failure by: bonded area; flat-on-cylinder contact; and, uniformly-loaded,
Accepted 13 April 2015
cantilevered-beam. Methods. Nine 2-mm dentin occlusal dentin discs for each radii tested were embedded in resin and bonded to resin-composite cylinders; radii (mm) = 0.79375; 1.5875; 2.38125; 3.175.
Keywords:
Samples were “shear” tested at 1.0 mm/min. Following testing, disks were finished with
Bond testing
silicone carbide paper (240–600 grit) to remove residual composite debris and tested again
Shear stress
using different radii. Failure stresses were calculated for: “shear”; flat-on-cylinder contact;
Dentin
and, bending of a uniformly-loaded cantilevered beam. Stress equations and constants were
Resin-based composite
evaluated for each model. Fracture-surface analysis was performed. Results. Failure stresses calculated as flat-on-cylinder contact scaled best with its radii relationship. Stress equation constants were constant for failure from the outside surface of the loaded cylinders and not with the bonded surface area or cantilevered beam. Contact failure stresses were constant over all specimen sizes. Fractography reinforced that failures originated from loaded cylinder surface and were unrelated to the bonded surface area. Conclusions. “Shear bond” testing does not appear to test the bonded interface. Load/area “stress” calculations have no physical meaning. While failure is related to contact stresses, the mechanism(s) likely involve non-linear damage accumulation, which may only indirectly be influenced by the interface. © 2015 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Advancements in dental adhesive technology have greatly changed restorative dentistry. Bond strength testing is essential for the analysis of new products and understanding
∗
testing and clinical variables [1]. In spite of many advances in adhesive technology, the one area needing further research has been assessing the bonded interface [2]. Van Meerbeek et al. describe the various methods and techniques for measuring dentin bonding interfaces, with the macro-shear bond-strength test reported as being the most popular (26% of
Corresponding author. Tel.: +1 860 679 3747; fax: +1 860 679 1370. E-mail address: [email protected] (J.R. Kelly).
http://dx.doi.org/10.1016/j.dental.2015.04.007 0109-5641/© 2015 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
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d e n t a l m a t e r i a l s 3 1 ( 2 0 1 5 ) 807–813
scientific papers reporting on bond strength) [2]. In spite of the fact that the shear bond-strength tests are the most easy and fastest material testing technique to perform, current literature questions that the shear stress tests: (1) use a meaningless calculation, (2) the origination of most failures likely does not involve the interface, and (3) failures are more consistent from external surfaces in tension than interfacial surfaces in shear based from Weibull scaling analysis [3]. In his opinion piece on adhesive strength testing, Darvell rightly challenged that mode II (shear) failure cannot occur in practice [4]. He argues that stress gradients will invariably be induced due to such effects as the discontinuity in elastic moduli across the interface and levering. He predicts that stress concentrations and gradients should be expected no matter how the loading is accomplished and therefore a uniform shear stress field is very unlikely. Such opinion was validated when Braga et al. demonstrated through 3D finite element analysis (FEA) that the stress distributions upon loading were not uniformly distributed across the measured surface area and that tensile stresses exceeded shear (Fig. 1) [5]. Many others have questioned the use of the simplistic stress equation, load/area. Thus the calculation by this simple equation has long been understood to give false results as interfacial stresses are invariably nonuniform and not described by load/area [6–10]. As a result, shear test calculations should not be determined through the measured surface area, but rather focus should be on understanding the non-uniform stress distributions found upon failure and the real mechanism(s) of failure. Stress distribution diagrams, illustrated by Braga et al., at the dentin side of the dentin/composite interface displayed stresses close to the loading area than the whole surface area [5]. In addition, the tensile stresses where much higher than the shear stresses, implying tensile stresses are the more probable causes of failure in “shear” testing. This confirmed earlier work by DeHoff and Anusavice that stresses were quite concentrated and had no relationship to the simplistic “stress” calculated by dividing the load by the bonded area [11].
Besides the apparent fact that uniform shear stresses likely do not exist and cannot be achieved, is the reality that brittle and quasi-brittle materials do not fail by shear stresses but only in tension. Metals can fail due to yielding along lines of shear stresses and in fact the most widely used model for the yielding of metals are von Mises stresses, being a combination of shear stresses. Mode I opening, not Mode II (shear), is the only stress intensity of interest in analysis of brittle fracture. The purpose of this study was to evaluate a variety of stress states during “shear” bond testing. Failure from the bonded surface has been traditionally assumed. Failure from the loaded cylinder could be due to (1) contact stress in flat-oncylinder loading or (2) bending stresses in a cantilevered beam, uniformly loaded. Failure modes were assessed by examining scaling effects of failure loads relative to known changes in bonding surface area (by r2 ), resin cylinder surface area (r0.5 ) and for a uniformly-loaded cantilevered beam (r3 ). Contact stresses (flat-on-cylinder) would appear to validly represent loading with the device used which loads the entire 5 mm length of the composite cylinder with a flat piston. Should the cylinder beam bend slightly in compliance, this would then turn the stress state into a uniformly-supported beam in bending. This analysis was reinforced by fractography of the fracture surfaces to determine failure origin.
2.
Mathematical background
(A) For typical “shear stress” testing, bond strength () is assumed to follow this simplistic formula: =
L r2
(1)
(B) For flat-on-cylinder loading, contact stress () is given by [12] =
2L bl
with
√ b=K L
(2)
with b as the half contact width and K [which has units of length/load—so b has units of length (i.e., r)]=where L = load
l = cylinder length
K=
2 2 2 1 − v1 /E1 + 1 − v2 /E2 l (1/d1 ) + (1/d2 )
1/2
v1 and v2 = Poisson’s ratios E1 and E2 = elastic moduli In addition, Braga et al. demonstrated through 3D finite element analysis (FEA) that the stress distributions upon failure were not necessarily focused at the true interface [5]. Through failure mode data collected from 37 studies published between 2007 and 2009, Braga et al. reported cohesive or mixed failure modes in 40–70% of specimens [5]. This form of failures implies that the fracture paths never involved the interface, from beginning through final propagation. Fracture paths not involving the interface (i.e., “cohesive failure”) have been addressed by many, including van Noort et al. and Versluis et al. [7,8].
d1 and d2 = diameter of cylinder and flat (=∞) [so K ≈ 1/[l(1/2r)] (C) Treating the system as a uniformly loaded, cantilevered cylinder the highest bending stress is given by =
L × l2 2×Z
(3)
where l is the cylinder length, Z is the section modulus = 0.78·r3 . By evaluating the stress equations in r2 , r1/2 , r3 and load (L √ and L/L), and assuming that failure stress () is a constant
d e n t a l m a t e r i a l s 3 1 ( 2 0 1 5 ) 807–813
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Fig. 1 – Stress distributions (maximum tensile stress, -max, and maximum shear stress, -max) at the dentin side of the dentin/composite interface according to the type of shear loading. Left: 0.2 mm knife-edge chisel; center: 2 mm flat rod; right: wire loop. Load was applied at 0.2 mm from the bonded interface. Line A–B indicates the diameter of the bonding area. [4].
the following relationships are derived which should be constant over the four radii used: 1 r2 = = constant L ×
(4a)
√ 2 L 1/2 = r 1/2 L 2 × l 4/l 1 − v1 /E1 + 1 − v22 /E2
(4b)
L 2 × × 0.78 = = constant r3 l2
(4c)
3.2.
with Eq. (4a) assuming failure involving the bonded interface, Eq. (4b) assuming failure due to contact stress (flat-on-cylinder) and Eq. (4c) treating the system as a cantilevered beam (uniformly loaded).
3.
Materials and methods
3.1.
Tooth preparation
each diameter of the total-etch resin-composite system. These were re-used until all diameters had been tested nine times each–with each test having specimens of all diameters.
Non-carious extracted human molar teeth were stored in 0.3% sodium azide solution for a minimum of one week after which they were placed under running water for 60 min before being transferred to normal saline. The teeth were assessed under magnification (Orascoptic 2.5x, Loupes, Middleton, WI, USA), and teeth displaying radicular cracks, visible caries, or tooth structure anomalies were excluded from the study. All soft tissue and extrinsic deposits of the collected teeth were removed using a hand scaler. The occlusal enamel of the teeth were removed with a low-speed sectioning saw (Isomet Buehler Ltd, Lake Bluff, Illinois, USA) and copious amounts of water to achieve a flat occlusal dentin plane just 0.5–1.0 mm inside the dentin-enamel junction. Two millimeter thick dental disks from the occlusal dentin were prepared using the same technique. Disks with pulp horn exposures were discarded. The disks were also examined for any possible enamel islands left on the surface. The occlusal surface of the dentin disks were sanded down with 240–600-grit silicon carbide papers to eliminate the possible enamel islands and/or flatten the surface. Nine 2.0 ± 0.2 mm thick disks were fabricated for testing
Specimen preparation and testing
Transparent tape was utilized in covering one side of the Ultradent mold (Ultradent Products, South Jordan, UT, USA). Each disk was placed flat against the tape within the cylinder molds and stabilized. The dentin disks were mounted using cold-cure ethylene glycol dimethacrylate dibutyl phthalate (orthodontic) acrylic resin (Coltene Whaledent, Cuyahoga Falls, OH, USA) that was mixed (under manufacturer guidelines) and poured into each cylinder mold. After hardening, the transparent tape was removed and each cylinder was punched out from the panel. The occlusal surface of the dentin disks were sanded down with sandpapers. A six millimeter diameter area on the tooth disk surface was prepared as instructed by the adhesive system manufacturing protocol. Silicon tubes of 4 varying inner radii (radii = 0.8 mm; 1.6 mm; 2.4 mm; 3.3 mm) were utilized in molding the resin composite (FiltekTM Supreme Ultra A1 Enamel, 3 M ESPE, St. Paul, MN, USA) cylinders on the tooth disk surface (approximately 5-mm high). Once condensed into the tubes, the tooth surfaces were prepared for bonding (ExciTE DSC, dual cure, total etch, Ivoclar Vivadent) and resin composite was light cured 600 mW/cm2 at 1.0 mm distance for 40 s from each of four aspects (buccal, lingual, mesial, distal) and from top/occlusal direction. The silicon tubes were cut off the composite cylinders and the specimens were stored in saline for 1-week prior to testing. The samples were then shear tested at room temperature using an Ultratester testing machine (Ultradent Products, South Jordan, UT, USA) set to operate at a 1.0 mm/min crosshead speed until failure occurred. Peak failure loads were recorded for each respective composite cylinder diameter and compared, respectively to cylinder radius (r). Following shear testing, each dentin disk was sanded once more to remove any residual resin composite debris and tested again with a bonded resin composite cylinder of a different random diameter following the same
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d e n t a l m a t e r i a l s 3 1 ( 2 0 1 5 ) 807–813
Table 1 – Peak failure load data and distribution statistics. Radius (mm) Mean (N) SD (N) Coefficient of variation
0.8
1.6
2.4
3.2
58.8 12.0 0.20
136.0 62.2 0.46
192.6 73.1 0.40
256.0 136.8 0.53
Table 3 – Values for the “constant” from Eq. (4c) for the case of uniform loading of a cantilevered beam. These values are clearly not constant over the range of radii tested. Radius (mm) Mean (N) SD (N)
0.8
1.6
2.4
3.2
101.6 24.0
34.0 15.6
14.3 5.4
8.0 4.3
Table 4 – Contact stresses (flat-on-cylinder) calculated from mean failure loads and standard deviations. Implies that failure stress (strength) of specimens did not depend on size over the range tested. Radius (mm) Mean (N) SD (N)
0.8
1.6
2.4
3.2
147.8 71.9
171.0 115.7
166.2 102.4
165.9 121.3
Table 5 – Failure stresses calculated assuming that failure was due to bonded surface area stresses. Radius (mm) Mean (N) SD (N)
Fig. 2 – Failure load/load1/2 scaled linearly with r0.5 as radii increased (as expected per Eq. (4b)).
bonding protocol. The fractured resin composite cylinders were saved for SEM Analysis and Microscope (Leica M205 C Stereo Microscope) images taken to qualitatively assess the origin of failure and direction of crack propagation.
4.
Results
4.1.
Peak fracture Loads
Peak failure loads and standard deviations are listed in Table 1. Failure involving the surface area of flat-loaded composite cylinder (contact stress) clearly scaled linearly with (radius)0.5 (r2 = 0.99, p = 0.005) (Fig. 2). This expression used in Fig. 2 was fit using Table Curve 2D (Systat Software, Richmond, CA) with: a = 5709.804; b = 8022.9726. Fig. 3a and b demonstrate the much better non-linear fit with r2 than the linear fit expected with L/r2 . Similarly to the analysis for r2 , the relationship for failure load to r3 should be linear if failure stresses were associated with uniform loading of a cantilevered beam, and this is not the case, as seen in Table 2. Stress equation “constants” were not constant over all values of radius (bonded surface area) as radius increased, as
0.8
1.6
2.4
3.2
273.7 48.5
549.8 251.0
778.6 295.5
1034.9 553.0
would be expected from Eq. (4a). However, stress equation relationships were constant as radius increased, with respect to flat-on-cylinder loading as per Eq. (4b) (Fig. 4). Table 3 presents calculated “constants” from Eq. (4c) for the case of a uniformly loaded, cantilevered beam in bending. These values are clearly not at all constant over the range of radii tested. Table 4 presents the calculated mean contact stresses (flaton-cylinder) as a function of cylinder radii (Eq. (2)). These breaking stresses are mid-way between compressive and tensile stresses of a hybrid resin-based composite [8]. Stresses are flat with respect to cylinder radius and little or no scaling with decreasing radius. Table 5 presents the failure stresses calculated for each cylinder radii assuming the mechanisms involves bonded surface area stess. Not only is there an extremely wide spread in failure stresses, such “strengths” are not consistent with either resin-based composites or dentin. Table 6 presents the failure stresses calculated for each cylinder radii assuming the mechanisms involves bending of a uniformly loaded cylindrical beam. Again, there is an extremely wide spread in failure stresses, such “strengths” are not consistent with either resin-based composites or dentin. Fig. 5 displays SEM view of a fracture surface (composite cylinder) indicating failure origin was from outside surface of resin beneath loading point.
Table 2 – For failure by uniform loading of a cantilevered beam the relationship between failure load and r3 should be linear. This was not found to be the case.
Table 6 – Failure stresses calculated assuming that failure was due to bending of a uniformly loaded cantilevered beam.
Radius3 (mm3 )
0.5
4.0
13.5
32.0
Radius (mm)
Mean (N) SD (N)
52.0 12.0
136.0 62.2
192.6 73.1
256.0 136.8
Mean (N) SD (N)
0.8
1.6
2.4
3.2
1628.0 384.5
544.8 249.2
228.6 86.8
128.2 68.5
d e n t a l m a t e r i a l s 3 1 ( 2 0 1 5 ) 807–813
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Fig. 3 – While failure loads do scale well linearly with r2 as radii increased ((a) left) the relationship is not as convincing as the much better non-linear fit ((b) right).
5.
Discussion
Peak failure loads did increase significantly with increased radii of the loaded cylinders. So the question becomes whether these scaled with the surface area of the loaded cylinder, with the increased bonded area, or in keeping with stresses in a cantilevered beam. One key assumption of this work was that the “strength” of the system was constant, i.e. neither bonding strength nor surface failure strength changed. The linear fit was quite good for failure due to flat-on-cylinder loading contact stresses and highly non-linear for stresses due to uniform loading of a cantilevered beam. This analysis appears to eliminate the system acting as a uniformly loaded cantilevered beam and favoring failure due to contact stresses
(flat-on-cylinder), but not eliminating failure involving the bonded interface. High incidences of cohesive failures reported by gross examination (approx. 45%) alone leads to results of shear tests being highly questionable as an interfacial test [5]. Most convincingly if shear tests measured failure involving the bonded surface area, the experimental values for the stress equation constant would have remained constant relative to Eq. (4a). That the stress equation for bonded area is not constant with increase in radius indicates that “shear bond” testing in fact does not appear to involve failure from the bonded interface. In contrast for contact stresses by flat-on-cylinder surface area loading: (1) the stress equation was constant over r (Eq. (3b)) in Fig. 4; (2) failure loads/loads1/2 scaled linearly with r1/2 (Fig. 2); (3) calculated contact stresses (flat-on-sphere) were
Fig. 4 – Stress equation relationships (“constants”) evaluated for cylinder surface and bonded surface areas. Relationship is not constant as r increases for bonded surface area.
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d e n t a l m a t e r i a l s 3 1 ( 2 0 1 5 ) 807–813
Fig. 5 – Representative SEM view of fracture surface (composite cylinder) indicating failure origin was from outside surface of resin beneath loading point. Arrows indicate “presumed” crack path (more analysis is provided in Section 5).
constant over all four specimen sizes (Table 5); and, (4) fracture surface analysis was consistent for failure involving flat-oncylinder contact stresses (as discussed below). In addition, calculated failure stresses were constant over r only for flaton-cylinder contact stresses (Table 4 versus Tables 5 and 6). Fracture surface analysis was not at all straightforward or conclusive. Our most telling image (Fig. 5) is not sufficiently definitive to establish a failure origin; i.e. no wake hackle or arrest lines and potential but not conclusive twist hackle—but failure did occur from the loaded surface and can reasonably be presumed to have taken the direction indicated in Fig. 5. One interesting feature seen in Fig. 5 is the apparent initial crack direction being at approximately 45◦ to the loaded surface before turning and running parallel with the bonded surface. One explanation for this would be that failure arose from Hertzian contact stresses resulting in a partial cone crack. This might be accentuated if slight beam compliance led to edge-loading by the flat piston. Another explanation is examined below. Also unique is that the surface around the presumed origin is much rougher than the subsequent fracture surface. Neither of these observations is usual for purely brittle fracture where (1) fracture occurs perpendicular to the principle tensile field and (2) the surface near the origin is usually rather smooth compared to later surfaces where increasing roughness is due to increasing crack tip energy. One feature just to the right of the right arrow in Fig. 5 might be interpreted as a “lance”, mentioned by Gopalakrishnan and Mecholsky as a twist hackle unique to mixed-mode failure [14]. While loading in this work clearly induced failure from the outside cylinder surface, the meaning of the calculated contact stresses remains murky—and this may not be the actual failure stress. As already mentioned, the calculated failure stress fell midway between literature values of tensile and compressive strengths [13]. While the testing started with 5 mm of flat steel contact against the composite cylinder, slight bending of the bonded cylinder could have occurred leading to edge loading. Edge loading would have created much higher
stresses than we calculated, perhaps as high as presumably created with knife edge or wire loop loading. This could drop the failure stresses down into the typical range for tensile failure of resin-based composites. An alternative explanation is given below involving a combination of compressive and tensile stresses. One very problematic feature that this proposed origin hypothesis is that it seemingly ignores results from studies where clear differences were found when the substrate was given different surface treatments. While these studies likely assume and calculate the wrong stresses, how can bonded surface differences be reconciled with our finding that failure is likely from surface contact stresses? The answer may lie in the nature of the stress state being a mixture of compressive and tensile stresses with: (1) damage accumulation occurring within a band of material; (2) strain softening occurring within this band; and, (3) final failure involving a coalescence of accumulated crack systems. Thus failure would not be explained by linear elastic fracture mechanics and fracture surface features would not match those expected from purely KI events. Such a model was examined by Swain’s group [15] based upon the fundamental mathematical analyses and experimental verifications of Klerck et al. [16]. Under strongly combined compressive-tensile loading, damage accumulation initially involves microcracks that develop in the direction of dilation parallel to the maximum compressive stress. These then propagate orthogonal to the maximum extensional strain generally coinciding with the direction of maximum applied compressive stress, leading to a series of parallel microcracks separated by material linkages. Mechanical instability develops with formation of a macroscopic fracture plane from the coalescence and complex interaction of microcracks. Final failure involves, “. . .rupture of material linkages and mobilization of the macroscopic failure plane” (Klerck et al., 2004) [16]. Thus failure involves highly non-linear processes under a mixed compressive-tensile stress state and cannot be completely modeled by any of the simple analytical solutions examined in this paper. However, since these events are caused primarily under compressive loading they should scale with the contact stresses assumed in the flat-on-cylinder loading model. Such mixed-mode failure is consistent with the fracture surface analysis and Fig. 5 [15]. Should the band of material experiencing damage accumulation and strain softening be adjacent to the bonded interface, it is conceivable that the surface condition of the substrate may influence events. For example, substrate surface features which inhibit crack-opening displacements could inhibit the rate of microcrack formation and extension delaying their coalescence. In Fig. 5 the initial crack appears at a 45◦ angle to the loaded surface, reminiscent of shear failure in metals, and the surface is remarkably rougher than the remainder of the fracture surface consistent with a zone of accumulated damage. Both of these features are consistent with failure involving compressive stresses and the development of series of microcracks beneath the loaded surface. In addition, the interface represents a strong discontinuity in elastic properties that will also very likely influence the development of system of microcrack and associated material linkages and their direction with respect to the loaded surface.
d e n t a l m a t e r i a l s 3 1 ( 2 0 1 5 ) 807–813
Many aspects of this study were not “ideal”. Assumptions of uniform flat-on-cylinder loading ignore the very real possibility of slight cylinder displacement leading to punch edge loading. This analytical solution was not developed for the cylinder being bonded at one end. These same criticisms apply to the cantilevered beam model as well. Taken as a whole, however, all of the evidence supports failure arising from contact stresses involving the cylinder surface and not the bonded surface. Tests designed to provide insights into ultimate clinical behavior must be held to certain standards. Foremost such tests should replicate clinical failure behavior involving realistic loading, clinically equivalent stresses and failure involving the same flaws. It is also imperative that the physics of the test be understood and followed faithfully—versus being assumed on a simplistic level as has been the case with “shear bond” testing. It has been clear for years that the approach of simply dividing the failure loads by the surface area was ill-conceived. At best such a test may provide a simple screening tool for adhesion versus non-adhesion; it will never be quantitative. One traditional test that may have clinical validity is the micro-tensile test, so long as it involves a water challenge and is compared with clinical data of at least five years observation time [17]. In our lab we are close to finishing development of a test for dentin-composite testing based on the ISO 9693 Schwickerath test for metal-ceramic systems. This test is fundamentally sound as an interfacial fracture test, although the calculated stress is for crack initiation and not bond strength.
6.
Conclusion
Failure loads did not scale with the bonded surface area but did scale with the external surface area of the loaded cylinder. The stress constant expressions only held for cylinder surface area and not bonded surface area indicating the stress state at failure involved loading contact on a cylinder surface. “Shear bond” testing does not appear to directly test the bonded interface and results based on the assumption and calculation of load/bonded area should not be published. While our results did scale in many ways with the flat-on-cylinder contact stresses, the meaning of these stresses and their relationship to the actual mechanism(s) of failure remains unclear. One possibility is that failure involves strongly interacting compressive and tensile stresses causing damage accumulation involving oriented microcracks and material ligaments with final failures due to the coalescence of microcracks following a period of strain softening.
Acknowledgement The authors gratefully acknowledge the donation of resincomposites and bonding materials from 3M-ESPE.
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references
[1] Armstrong Steve, Geraldeli Saulo, Maia Rodrigo, Araújo Raposo Luís Henrique, Soares Carlos José, Yamagawa Junichiro. Adhesion to tooth structure: a critical review of “micro” bond strength test methods. Dent Mater 2010;26:E50–62. [2] Van Meerbeek B, Peumans M, Poitevin A, Mine A, Ende AV, Neves A, et al. Review: relationship between bond-strength tests and clinical outcomes. Dent Mater 2010;26: E101–21. [3] Kelly JR, Benetti P, Rungruanganunt P, Della Bona A. The slippery slope—critical perspectives on in vitro research methodologies. Dent Mater 2011;28(1):41–51. [4] Darvell BW. Adhesion strength testing—time to fail or a waste of time? J Adhes Sci Technol 2009;23:935–44. [5] Braga Roberto R, Meira Josete BC, Boaro Leticia C, Xavier Tathy A. Adhesion to tooth structure: a critical review of “macro” test methods. Dent Mater 2010;26: E38–49. [6] van Noort R, Cardew G, Howard I. A study of the interfacial stresses between the tooth tissues and the restorative materials in a restored tooth. J Dentistry 1988;16: 286–93. [7] van Noort R, Noroozi S, Howard IC, Cardew GE. A critique of bond strength measurements. J Dentistry 1989;17:61–76. [8] Versluis A, Tantbirojn D, Douglas WH. Why do shear bond tests pull out dentin? J Dent Res 1997;76(6):1298–307. [9] Sudsangiam S, van Noort R. Do dentine bond strength tests serve a useful purpose? J Adhes Dentistry 1999;1:57–67. [10] Tantbirojn D, Cheng YS, Versluis A, Hodges JS, Douglas WH. Nominal shear or fracture mechanics in the assessment of composite-dentin adhesion? J Dent Res 2000;79(1): 41–8. [11] Dehoff PH, Anusavice KJ, Wang Z. Three-dimensional finite element analysis of the shear bond test. Dent Mater 1995;11(2):126–31. [12] Shigley’s Mechanical Engineering Design. Tutorial 3-19: Hertz Contact Stresses. http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source= web&cd=2&ved=0CCQQFjAB&url=http%3A%2F%2Fhighered. mheducation.com%2Fsites%2Fdl%2Ffree%2F0073529281% 2F365764%2FCh03 Section19 Hertz Contact Stresses.pdf& ei=BMVHVb32LcHksATBn4DIAw&usg=AFQjCNGqNaQc9BFv Ck8T98- krZFjHP9Ig&bvm=bv.92291466,d.aWw [accessed 10.06.14]. [13] Anusavice KJ. Phillips’ science of dental materials. 10th ed Philadelphia, PA: Saunders; 1996. p. 285. [14] Gopalakrishnan K, Mecholsky JJ. Quantitative fractography of mixed-mode fracture in an R-curve material. J Mater Sci 2013;48:7081–7. [15] Ichin I, Li Q, Swain MV, Kieser J. Modelling of fracture behavior in biomaterials. Biomaterials 2007;28:1317–26. [16] Klerck PA, Sellers EJ, Owen DRJ. Discrete fracture in quasi-brittle materials under compressive and tensile stress states. Compt Meth Appl Mech Eng 2004;193:3035–56. [17] Van Meerbeek B, Peumans M, Poitevin A, et al. Relationship between bond-strength tests and clinical outcomes. Dent Mater 2010;26:e100–21.
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Investigating failure behavior and origins under supposed “shear bond” loading Hassam Sultan, J. Robert Kelly ∗ , Reza B. Kazemi School of Dental Medicine University of Connecticut Health Center, 263 Farmington Avenue, Farmington, CT 06030-1615, United States
a r t i c l e
i n f o
a b s t r a c t
Article history:
Purpose. This study evaluated failure behavior when resin-composite cylinders bonded to
Received 15 January 2015
dentin fractured under traditional “shear” testing. Failure was assessed by scaling of failure
Received in revised form
loads to changes in cylinder radii and fracture surface analysis. Three stress models were
17 March 2015
examined including failure by: bonded area; flat-on-cylinder contact; and, uniformly-loaded,
Accepted 13 April 2015
cantilevered-beam. Methods. Nine 2-mm dentin occlusal dentin discs for each radii tested were embedded in resin and bonded to resin-composite cylinders; radii (mm) = 0.79375; 1.5875; 2.38125; 3.175.
Keywords:
Samples were “shear” tested at 1.0 mm/min. Following testing, disks were finished with
Bond testing
silicone carbide paper (240–600 grit) to remove residual composite debris and tested again
Shear stress
using different radii. Failure stresses were calculated for: “shear”; flat-on-cylinder contact;
Dentin
and, bending of a uniformly-loaded cantilevered beam. Stress equations and constants were
Resin-based composite
evaluated for each model. Fracture-surface analysis was performed. Results. Failure stresses calculated as flat-on-cylinder contact scaled best with its radii relationship. Stress equation constants were constant for failure from the outside surface of the loaded cylinders and not with the bonded surface area or cantilevered beam. Contact failure stresses were constant over all specimen sizes. Fractography reinforced that failures originated from loaded cylinder surface and were unrelated to the bonded surface area. Conclusions. “Shear bond” testing does not appear to test the bonded interface. Load/area “stress” calculations have no physical meaning. While failure is related to contact stresses, the mechanism(s) likely involve non-linear damage accumulation, which may only indirectly be influenced by the interface. © 2015 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Advancements in dental adhesive technology have greatly changed restorative dentistry. Bond strength testing is essential for the analysis of new products and understanding
∗
testing and clinical variables [1]. In spite of many advances in adhesive technology, the one area needing further research has been assessing the bonded interface [2]. Van Meerbeek et al. describe the various methods and techniques for measuring dentin bonding interfaces, with the macro-shear bond-strength test reported as being the most popular (26% of
Corresponding author. Tel.: +1 860 679 3747; fax: +1 860 679 1370. E-mail address: [email protected] (J.R. Kelly).
http://dx.doi.org/10.1016/j.dental.2015.04.007 0109-5641/© 2015 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
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scientific papers reporting on bond strength) [2]. In spite of the fact that the shear bond-strength tests are the most easy and fastest material testing technique to perform, current literature questions that the shear stress tests: (1) use a meaningless calculation, (2) the origination of most failures likely does not involve the interface, and (3) failures are more consistent from external surfaces in tension than interfacial surfaces in shear based from Weibull scaling analysis [3]. In his opinion piece on adhesive strength testing, Darvell rightly challenged that mode II (shear) failure cannot occur in practice [4]. He argues that stress gradients will invariably be induced due to such effects as the discontinuity in elastic moduli across the interface and levering. He predicts that stress concentrations and gradients should be expected no matter how the loading is accomplished and therefore a uniform shear stress field is very unlikely. Such opinion was validated when Braga et al. demonstrated through 3D finite element analysis (FEA) that the stress distributions upon loading were not uniformly distributed across the measured surface area and that tensile stresses exceeded shear (Fig. 1) [5]. Many others have questioned the use of the simplistic stress equation, load/area. Thus the calculation by this simple equation has long been understood to give false results as interfacial stresses are invariably nonuniform and not described by load/area [6–10]. As a result, shear test calculations should not be determined through the measured surface area, but rather focus should be on understanding the non-uniform stress distributions found upon failure and the real mechanism(s) of failure. Stress distribution diagrams, illustrated by Braga et al., at the dentin side of the dentin/composite interface displayed stresses close to the loading area than the whole surface area [5]. In addition, the tensile stresses where much higher than the shear stresses, implying tensile stresses are the more probable causes of failure in “shear” testing. This confirmed earlier work by DeHoff and Anusavice that stresses were quite concentrated and had no relationship to the simplistic “stress” calculated by dividing the load by the bonded area [11].
Besides the apparent fact that uniform shear stresses likely do not exist and cannot be achieved, is the reality that brittle and quasi-brittle materials do not fail by shear stresses but only in tension. Metals can fail due to yielding along lines of shear stresses and in fact the most widely used model for the yielding of metals are von Mises stresses, being a combination of shear stresses. Mode I opening, not Mode II (shear), is the only stress intensity of interest in analysis of brittle fracture. The purpose of this study was to evaluate a variety of stress states during “shear” bond testing. Failure from the bonded surface has been traditionally assumed. Failure from the loaded cylinder could be due to (1) contact stress in flat-oncylinder loading or (2) bending stresses in a cantilevered beam, uniformly loaded. Failure modes were assessed by examining scaling effects of failure loads relative to known changes in bonding surface area (by r2 ), resin cylinder surface area (r0.5 ) and for a uniformly-loaded cantilevered beam (r3 ). Contact stresses (flat-on-cylinder) would appear to validly represent loading with the device used which loads the entire 5 mm length of the composite cylinder with a flat piston. Should the cylinder beam bend slightly in compliance, this would then turn the stress state into a uniformly-supported beam in bending. This analysis was reinforced by fractography of the fracture surfaces to determine failure origin.
2.
Mathematical background
(A) For typical “shear stress” testing, bond strength () is assumed to follow this simplistic formula: =
L r2
(1)
(B) For flat-on-cylinder loading, contact stress () is given by [12] =
2L bl
with
√ b=K L
(2)
with b as the half contact width and K [which has units of length/load—so b has units of length (i.e., r)]=where L = load
l = cylinder length
K=
2 2 2 1 − v1 /E1 + 1 − v2 /E2 l (1/d1 ) + (1/d2 )
1/2
v1 and v2 = Poisson’s ratios E1 and E2 = elastic moduli In addition, Braga et al. demonstrated through 3D finite element analysis (FEA) that the stress distributions upon failure were not necessarily focused at the true interface [5]. Through failure mode data collected from 37 studies published between 2007 and 2009, Braga et al. reported cohesive or mixed failure modes in 40–70% of specimens [5]. This form of failures implies that the fracture paths never involved the interface, from beginning through final propagation. Fracture paths not involving the interface (i.e., “cohesive failure”) have been addressed by many, including van Noort et al. and Versluis et al. [7,8].
d1 and d2 = diameter of cylinder and flat (=∞) [so K ≈ 1/[l(1/2r)] (C) Treating the system as a uniformly loaded, cantilevered cylinder the highest bending stress is given by =
L × l2 2×Z
(3)
where l is the cylinder length, Z is the section modulus = 0.78·r3 . By evaluating the stress equations in r2 , r1/2 , r3 and load (L √ and L/L), and assuming that failure stress () is a constant
d e n t a l m a t e r i a l s 3 1 ( 2 0 1 5 ) 807–813
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Fig. 1 – Stress distributions (maximum tensile stress, -max, and maximum shear stress, -max) at the dentin side of the dentin/composite interface according to the type of shear loading. Left: 0.2 mm knife-edge chisel; center: 2 mm flat rod; right: wire loop. Load was applied at 0.2 mm from the bonded interface. Line A–B indicates the diameter of the bonding area. [4].
the following relationships are derived which should be constant over the four radii used: 1 r2 = = constant L ×
(4a)
√ 2 L 1/2 = r 1/2 L 2 × l 4/l 1 − v1 /E1 + 1 − v22 /E2
(4b)
L 2 × × 0.78 = = constant r3 l2
(4c)
3.2.
with Eq. (4a) assuming failure involving the bonded interface, Eq. (4b) assuming failure due to contact stress (flat-on-cylinder) and Eq. (4c) treating the system as a cantilevered beam (uniformly loaded).
3.
Materials and methods
3.1.
Tooth preparation
each diameter of the total-etch resin-composite system. These were re-used until all diameters had been tested nine times each–with each test having specimens of all diameters.
Non-carious extracted human molar teeth were stored in 0.3% sodium azide solution for a minimum of one week after which they were placed under running water for 60 min before being transferred to normal saline. The teeth were assessed under magnification (Orascoptic 2.5x, Loupes, Middleton, WI, USA), and teeth displaying radicular cracks, visible caries, or tooth structure anomalies were excluded from the study. All soft tissue and extrinsic deposits of the collected teeth were removed using a hand scaler. The occlusal enamel of the teeth were removed with a low-speed sectioning saw (Isomet Buehler Ltd, Lake Bluff, Illinois, USA) and copious amounts of water to achieve a flat occlusal dentin plane just 0.5–1.0 mm inside the dentin-enamel junction. Two millimeter thick dental disks from the occlusal dentin were prepared using the same technique. Disks with pulp horn exposures were discarded. The disks were also examined for any possible enamel islands left on the surface. The occlusal surface of the dentin disks were sanded down with 240–600-grit silicon carbide papers to eliminate the possible enamel islands and/or flatten the surface. Nine 2.0 ± 0.2 mm thick disks were fabricated for testing
Specimen preparation and testing
Transparent tape was utilized in covering one side of the Ultradent mold (Ultradent Products, South Jordan, UT, USA). Each disk was placed flat against the tape within the cylinder molds and stabilized. The dentin disks were mounted using cold-cure ethylene glycol dimethacrylate dibutyl phthalate (orthodontic) acrylic resin (Coltene Whaledent, Cuyahoga Falls, OH, USA) that was mixed (under manufacturer guidelines) and poured into each cylinder mold. After hardening, the transparent tape was removed and each cylinder was punched out from the panel. The occlusal surface of the dentin disks were sanded down with sandpapers. A six millimeter diameter area on the tooth disk surface was prepared as instructed by the adhesive system manufacturing protocol. Silicon tubes of 4 varying inner radii (radii = 0.8 mm; 1.6 mm; 2.4 mm; 3.3 mm) were utilized in molding the resin composite (FiltekTM Supreme Ultra A1 Enamel, 3 M ESPE, St. Paul, MN, USA) cylinders on the tooth disk surface (approximately 5-mm high). Once condensed into the tubes, the tooth surfaces were prepared for bonding (ExciTE DSC, dual cure, total etch, Ivoclar Vivadent) and resin composite was light cured 600 mW/cm2 at 1.0 mm distance for 40 s from each of four aspects (buccal, lingual, mesial, distal) and from top/occlusal direction. The silicon tubes were cut off the composite cylinders and the specimens were stored in saline for 1-week prior to testing. The samples were then shear tested at room temperature using an Ultratester testing machine (Ultradent Products, South Jordan, UT, USA) set to operate at a 1.0 mm/min crosshead speed until failure occurred. Peak failure loads were recorded for each respective composite cylinder diameter and compared, respectively to cylinder radius (r). Following shear testing, each dentin disk was sanded once more to remove any residual resin composite debris and tested again with a bonded resin composite cylinder of a different random diameter following the same
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Table 1 – Peak failure load data and distribution statistics. Radius (mm) Mean (N) SD (N) Coefficient of variation
0.8
1.6
2.4
3.2
58.8 12.0 0.20
136.0 62.2 0.46
192.6 73.1 0.40
256.0 136.8 0.53
Table 3 – Values for the “constant” from Eq. (4c) for the case of uniform loading of a cantilevered beam. These values are clearly not constant over the range of radii tested. Radius (mm) Mean (N) SD (N)
0.8
1.6
2.4
3.2
101.6 24.0
34.0 15.6
14.3 5.4
8.0 4.3
Table 4 – Contact stresses (flat-on-cylinder) calculated from mean failure loads and standard deviations. Implies that failure stress (strength) of specimens did not depend on size over the range tested. Radius (mm) Mean (N) SD (N)
0.8
1.6
2.4
3.2
147.8 71.9
171.0 115.7
166.2 102.4
165.9 121.3
Table 5 – Failure stresses calculated assuming that failure was due to bonded surface area stresses. Radius (mm) Mean (N) SD (N)
Fig. 2 – Failure load/load1/2 scaled linearly with r0.5 as radii increased (as expected per Eq. (4b)).
bonding protocol. The fractured resin composite cylinders were saved for SEM Analysis and Microscope (Leica M205 C Stereo Microscope) images taken to qualitatively assess the origin of failure and direction of crack propagation.
4.
Results
4.1.
Peak fracture Loads
Peak failure loads and standard deviations are listed in Table 1. Failure involving the surface area of flat-loaded composite cylinder (contact stress) clearly scaled linearly with (radius)0.5 (r2 = 0.99, p = 0.005) (Fig. 2). This expression used in Fig. 2 was fit using Table Curve 2D (Systat Software, Richmond, CA) with: a = 5709.804; b = 8022.9726. Fig. 3a and b demonstrate the much better non-linear fit with r2 than the linear fit expected with L/r2 . Similarly to the analysis for r2 , the relationship for failure load to r3 should be linear if failure stresses were associated with uniform loading of a cantilevered beam, and this is not the case, as seen in Table 2. Stress equation “constants” were not constant over all values of radius (bonded surface area) as radius increased, as
0.8
1.6
2.4
3.2
273.7 48.5
549.8 251.0
778.6 295.5
1034.9 553.0
would be expected from Eq. (4a). However, stress equation relationships were constant as radius increased, with respect to flat-on-cylinder loading as per Eq. (4b) (Fig. 4). Table 3 presents calculated “constants” from Eq. (4c) for the case of a uniformly loaded, cantilevered beam in bending. These values are clearly not at all constant over the range of radii tested. Table 4 presents the calculated mean contact stresses (flaton-cylinder) as a function of cylinder radii (Eq. (2)). These breaking stresses are mid-way between compressive and tensile stresses of a hybrid resin-based composite [8]. Stresses are flat with respect to cylinder radius and little or no scaling with decreasing radius. Table 5 presents the failure stresses calculated for each cylinder radii assuming the mechanisms involves bonded surface area stess. Not only is there an extremely wide spread in failure stresses, such “strengths” are not consistent with either resin-based composites or dentin. Table 6 presents the failure stresses calculated for each cylinder radii assuming the mechanisms involves bending of a uniformly loaded cylindrical beam. Again, there is an extremely wide spread in failure stresses, such “strengths” are not consistent with either resin-based composites or dentin. Fig. 5 displays SEM view of a fracture surface (composite cylinder) indicating failure origin was from outside surface of resin beneath loading point.
Table 2 – For failure by uniform loading of a cantilevered beam the relationship between failure load and r3 should be linear. This was not found to be the case.
Table 6 – Failure stresses calculated assuming that failure was due to bending of a uniformly loaded cantilevered beam.
Radius3 (mm3 )
0.5
4.0
13.5
32.0
Radius (mm)
Mean (N) SD (N)
52.0 12.0
136.0 62.2
192.6 73.1
256.0 136.8
Mean (N) SD (N)
0.8
1.6
2.4
3.2
1628.0 384.5
544.8 249.2
228.6 86.8
128.2 68.5
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Fig. 3 – While failure loads do scale well linearly with r2 as radii increased ((a) left) the relationship is not as convincing as the much better non-linear fit ((b) right).
5.
Discussion
Peak failure loads did increase significantly with increased radii of the loaded cylinders. So the question becomes whether these scaled with the surface area of the loaded cylinder, with the increased bonded area, or in keeping with stresses in a cantilevered beam. One key assumption of this work was that the “strength” of the system was constant, i.e. neither bonding strength nor surface failure strength changed. The linear fit was quite good for failure due to flat-on-cylinder loading contact stresses and highly non-linear for stresses due to uniform loading of a cantilevered beam. This analysis appears to eliminate the system acting as a uniformly loaded cantilevered beam and favoring failure due to contact stresses
(flat-on-cylinder), but not eliminating failure involving the bonded interface. High incidences of cohesive failures reported by gross examination (approx. 45%) alone leads to results of shear tests being highly questionable as an interfacial test [5]. Most convincingly if shear tests measured failure involving the bonded surface area, the experimental values for the stress equation constant would have remained constant relative to Eq. (4a). That the stress equation for bonded area is not constant with increase in radius indicates that “shear bond” testing in fact does not appear to involve failure from the bonded interface. In contrast for contact stresses by flat-on-cylinder surface area loading: (1) the stress equation was constant over r (Eq. (3b)) in Fig. 4; (2) failure loads/loads1/2 scaled linearly with r1/2 (Fig. 2); (3) calculated contact stresses (flat-on-sphere) were
Fig. 4 – Stress equation relationships (“constants”) evaluated for cylinder surface and bonded surface areas. Relationship is not constant as r increases for bonded surface area.
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Fig. 5 – Representative SEM view of fracture surface (composite cylinder) indicating failure origin was from outside surface of resin beneath loading point. Arrows indicate “presumed” crack path (more analysis is provided in Section 5).
constant over all four specimen sizes (Table 5); and, (4) fracture surface analysis was consistent for failure involving flat-oncylinder contact stresses (as discussed below). In addition, calculated failure stresses were constant over r only for flaton-cylinder contact stresses (Table 4 versus Tables 5 and 6). Fracture surface analysis was not at all straightforward or conclusive. Our most telling image (Fig. 5) is not sufficiently definitive to establish a failure origin; i.e. no wake hackle or arrest lines and potential but not conclusive twist hackle—but failure did occur from the loaded surface and can reasonably be presumed to have taken the direction indicated in Fig. 5. One interesting feature seen in Fig. 5 is the apparent initial crack direction being at approximately 45◦ to the loaded surface before turning and running parallel with the bonded surface. One explanation for this would be that failure arose from Hertzian contact stresses resulting in a partial cone crack. This might be accentuated if slight beam compliance led to edge-loading by the flat piston. Another explanation is examined below. Also unique is that the surface around the presumed origin is much rougher than the subsequent fracture surface. Neither of these observations is usual for purely brittle fracture where (1) fracture occurs perpendicular to the principle tensile field and (2) the surface near the origin is usually rather smooth compared to later surfaces where increasing roughness is due to increasing crack tip energy. One feature just to the right of the right arrow in Fig. 5 might be interpreted as a “lance”, mentioned by Gopalakrishnan and Mecholsky as a twist hackle unique to mixed-mode failure [14]. While loading in this work clearly induced failure from the outside cylinder surface, the meaning of the calculated contact stresses remains murky—and this may not be the actual failure stress. As already mentioned, the calculated failure stress fell midway between literature values of tensile and compressive strengths [13]. While the testing started with 5 mm of flat steel contact against the composite cylinder, slight bending of the bonded cylinder could have occurred leading to edge loading. Edge loading would have created much higher
stresses than we calculated, perhaps as high as presumably created with knife edge or wire loop loading. This could drop the failure stresses down into the typical range for tensile failure of resin-based composites. An alternative explanation is given below involving a combination of compressive and tensile stresses. One very problematic feature that this proposed origin hypothesis is that it seemingly ignores results from studies where clear differences were found when the substrate was given different surface treatments. While these studies likely assume and calculate the wrong stresses, how can bonded surface differences be reconciled with our finding that failure is likely from surface contact stresses? The answer may lie in the nature of the stress state being a mixture of compressive and tensile stresses with: (1) damage accumulation occurring within a band of material; (2) strain softening occurring within this band; and, (3) final failure involving a coalescence of accumulated crack systems. Thus failure would not be explained by linear elastic fracture mechanics and fracture surface features would not match those expected from purely KI events. Such a model was examined by Swain’s group [15] based upon the fundamental mathematical analyses and experimental verifications of Klerck et al. [16]. Under strongly combined compressive-tensile loading, damage accumulation initially involves microcracks that develop in the direction of dilation parallel to the maximum compressive stress. These then propagate orthogonal to the maximum extensional strain generally coinciding with the direction of maximum applied compressive stress, leading to a series of parallel microcracks separated by material linkages. Mechanical instability develops with formation of a macroscopic fracture plane from the coalescence and complex interaction of microcracks. Final failure involves, “. . .rupture of material linkages and mobilization of the macroscopic failure plane” (Klerck et al., 2004) [16]. Thus failure involves highly non-linear processes under a mixed compressive-tensile stress state and cannot be completely modeled by any of the simple analytical solutions examined in this paper. However, since these events are caused primarily under compressive loading they should scale with the contact stresses assumed in the flat-on-cylinder loading model. Such mixed-mode failure is consistent with the fracture surface analysis and Fig. 5 [15]. Should the band of material experiencing damage accumulation and strain softening be adjacent to the bonded interface, it is conceivable that the surface condition of the substrate may influence events. For example, substrate surface features which inhibit crack-opening displacements could inhibit the rate of microcrack formation and extension delaying their coalescence. In Fig. 5 the initial crack appears at a 45◦ angle to the loaded surface, reminiscent of shear failure in metals, and the surface is remarkably rougher than the remainder of the fracture surface consistent with a zone of accumulated damage. Both of these features are consistent with failure involving compressive stresses and the development of series of microcracks beneath the loaded surface. In addition, the interface represents a strong discontinuity in elastic properties that will also very likely influence the development of system of microcrack and associated material linkages and their direction with respect to the loaded surface.
d e n t a l m a t e r i a l s 3 1 ( 2 0 1 5 ) 807–813
Many aspects of this study were not “ideal”. Assumptions of uniform flat-on-cylinder loading ignore the very real possibility of slight cylinder displacement leading to punch edge loading. This analytical solution was not developed for the cylinder being bonded at one end. These same criticisms apply to the cantilevered beam model as well. Taken as a whole, however, all of the evidence supports failure arising from contact stresses involving the cylinder surface and not the bonded surface. Tests designed to provide insights into ultimate clinical behavior must be held to certain standards. Foremost such tests should replicate clinical failure behavior involving realistic loading, clinically equivalent stresses and failure involving the same flaws. It is also imperative that the physics of the test be understood and followed faithfully—versus being assumed on a simplistic level as has been the case with “shear bond” testing. It has been clear for years that the approach of simply dividing the failure loads by the surface area was ill-conceived. At best such a test may provide a simple screening tool for adhesion versus non-adhesion; it will never be quantitative. One traditional test that may have clinical validity is the micro-tensile test, so long as it involves a water challenge and is compared with clinical data of at least five years observation time [17]. In our lab we are close to finishing development of a test for dentin-composite testing based on the ISO 9693 Schwickerath test for metal-ceramic systems. This test is fundamentally sound as an interfacial fracture test, although the calculated stress is for crack initiation and not bond strength.
6.
Conclusion
Failure loads did not scale with the bonded surface area but did scale with the external surface area of the loaded cylinder. The stress constant expressions only held for cylinder surface area and not bonded surface area indicating the stress state at failure involved loading contact on a cylinder surface. “Shear bond” testing does not appear to directly test the bonded interface and results based on the assumption and calculation of load/bonded area should not be published. While our results did scale in many ways with the flat-on-cylinder contact stresses, the meaning of these stresses and their relationship to the actual mechanism(s) of failure remains unclear. One possibility is that failure involves strongly interacting compressive and tensile stresses causing damage accumulation involving oriented microcracks and material ligaments with final failures due to the coalescence of microcracks following a period of strain softening.
Acknowledgement The authors gratefully acknowledge the donation of resincomposites and bonding materials from 3M-ESPE.
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