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Calculation of contraction stresses in dental composites by analysis of crack propagation in the matrix surrounding a cavity
d e n t a l m a t e r i a l s 2 5 ( 2 0 0 9 ) 543–550
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Calculation of contraction stresses in dental composites by analysis of crack propagation in the matrix surrounding a cavity Takatsugu Yamamoto a,∗ , Jack L. Ferracane b , Ronald L. Sakaguchi b , Michael V. Swain c a
Department of Operative Dentistry, Tsurumi University School of Dental Medicine, 2-1-3, Tsurumi, Tsurumi-ku, Yokohama, Kanagawa 230-8501, Japan b Division of Biomaterials and Biomechanics, Department of Restorative Dentistry, School of Dentistry, Oregon Health & Science University, 611 SW Campus Drive, Portland, OR 97239-3097, USA c Biomaterials Science Research Unit, Faculty of Dentistry, University of Sydney, Surry Hills, NSW 2010, Australia
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objectives. Polymerization contraction of dental composite produces a stress field in the
Received 3 October 2007
bonded surrounding substrate that may be capable of propagating cracks from pre-existing
Received in revised form
flaws. The objectives of this study were to assess the extent of crack propagation from
20 August 2008
flaws in the surrounding ceramic substrate caused by composite contraction stresses, and
Accepted 30 October 2008
to propose a method to calculate the contraction stress in the ceramic using indentation fracture. Methods. Initial cracks were introduced with a Vickers indenter near a cylindrical hole drilled
Keywords:
into a glass-ceramic simulating enamel. Lengths of the radial indentation cracks were mea-
Dental composite
sured. Three composites having different contraction stresses were cured within the hole
Ceramic
using one- or two-step light-activation methods and the crack lengths were measured. The
Indentation
contraction stress in the ceramic was calculated from the crack length and the fracture
Polymerization contraction stress
toughness of the glass-ceramic. Interfacial gaps between the composite and the ceramic were expressed as the ratio of the gap length to the hole perimeter, as well as the maximum gap width. Results. All groups revealed crack propagation and the formation of contraction gaps. The calculated contraction stresses ranged from 4.2 MPa to 7.0 MPa. There was no correlation between the stress values and the contraction gaps. Significance. This method for calculating the stresses produced by composites is a relatively simple technique requiring a conventional hardness tester. The method can investigate two clinical phenomena that may occur during the placement of composite restorations, i.e. simulated enamel cracking near the margins and the formation of contraction gaps. © 2008 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
∗
Corresponding author. Tel.: +81 45 581 1001x8550/8429; fax: +81 45 573 9599. E-mail address: [email protected] (T. Yamamoto). 0109-5641/$ – see front matter © 2008 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.dental.2008.10.008
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1.
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Introduction
Forces are generated by the polymerization contraction of bonded dental resin composite. These forces may result in stresses in three regions: (1) within the composite, (2) at the interface between the composite and the surrounding enamel and dentin, and (3) in the surrounding enamel and dentin. The stresses may induce several phenomena including deformation of the composite [1] and tooth [2–4], formation of contraction gaps [5–7], and cracking in the surrounding substrate [8,9]. The contraction stress may be one of the factors causing postoperative problems with composite restorations. When a pyramidal indenter, such as Vickers or Knoop, is loaded onto a brittle material, radial cracks initiate from the indentation corners [10–12]. The dimensions of the indentation and the cracks can be used to calculate fracture toughness [11,13–15]. Recently Quinn and Bradt [16] have argued that indentation is not an absolute measure of fracture toughness of a brittle material because of the poorly defined shape of the cracks developed. This is indeed the case and most authors associated with the development of the indentation technique have not stated that a K1c was measured, but that a very good correlation between traditional and indentation derived values of fracture toughness was achieved with an empirical modifying factor. The propagation of the radial cracks is sensitive to the stress distribution in the indented material [11,17–21]. Taskonak et al. reported a significant difference between lengths of two radial cracks running orthogonally when a Vickers indentation was imprinted in a ceramic having anisotropic stresses [21]. The direction of the radial cracks is also affected by the stress distribution. Radial cracks will curve based on their position within stress fields [12,22]. Utilizing the behavior of a pre-existing crack to stress, methods have been proposed for calculating residual stress in brittle materials using indentation fracture mechanics, i.e. the dimensions of the indentation and the cracks [17–19]. Cracks in brittle materials propagate through regions where tensile stresses are distributed [23–26], and extend further when additional remote tensile stress is applied and concentrated at the crack tip [26]. It is expected that an appropriately oriented pre-existing crack in a brittle material bonded to resin composite will propagate under the radial tensile stresses generated during composite curing contraction, and the additional length of the propagation will depend on the magnitude of the final tensile stress. If the contraction stress at a specific point in a substrate bonded to composite can be calculated from the propagation length, distributions of the stresses around the composite restoration can be quantified. Clinically, knowledge of the stress magnitude and distribution would aid composite material selection and restoration design. This could minimize postoperative discomfort and fracture of enamel induced by the contraction stress. The objectives of this study were (1) to assess crack propagation adjacent to a cavity in a brittle ceramic simulating enamel as a result of composite contraction stress, and (2) to propose a method to calculate the contraction stress in the ceramic using the increased dimensions of the indentation fracture. The hypothesis tested was that the contraction
stress generated during polymerization of a composite propagates cracks from existing flaws in a ceramic material that surrounds the composite in a consistent, predictable manner.
2.
Materials and methods
The ceramic material used in this study was a micaceous glass-ceramic (OCC, lot no. 48080, Olympus Optical Co., Tokyo, Japan) whose elastic modulus and glass transition temperature were reportedly 53 GPa and 550 ◦ C, respectively [27,28]. Fracture toughness of the ceramic was 1.08 MPa m0.5 measured with the indentation method (58.8 N-load for 15 s) in a preliminary study. The toughness was calculated using the following equation [19]: Kc = 0.026(EP)
1/2
d 2
−3/2
(c)
(1)
where E is the elastic modulus, P is the indentation load, d is the diagonal length of the indentation, and c is the length from the indentation center to the end of the crack. This material was chosen to simulate enamel and the toughness of the ceramic was within the range of values reported for human enamel [29,30]. An ingot of the ceramic was drilled through using a drill press to make a cylindrical hole of 2.5-mm-diameter. The drilled ceramic ingot was sliced into 2.1-mm-thick disks using a diamond saw (Accutom-5, Struers A/S, Rodovre, Denmark). The disks were essentially oval in shape with long and short axes ranging from 12.4 to 12.8 mm and from 10.5 to 12.2 mm, respectively. Fifteen disks were prepared and the top flat surface of each ceramic disk was serially wet-polished using various grit papers then finished with 1 m diamond paste. The bottom flat surface of each disk was wet-ground with 600grit SiC paper to adjust the disk thickness to 2.0 mm. An equal quantity of ceramic plates was then cut from ingots and their surfaces were wet-ground with 600-grit SiC paper. The minimum dimensions of the plates were 5 mm × 5 mm × 2 mm. The disks and the plates were annealed at 450 ◦ C for 10 h to release any residual stresses present [20]. A 5 × 5 × 2 plate was bonded to the wet-ground surface of a disk with a cyanoacrylate glue to serve as the bottom of the cylindrical hole in the disk. The specimen was designed such that when the composite was bonded within the hole, the ratio of bonded (internal surface area of cavity ∼ 20.6 mm2 ) to unbonded surface area (free surface at top of cavity ∼ 4.9 mm2 ), termed the configuration factor was approximately 4.2. To introduce initial cracks, four Vickers indentations were made in the polished ceramic surface adjacent to the perimeter of the hole using a force of 58.8 N for 15 s delivered with a microhardness tester (Kentron Microhardness Tester, The Torsion Balance Company, Clifton, NJ, USA). Each indentation was located in a quadrant and centered at a distance of approximately 570 m from the cavity edge. The Vickers indenter was oriented so that the two radial cracks from each indentation were aligned parallel with the cavity edge (Fig. 1). A preliminary study demonstrated that indentations at the same load placed at a shorter distance from the cavity edge developed radial cracks that were too long and became excessively curved, thus making it difficult to
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Table 2 – Protocols for light-activation in this study. One-step method Two-step method
Fig. 1 – A schematic diagram that shows a Vickers indentation (square), the radial cracks (bold lines) and the cavity edge. Lengths of the indentation cracks (c1 and c2 ) were measured.
measure their length. The distance of approximately 570 m was determined to be an appropriate distance for the measurement of the crack length with the indentation force of 58.8 N. After indenting, the ceramic was set aside for a day in a desiccator at room temperature to allow for the slow crack growth that is induced by residual indentation stress [24,31]. Two lengths from the indentation center to the crack ends (c1 and c2 in Fig. 1) were measured at 250× magnification using a monocular light microscope attached to the hardness tester, and an average of the lengths (c) was obtained for each specimen. Three experimental groups (n = 5) were defined based on composite brand (Table 1). The indentations were covered with removable tape. The inner walls and the floor of the cavity were treated with a silane coupling agent (Clearfil Porcelain Bond Activator, lot no. 00195A, Kuraray Medical, Tokyo, Japan) and an adhesive system (Clearfil SE Bond, lot no. Primer: 00641A; Bond: 00909A, Kuraray Medical, Tokyo, Japan). One drop each of Clearfil Porcelain Bond Activator and Clearfil SE Bond Primer were mixed and applied to the inner surface of the ceramic hole for 20 s and gently dispersed with compressed air for 5 s. The Bond component of the Clearfil SE Bond system was applied to the primed ceramic surface and air-thinned. The adhesive was light-activated for 20 s using a quartz halogen curing unit (Optilux 401, SDS Kerr, Orange, CA, USA). Light intensity of the light source was measured with a radiometer (Cure Rite, Caulk, Milford, DE, USA) prior to each light exposure. The hole was then filled with a single increment of one of the three dental resin composites (Table 1). The composite was then light-cured according to two different protocols (Table 2). For the one-step method, the composite was light-activated
60 s @ 560 mW/cm2 5 s @ 60 mW/cm2 + 2 min delay + 104 s @ 320 mW/cm2
using the quartz halogen source after an initial equilibration period of 30 s. The specimen was covered with clear mylar matrix and the tip of the light guide was placed in contact with the matrix. The total radiant exposure for this one-step method was 33,600 mJ/cm2 . The removable tape was peeled from the surface immediately after irradiating the composite and the filled specimen was left for more than 10 min prior to making any measurements of crack length. The indentations and the cracks were checked microscopically to ensure they were not covered by the adhesive or the composite. The two lengths (c1 and c2 ) were measured again as described previously, and an average length (c ) was calculated. The resulting lengths were statistically analyzed for each composite using paired t-tests comparing before and after curing (˛ < 0.05). To evaluate the influence of the light-activation mode on the crack length, three additional experimental groups (fifteen disks) were prepared and indented as previously described. Following the first length measurements (c1 and c2 ), the hole was filled as before and the composite was cured with a two-step light-activation sequence (Table 2) [32]. For the two-step method, the filled specimens were light-activated using a programmable quartz halogen light source (VIP, Bisco, Schaumburg, IL, USA). The tip of the light guide was placed at a distance of 4.5 mm from the specimen surface. The total radiant exposure for this two-step method was 33,580 mJ/cm2 , which was within 99.9% of that for the one-step method. The crack lengths were measured and compared as previously described. Differences in the crack lengths, i.e. propagation lengths (c − c), were calculated for each group. Additional statistical analyses were performed using unpaired t-tests between the propagation lengths of the one- and the twostep methods for each composite (˛ < 0.05) and using one-way ANOVA and Tukey’s test for the propagation lengths of the three composites for each curing method (˛ < 0.05). After the second measurement, the surface of the specimen was ground to remove any overfilled composite and superficial ceramic layer (less than 90-m-thick) using #1000 SiC paper. The resultant surfaces were polished with 0.25 m diamond paste to evaluate the contraction gap between the ceramic and composite [6,7]. In order to enhance the visualization of the gap, the interface was stained with permanent blue ink, and the excess ink was removed with ethanol. The stained gap were visualized with a digital microscope attached to a computer and measurements were recorded (VHX-200, Keyence, Osaka, Japan). Gap evaluation was performed by calculating the ratio of the stained interface to the entire interface
Table 1 – Resin composites tested in this study and their characteristics. Brand Heliomolar Herculite XRV Z100
Manufacturer
Filler vol.%
Ivoclar Vivadent, Schaan, Liechtenstein SDS Kerr, Orange, CA, USA 3M ESPE, St Paul, MN, USA
49 57 66
Average filler size (m) 0.04 0.8–1.0 1
Lot no. F52559 309181 3EY
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where a is stress in the ceramic, Kc is fracture toughness of the ceramic, ˚ is Kc c3/2 , Y is a geometrical term equal to 1.121/2 . The calculated values were statistically analyzed for each composite using Student’s t-test comparing the one- and the two-step methods (˛ < 0.05). Assumptions associated with the derivation of Eq. (3) are: 1. The stress within the resin composite is uniform and the problem is considered two-dimensional, that is, the hole continues completely through the ceramic. 2. Cracks are small compared with the distance between the indentation and the hole edge. 3. The ceramic body is a semi-infinite structure, that is, the outline of the ceramic disk is remote from the hole edge. For an indentation in a brittle structure, the classic relationship between radial crack length, indentation load, residual stress, indenter form and fracture toughness of the specimen is:
Fig. 2 – A schematic diagram illustrating the extent of interface cracking along the circumference of the resin composite in the cylindrical hole. Bold and dotted circumferences indicate the stained portion (the circumference having the contraction gap) and the unstained portion (the gap free circumference), respectively. The ratio (%) was calculated as follows: Ratio = (1 − 2 sin(r/a)/2rad) × 100.
length (Fig. 2) [33]. To calculate the ratio (%), the length of a chord running between two ends of the stained gap (2a in Fig. 2) was measured at 100× and 1000×, and substituted into the following equation:
Ratio =
1−
2 sin(r/a) 2rad
× 100
(2)
where r is the radius of the hole, a is a half length of the chord. In addition, maximum gap width was recorded at the point where the blue stain was widest. Five widths were measured in the area at 1000× and the average was calculated. The resulting data were statistically analyzed for each composite using unpaired t-tests between the one- and the two-step methods (˛ < 0.05). Although the indentation fracture method has been used for evaluating stresses in brittle materials [17–19,21], in the previous studies, indentations were introduced in an area where stress had already been generated. In contrast, in our study, indentations were introduced before stress generation. Therefore, the calculation methods used previously were not applicable. Values of c and c obtained from the length measurements were used to calculate stress around the indentation in the ceramic generated by polymerization of the composite using the following equation [17]:
a =
[Kc − ˚/c 3/2 ] Yc 1/2
(3)
Kc =
P c3/2
(4)
where is a constant that includes the residual stress related to the hardness indent, elastic modulus and geometry of indenter, P is the indentation load and c is the radial crack length [13]. Eq. (4) may be rewritten, Kc =
˚ c3/2
(5)
where ˚ is P, and the value of ˚ is Kc c3/2 . In the case of the indentation crack experiencing an applied stress, an additional term is added to Eq. (4) [34], Kc =
P c 3/2
+ Ya c
1/2
(6)
where the second term is the stress intensity factor for a crack in a uniform stress field, Y is a geometrical term 1.121/2 as described, a is the applied stress, and c is the new radial crack length. Re-arranging Eq. (6), the value of the stress a can be determined using Eq. (3).
3.
Results
Crack propagation was demonstrated in all groups. Fig. 3 shows representative images of the crack propagation found in Z100/one-step specimen. The top and bottom images are the same crack before and after curing the composite, respectively. White arrows indicate length between the indentation corner (left vertical lines) and the crack end (right vertical line). The length after composite polymerization was longer than that before light activation. The crack propagated about 30 m as an extension of the original indentation crack. The crack lengths after curing (c ) were significantly longer than that before curing (c) in all the groups (p < 0.05) (Table 3). The propagation lengths with the one-step method were equivalent among the three composites and were approximately 37 m. The lengths with the two-step method ranged from 32.3 ± 6.2 m with Heliomolar to 62.4 ± 16.6 m with
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Table 4 – Ratio of contraction gap as percent of total perimeter (%) in each group. Heliomolar One-step Two-step ∗
87.8 ± 17.8 96.3 ± 5.2
Herculite XRV
Z100
100.0 ± 0.0 90.9 ± 8.4*
98.5 ± 3.4 92.1 ± 14.2
Mean of two-step with an asterisk was significantly lower than mean of the corresponding one-step.
Table 5 – Maximum gap width (m) in each group. Heliomolar One-step Two-step
Fig. 3 – Same crack in a Z100/one-step specimen before (top) and after (bottom) curing the composite. White arrows indicate lengths between the indentation corner and crack end.
7.4 ± 1.6 10.6 ± 0.8
Herculite XRV
Z100
9.8 ± 1.9 9.2 ± 2.6
10.5 ± 3.4 8.0 ± 1.4
8.0 ± 1.4 m with Z100 to 10.6 ± 0.8 m with Heliomolar. There were no significant differences between the one- and the twostep methods for the composites.
4.
Z100. The propagation length was independent of the activation method for Heliomolar and Herculite XRV. A significant difference was recognized between the one- and the two-steps with Z100 (p = 0.0128). Within each curing method, there was no significant difference among the propagation lengths of the three composites with the one-step method. However, with the two-step method, Z100 showed the longest propagation among the composites, being significantly longer than the propagation of Heliomolar (p < 0.05). Table 3 also shows the stress values calculated from the propagation lengths in the six groups. Similar to the results of the propagation length, the stress values with the onestep method were equivalent among the three composites and approximated 4.8 MPa. The stresses with the two-step method ranged from 4.2 ± 0.7 MPa with Heliomolar to 7.0 ± 1.5 MPa with Z100. A significant difference was demonstrated between the one- and the two-steps with Z100 (p = 0.0201). Contraction gaps were demonstrated in all groups and the ratios of the gap length to the hole perimeter were more than 85% (Table 4). A significant difference was recognized between the one- and the two-step light activation methods with Herculite XRV only (p = 0.0413). Table 5 shows the maximum gap widths in the groups. The one-step method ranged from 7.4 ± 1.6 m with Heliomolar to 10.5 ± 3.4 m with Z100, and the two-step method ranged from
Discussion
All groups exhibited propagation of the initial crack after polymerization of the composite. In the preliminary study, lengths of the radial cracks were measured to evaluate whether the steps prior to light activation of the composite resulted in propagation of the cracks. It was confirmed that the crack was not propagated by irradiation of the curing light alone, placement and removal of the removable tape, or application of the resin adhesive. Thus, we are confident in concluding that the cracks were propagated by stresses induced in the ceramic by the polymerization contraction of the resin composite. Lim et al. [32] evaluated the influence of light-activation method on polymerization contraction stress of the same composites as those used in the present study. They found that the polymerization contraction stresses of the composites with the two-step activation were smaller than those with one-step activation. In the present study, the propagation length and the stress values had been expected to be lower with two-step activation. However, neither propagation length nor stress decreased significantly with two-step activation. Furthermore, a significant increase was seen for the two-step activation of Z100 (Table 3). The inconsistency between the present study and the previous report [32] might have been
Table 3 – Crack lengths (m) before curing (c), after curing (c ) and propagation length (c − c), and calculated stress (MPa) in each group. Composite Irradiation c c (c − c) a ∗ ∗∗ #
Heliomolar One-step 294.0 333.1 39.1 4.9
± ± ± ±
9.6 18.3* 13.1 1.3
Herculite XRV
Two-step 299.9 332.2 32.3 4.2
± ± ± ±
14.8 17.3* 6.2 0.7
One-step 291.7 329.4 37.7 4.8
± ± ± ±
13.0 21.2* 9.7 0.9
Z100
Two-step 301.7 349.2 47.5 5.5
± ± ± ±
20.8 26.7* 11.5 1.1
Mean of c with an asterisk was significantly higher than mean of the corresponding c. Mean of two-step with an asterisk was significantly higher than mean of the corresponding one-step. Mean of two-step with an asterisk was significantly higher than mean of the corresponding one-step.
One-step 294.5 330.0 35.5 4.6
± ± ± ±
7.6 8.6* 5.5 0.6
Two-step 293.6 356.0 62.4 7.0
± ± ± ±
7.0 15.6* 16.6** 1.5#
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Fig. 4 – Contraction gap in a Heliomolar/two-step specimen. Fragments of the ceramic (*) delaminated from the ceramic body and were incorporated in the adhesive resin.
the result of gaps formed at the ceramic–composite interface observed in all groups (Tables 4 and 5). The relation between stresses at the interface and gap formation is complex. Initially, shrinkage stress develops in the composite, and this generates a radial tensile stress in the surrounding ceramic material and at the composite–ceramic interface when there is good bonding. As the stress builds up, the indentation crack begins to extend. However, when the interfacial stresses reach a critical value, debonding at the composite–ceramic interface occurs. At this time, the stresses within the surrounding ceramic begin to drop and the extending indentation crack arrests. This arises because the interfacial crack at the composite–ceramic interface enables stored strain energy within the composite to be released. On this basis the stresses developed in the ceramic as measured by the current analysis from the extension of the indentation crack are an underestimate because of the interfacial separation. In this study, the contraction gaps were formed not only at the composite–ceramic interface, but in the ceramic itself near the interface. Xu and Jahanmir [35], and Xu et al. [36] reported that subsurface damage was generated in ceramic materials by machining. Subsurface damage is also produced in human enamel when the enamel is machined by diamond burs [37]. Fig. 4 is an SEM image revealing the contraction gap in a Heliomolar/two-step specimen. Some fragments of the ceramic (* in Fig. 4) detached from the ceramic body and incorporated in the adhesive layer, and the gap was formed between the ceramic fragments and the ceramic body. This image indicates that the gap was formed after the application of the adhesive. The ceramic surface bonded to the adhesive delaminated from the rest of the ceramic when contraction stresses were generated by composite polymerization. The tensile strength measured by flexure of the ceramic used in this study is 290 MPa [27] and is much higher than the reported contraction stresses of the composites (5.4–12.5 MPa) [32]. However, in general, the tensile strength of ceramics is dramatically decreased once the ceramics contain critical flaws
in the surface where tensile stress is generated [25]. Consequently, subsurface damage created by drilling the cylindrical hole in the ceramic may serve as the origin of the critical flaws that result in subsequent gap formation. We expected crack propagation magnitudes to be correlated with the contraction force transferred to the ceramic. Z100 was expected to produce greater crack propagation than Herculite XRV, which in turn would be higher than Heliomolar, based on the previously reported contraction stress differences among these materials [32]. This trend was not observed for one-step light activation, but was for the two-step method. It is likely that high stresses caused by the rapid curing in the one-step method resulted in initial stress transfer as described above. Critical stress levels were then reached that led to interfacial gap formation, stress reduction and crack arrest. The two-step method, which was previously shown to yield a reduced rate of stress buildup [32,38], may have reached the critical stress for debonding and gap formation more slowly, thus allowing greater opportunity for force transfer and evidence of the differences in stress production among the three composites. The Z100/two-step group had the greatest force transfer among the six groups. In addition, the irradiance of the light source in the two-step activation mode was lower than that for the one-step mode. Others have shown that light sources with lower irradiance produce slower development of polymerization contraction stress and reduced rates of polymerization [32,38]. Though similar tendencies were shown in the statistical results of the propagation length and the stress, the statistical results of the ratio and the gap width did not coincide with the results of the propagation length and the stress (Tables 3–5). Therefore, there were no apparent relationships between the propagation length and the ratio or the width of the crack in this experimental system. A new method to calculate the contraction stress has been proposed. This method can evaluate two clinical phenomena in resin composite restorations, the formation of contraction gaps [39] and cracking in the surrounding “simulated” enamel material [9,40]. Utilizing the indentation fracture technique, which is essentially non-destructive, it is possible to calculate the stresses at certain points in the surrounding material simultaneously and to understand the stress distribution around the composite restoration. The proposed indentation method has advantages in comparison with other stress analyses such as photoelastic analysis or strain gage methods [41,42]. The photoelastic material is not appropriate for the “simulated” enamel because the elastic modulus of the photoelastic material is much lower than that of enamel. The strain gage requires a gage bonding area that is wider than the dimension of the indentation and the cracks in this method. Thus, the indentation method can measure stress magnitudes over a much smaller area. In addition, the method only requires a conventional hardness tester and a measuring microscope. A limitation of this method is that a prescribed distance between the cavity edge and the indentation is required to avoid chipping of the cavity edge during indentation. The distance is determined by the edge strength of surrounding matrix [43]. In order to simplify the stress distribution around the composite, a ceramic material was used as the surrounding
d e n t a l m a t e r i a l s 2 5 ( 2 0 0 9 ) 543–550
substrate in this study. The magnitude of contraction stress in tooth tissue is likely to be different from that in the ceramic because of a difference in elastic modulus and compliance [30]. Further investigations using natural teeth are required to obtain a better understanding of composite resin contraction stress in tooth tissue.
5.
Conclusion
Contraction stresses generated by curing dental resin composites are sufficient to cause propagation of cracks from flaws existing in a surrounding brittle material. The proposed method for the stress calculation using indentation crack extension is a simple technique requiring only a conventional hardness tester and can evaluate two clinical phenomena of the composite restoration, that is, enamel cracking and interfacial contraction gap formation.
references
[1] Park J-W, Ferracane JL. Measuring the residual stress in dental composites using a ring slitting method. Dent Mater 2005;21:882–9. [2] Pearson GJ, Hegarty SM. Cusp movement of molar teeth with composite filling materials in conventional and modified MOD cavities. Br Dent J 1989;166:162–5. [3] Suliman AA, Boyer DB, Lakes RS. Cusp movement in premolars resulting from composite polymerization shrinkage. Dent Mater 1993;9:6–10. [4] Tantbirojn D, Versluis A, Pintado MR, DeLong R, Douglas WH. Tooth deformation patterns in molars after composite restoration. Dent Mater 2004;20:535–42. [5] Asmussen E. Composite restorative resins. Composition versus wall-to-wall polymerization contraction. Acta Odontol Scand 1975;33:337–44. [6] Munksgaard EC, Irie M, Asmussen E. Dentin-polymer bond promoted by Gluma and various resins. J Dent Res 1985;64:1409–11. [7] Irie M, Suzuki K, Watts DC. Marginal gap formation of light-activated restorative materials: effects of immediate setting shrinkage and bond strength. Dent Mater 2002;18:203–10. [8] Kanca J, Suh BI. Pulse activation: reducing resin-based composite contraction stresses at the enamel cavosurface margins. Am J Dent 1999;12:107–12. [9] Jørgensen KD, Asmussen E, Shimokobe H. Enamel damages caused by contracting restorative resins. Scand J Dent Res 1975;83:120–2. [10] Lawn BR, Swain MV. Microfracture beneath point indentations in brittle solids. J Mater Sci 1975;10:113–22. [11] Niihara K, Morena R, Hasselman DPH. Evaluation of K1c of brittle solids by the indentation method with low crack-to-indent ratios. J Mater Sci Lett 1982;1:13–6. [12] Lardner TJ, Ritter JE, Shiao ML, Lin MR. Behavior of indentation cracks near free surfaces and interfaces. Int J Fracture 1990;44:133–43. [13] Anstis GR, Chantikul P, Lawn BR, Marshall DB. A critical evaluation of indentation techniques for measuring fracture toughness. I. Direct crack measurements. J Am Ceram Soc 1981;64:533–8. [14] Maehara S, Fujishima A, Hotta Y, Miyazaki T. Fracture toughness measurement of dental ceramics using the indentation fracture method with different formulas. Dent Mater J 2005;24:328–34.
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[15] Sakar-Deliormanli A, Güden M. Microhardness and fracture toughness of dental materials by indentation method. J Biomed Mater Res Part B: Appl Biomater 2006;76B:257–64. [16] Quinn GD, Bradt RC. On the Vickers indentation fracture toughness test. J Am Ceram Soc 2007;90:673–80. [17] Marshall DB, Lawn BR. An indentation technique for measuring stresses in tempered glass surfaces. J Am Ceram Soc 1977;60:86–7. [18] Niihara K. Indentation microfracture of ceramics—its application and problems. Ceram Jpn 1985;20:12–8. [19] JSMS-SD-4-01. Residual stress measurement for engineering ceramics by indentation fracture method. The Society of Material Science Japan (JSMS) Committee on Fatigue of Materials, Kyoto, Japan, 2001. [20] Fisher H, Marx R. Fracture toughness of dental ceramics: comparison of bending and indentation method. Dent Mater 2002;18:12–9. [21] Taskonak B, Mecholsky Jr JJ, Anusavice KJ. Residual stress in bilayer dental ceramics. Biomaterials 2005;26:3235–41. [22] Yamamoto T, Nishiura R. Marginal toughness of bonded dental ceramics evaluated by determination of the crack length. J Dent 2006;34:146–54. [23] Lawn BR, Wilshaw TR. Indentation fracture: principles and applications. J Mater Sci 1975;10:1049–81. [24] Marshall DB, Lawn BR. Residual stress effects in sharp contact cracking. Part 1. Indentation fracture mechanics. J Mater Sci 1979;14:2001–12. [25] Anusavice KJ. Dental ceramics. In: Anusavice KJ, editor. Phillips’ science of dental materials. tenth edition Philadelphia: W.B. Saunders Company; 1996. p. 583–618. [26] Darvell BW. Griffith’s law. In: Darvell BW, editor. Material science for dentistry. sixth edition Pokfulam: BW Darvell; 2000. p. 20–1. [27] Hata Y, Suzuki H, Iijima H, Yamazaki H, Iwashita H, Hakamatsuka Y, et al. Preparation and properties of castable ceramics (OCC). J Jpn Prosthodont Soc 1988;32:52–61. [28] Yamamoto T, Takamizu M, Kohno A. Influence of residual surface investment material on crystallization shrinkage of a mica-based glass-ceramic. Dent Mater 2002;18:336–42. [29] Hassan R, Caputo AA, Bunshah RF. Fracture toughness of human enamel. J Dent Res 1981;60:820–7. [30] Xu HHK, Smith DT, Jahanmir S, Romberg E, Kelly JR, Thompson VP, et al. Indentation damage and mechanical properties of human enamel and dentin. J Dent Res 1998;77:472–80. [31] Wuttiphan S, Lawn BR, Padture NP. Crack suppression in strongly bonded homogeneous/heterogeneous laminates: a study on glass/glass-ceramic bilayers. J Am Ceram Soc 1996;79:634–40. [32] Lim B-S, Ferracane JL, Sakaguchi RL, Condon JR. Reduction of polymerization stress for dental composites by two-step light-activation. Dent Mater 2002;18:436–44. [33] de Andrade OS, de Goes MF, Montes MAJR. Marginal adaptation and microtensile bond strength of composite indirect restorations bonded to dentin treated with adhesive and low-viscosity composite. Dent Mater 2007;23:279–87. [34] Lawn BR. Indentation cracks as controlled flaws: inert strength, toughness, and T-curves. In: Davis EA, Ward IM, editors. Fracture of brittle solids. second edition Cambridge: Cambridge University Press; 1993. p. 263–76. [35] Xu HHK, Jahanmir S. Simple technique for observing subsurface damage in machining of ceramics. J Am Ceram Soc 1994;77:1388–90. [36] Xu HHK, Smith DT, Jahanmir S. Influence of microstructure on indentation and machining of dental glass-ceramics. J Mater Res 1996;11:2325–37. [37] Xu HHK, Kelly JR, Jahanmir S, Thompson VP, Rekow ED. Enamel subsurface damage due to tooth preparation with diamonds. J Dent Res 1997;76:1698–706.
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[38] Watts DC, Cash AJ. Determination of polymerization shrinkage kinetics in visible-light-cured materials: methods development. Dent Mater 1991;7:281–7. [39] Davidson CL, de Gee AJ. Relaxation of polymerization contraction stresses by flow in dental composites. J Dent Res 1984;63:146–8. [40] Hilton TJ, Broome JC. Direct posterior esthetic restorations. In: Summitt JB, et al., editors. Fundamentals of operative dentistry: a contemporary approach. third edition Hanover Park: Quintessence Publishing Co., Inc.; 2006. p. 289–339.
[41] Kinomoto Y, Torii M. Photoelastic analysis of polymerization contraction stresses in resin composite restorations. J Dent 1998;26:165–71. [42] Sakaguchi RL, Ferracane JL. Stress transfer from polymerization shrinkage of a chemical-cured composite bonded to a pre-cast composite substrate. Dent Mater 1998;14:106–11. [43] Watts DC, Issa M, Ibrahim A, Wakiaga J, Al-Samadani K, Al-Azraqi M, et al. Edge strength of resin-composite margins. Dent Mater 2008;24:129–33.
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Calculation of contraction stresses in dental composites by analysis of crack propagation in the matrix surrounding a cavity Takatsugu Yamamoto a,∗ , Jack L. Ferracane b , Ronald L. Sakaguchi b , Michael V. Swain c a
Department of Operative Dentistry, Tsurumi University School of Dental Medicine, 2-1-3, Tsurumi, Tsurumi-ku, Yokohama, Kanagawa 230-8501, Japan b Division of Biomaterials and Biomechanics, Department of Restorative Dentistry, School of Dentistry, Oregon Health & Science University, 611 SW Campus Drive, Portland, OR 97239-3097, USA c Biomaterials Science Research Unit, Faculty of Dentistry, University of Sydney, Surry Hills, NSW 2010, Australia
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objectives. Polymerization contraction of dental composite produces a stress field in the
Received 3 October 2007
bonded surrounding substrate that may be capable of propagating cracks from pre-existing
Received in revised form
flaws. The objectives of this study were to assess the extent of crack propagation from
20 August 2008
flaws in the surrounding ceramic substrate caused by composite contraction stresses, and
Accepted 30 October 2008
to propose a method to calculate the contraction stress in the ceramic using indentation fracture. Methods. Initial cracks were introduced with a Vickers indenter near a cylindrical hole drilled
Keywords:
into a glass-ceramic simulating enamel. Lengths of the radial indentation cracks were mea-
Dental composite
sured. Three composites having different contraction stresses were cured within the hole
Ceramic
using one- or two-step light-activation methods and the crack lengths were measured. The
Indentation
contraction stress in the ceramic was calculated from the crack length and the fracture
Polymerization contraction stress
toughness of the glass-ceramic. Interfacial gaps between the composite and the ceramic were expressed as the ratio of the gap length to the hole perimeter, as well as the maximum gap width. Results. All groups revealed crack propagation and the formation of contraction gaps. The calculated contraction stresses ranged from 4.2 MPa to 7.0 MPa. There was no correlation between the stress values and the contraction gaps. Significance. This method for calculating the stresses produced by composites is a relatively simple technique requiring a conventional hardness tester. The method can investigate two clinical phenomena that may occur during the placement of composite restorations, i.e. simulated enamel cracking near the margins and the formation of contraction gaps. © 2008 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
∗
Corresponding author. Tel.: +81 45 581 1001x8550/8429; fax: +81 45 573 9599. E-mail address: [email protected] (T. Yamamoto). 0109-5641/$ – see front matter © 2008 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.dental.2008.10.008
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1.
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Introduction
Forces are generated by the polymerization contraction of bonded dental resin composite. These forces may result in stresses in three regions: (1) within the composite, (2) at the interface between the composite and the surrounding enamel and dentin, and (3) in the surrounding enamel and dentin. The stresses may induce several phenomena including deformation of the composite [1] and tooth [2–4], formation of contraction gaps [5–7], and cracking in the surrounding substrate [8,9]. The contraction stress may be one of the factors causing postoperative problems with composite restorations. When a pyramidal indenter, such as Vickers or Knoop, is loaded onto a brittle material, radial cracks initiate from the indentation corners [10–12]. The dimensions of the indentation and the cracks can be used to calculate fracture toughness [11,13–15]. Recently Quinn and Bradt [16] have argued that indentation is not an absolute measure of fracture toughness of a brittle material because of the poorly defined shape of the cracks developed. This is indeed the case and most authors associated with the development of the indentation technique have not stated that a K1c was measured, but that a very good correlation between traditional and indentation derived values of fracture toughness was achieved with an empirical modifying factor. The propagation of the radial cracks is sensitive to the stress distribution in the indented material [11,17–21]. Taskonak et al. reported a significant difference between lengths of two radial cracks running orthogonally when a Vickers indentation was imprinted in a ceramic having anisotropic stresses [21]. The direction of the radial cracks is also affected by the stress distribution. Radial cracks will curve based on their position within stress fields [12,22]. Utilizing the behavior of a pre-existing crack to stress, methods have been proposed for calculating residual stress in brittle materials using indentation fracture mechanics, i.e. the dimensions of the indentation and the cracks [17–19]. Cracks in brittle materials propagate through regions where tensile stresses are distributed [23–26], and extend further when additional remote tensile stress is applied and concentrated at the crack tip [26]. It is expected that an appropriately oriented pre-existing crack in a brittle material bonded to resin composite will propagate under the radial tensile stresses generated during composite curing contraction, and the additional length of the propagation will depend on the magnitude of the final tensile stress. If the contraction stress at a specific point in a substrate bonded to composite can be calculated from the propagation length, distributions of the stresses around the composite restoration can be quantified. Clinically, knowledge of the stress magnitude and distribution would aid composite material selection and restoration design. This could minimize postoperative discomfort and fracture of enamel induced by the contraction stress. The objectives of this study were (1) to assess crack propagation adjacent to a cavity in a brittle ceramic simulating enamel as a result of composite contraction stress, and (2) to propose a method to calculate the contraction stress in the ceramic using the increased dimensions of the indentation fracture. The hypothesis tested was that the contraction
stress generated during polymerization of a composite propagates cracks from existing flaws in a ceramic material that surrounds the composite in a consistent, predictable manner.
2.
Materials and methods
The ceramic material used in this study was a micaceous glass-ceramic (OCC, lot no. 48080, Olympus Optical Co., Tokyo, Japan) whose elastic modulus and glass transition temperature were reportedly 53 GPa and 550 ◦ C, respectively [27,28]. Fracture toughness of the ceramic was 1.08 MPa m0.5 measured with the indentation method (58.8 N-load for 15 s) in a preliminary study. The toughness was calculated using the following equation [19]: Kc = 0.026(EP)
1/2
d 2
−3/2
(c)
(1)
where E is the elastic modulus, P is the indentation load, d is the diagonal length of the indentation, and c is the length from the indentation center to the end of the crack. This material was chosen to simulate enamel and the toughness of the ceramic was within the range of values reported for human enamel [29,30]. An ingot of the ceramic was drilled through using a drill press to make a cylindrical hole of 2.5-mm-diameter. The drilled ceramic ingot was sliced into 2.1-mm-thick disks using a diamond saw (Accutom-5, Struers A/S, Rodovre, Denmark). The disks were essentially oval in shape with long and short axes ranging from 12.4 to 12.8 mm and from 10.5 to 12.2 mm, respectively. Fifteen disks were prepared and the top flat surface of each ceramic disk was serially wet-polished using various grit papers then finished with 1 m diamond paste. The bottom flat surface of each disk was wet-ground with 600grit SiC paper to adjust the disk thickness to 2.0 mm. An equal quantity of ceramic plates was then cut from ingots and their surfaces were wet-ground with 600-grit SiC paper. The minimum dimensions of the plates were 5 mm × 5 mm × 2 mm. The disks and the plates were annealed at 450 ◦ C for 10 h to release any residual stresses present [20]. A 5 × 5 × 2 plate was bonded to the wet-ground surface of a disk with a cyanoacrylate glue to serve as the bottom of the cylindrical hole in the disk. The specimen was designed such that when the composite was bonded within the hole, the ratio of bonded (internal surface area of cavity ∼ 20.6 mm2 ) to unbonded surface area (free surface at top of cavity ∼ 4.9 mm2 ), termed the configuration factor was approximately 4.2. To introduce initial cracks, four Vickers indentations were made in the polished ceramic surface adjacent to the perimeter of the hole using a force of 58.8 N for 15 s delivered with a microhardness tester (Kentron Microhardness Tester, The Torsion Balance Company, Clifton, NJ, USA). Each indentation was located in a quadrant and centered at a distance of approximately 570 m from the cavity edge. The Vickers indenter was oriented so that the two radial cracks from each indentation were aligned parallel with the cavity edge (Fig. 1). A preliminary study demonstrated that indentations at the same load placed at a shorter distance from the cavity edge developed radial cracks that were too long and became excessively curved, thus making it difficult to
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Table 2 – Protocols for light-activation in this study. One-step method Two-step method
Fig. 1 – A schematic diagram that shows a Vickers indentation (square), the radial cracks (bold lines) and the cavity edge. Lengths of the indentation cracks (c1 and c2 ) were measured.
measure their length. The distance of approximately 570 m was determined to be an appropriate distance for the measurement of the crack length with the indentation force of 58.8 N. After indenting, the ceramic was set aside for a day in a desiccator at room temperature to allow for the slow crack growth that is induced by residual indentation stress [24,31]. Two lengths from the indentation center to the crack ends (c1 and c2 in Fig. 1) were measured at 250× magnification using a monocular light microscope attached to the hardness tester, and an average of the lengths (c) was obtained for each specimen. Three experimental groups (n = 5) were defined based on composite brand (Table 1). The indentations were covered with removable tape. The inner walls and the floor of the cavity were treated with a silane coupling agent (Clearfil Porcelain Bond Activator, lot no. 00195A, Kuraray Medical, Tokyo, Japan) and an adhesive system (Clearfil SE Bond, lot no. Primer: 00641A; Bond: 00909A, Kuraray Medical, Tokyo, Japan). One drop each of Clearfil Porcelain Bond Activator and Clearfil SE Bond Primer were mixed and applied to the inner surface of the ceramic hole for 20 s and gently dispersed with compressed air for 5 s. The Bond component of the Clearfil SE Bond system was applied to the primed ceramic surface and air-thinned. The adhesive was light-activated for 20 s using a quartz halogen curing unit (Optilux 401, SDS Kerr, Orange, CA, USA). Light intensity of the light source was measured with a radiometer (Cure Rite, Caulk, Milford, DE, USA) prior to each light exposure. The hole was then filled with a single increment of one of the three dental resin composites (Table 1). The composite was then light-cured according to two different protocols (Table 2). For the one-step method, the composite was light-activated
60 s @ 560 mW/cm2 5 s @ 60 mW/cm2 + 2 min delay + 104 s @ 320 mW/cm2
using the quartz halogen source after an initial equilibration period of 30 s. The specimen was covered with clear mylar matrix and the tip of the light guide was placed in contact with the matrix. The total radiant exposure for this one-step method was 33,600 mJ/cm2 . The removable tape was peeled from the surface immediately after irradiating the composite and the filled specimen was left for more than 10 min prior to making any measurements of crack length. The indentations and the cracks were checked microscopically to ensure they were not covered by the adhesive or the composite. The two lengths (c1 and c2 ) were measured again as described previously, and an average length (c ) was calculated. The resulting lengths were statistically analyzed for each composite using paired t-tests comparing before and after curing (˛ < 0.05). To evaluate the influence of the light-activation mode on the crack length, three additional experimental groups (fifteen disks) were prepared and indented as previously described. Following the first length measurements (c1 and c2 ), the hole was filled as before and the composite was cured with a two-step light-activation sequence (Table 2) [32]. For the two-step method, the filled specimens were light-activated using a programmable quartz halogen light source (VIP, Bisco, Schaumburg, IL, USA). The tip of the light guide was placed at a distance of 4.5 mm from the specimen surface. The total radiant exposure for this two-step method was 33,580 mJ/cm2 , which was within 99.9% of that for the one-step method. The crack lengths were measured and compared as previously described. Differences in the crack lengths, i.e. propagation lengths (c − c), were calculated for each group. Additional statistical analyses were performed using unpaired t-tests between the propagation lengths of the one- and the twostep methods for each composite (˛ < 0.05) and using one-way ANOVA and Tukey’s test for the propagation lengths of the three composites for each curing method (˛ < 0.05). After the second measurement, the surface of the specimen was ground to remove any overfilled composite and superficial ceramic layer (less than 90-m-thick) using #1000 SiC paper. The resultant surfaces were polished with 0.25 m diamond paste to evaluate the contraction gap between the ceramic and composite [6,7]. In order to enhance the visualization of the gap, the interface was stained with permanent blue ink, and the excess ink was removed with ethanol. The stained gap were visualized with a digital microscope attached to a computer and measurements were recorded (VHX-200, Keyence, Osaka, Japan). Gap evaluation was performed by calculating the ratio of the stained interface to the entire interface
Table 1 – Resin composites tested in this study and their characteristics. Brand Heliomolar Herculite XRV Z100
Manufacturer
Filler vol.%
Ivoclar Vivadent, Schaan, Liechtenstein SDS Kerr, Orange, CA, USA 3M ESPE, St Paul, MN, USA
49 57 66
Average filler size (m) 0.04 0.8–1.0 1
Lot no. F52559 309181 3EY
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where a is stress in the ceramic, Kc is fracture toughness of the ceramic, ˚ is Kc c3/2 , Y is a geometrical term equal to 1.121/2 . The calculated values were statistically analyzed for each composite using Student’s t-test comparing the one- and the two-step methods (˛ < 0.05). Assumptions associated with the derivation of Eq. (3) are: 1. The stress within the resin composite is uniform and the problem is considered two-dimensional, that is, the hole continues completely through the ceramic. 2. Cracks are small compared with the distance between the indentation and the hole edge. 3. The ceramic body is a semi-infinite structure, that is, the outline of the ceramic disk is remote from the hole edge. For an indentation in a brittle structure, the classic relationship between radial crack length, indentation load, residual stress, indenter form and fracture toughness of the specimen is:
Fig. 2 – A schematic diagram illustrating the extent of interface cracking along the circumference of the resin composite in the cylindrical hole. Bold and dotted circumferences indicate the stained portion (the circumference having the contraction gap) and the unstained portion (the gap free circumference), respectively. The ratio (%) was calculated as follows: Ratio = (1 − 2 sin(r/a)/2rad) × 100.
length (Fig. 2) [33]. To calculate the ratio (%), the length of a chord running between two ends of the stained gap (2a in Fig. 2) was measured at 100× and 1000×, and substituted into the following equation:
Ratio =
1−
2 sin(r/a) 2rad
× 100
(2)
where r is the radius of the hole, a is a half length of the chord. In addition, maximum gap width was recorded at the point where the blue stain was widest. Five widths were measured in the area at 1000× and the average was calculated. The resulting data were statistically analyzed for each composite using unpaired t-tests between the one- and the two-step methods (˛ < 0.05). Although the indentation fracture method has been used for evaluating stresses in brittle materials [17–19,21], in the previous studies, indentations were introduced in an area where stress had already been generated. In contrast, in our study, indentations were introduced before stress generation. Therefore, the calculation methods used previously were not applicable. Values of c and c obtained from the length measurements were used to calculate stress around the indentation in the ceramic generated by polymerization of the composite using the following equation [17]:
a =
[Kc − ˚/c 3/2 ] Yc 1/2
(3)
Kc =
P c3/2
(4)
where is a constant that includes the residual stress related to the hardness indent, elastic modulus and geometry of indenter, P is the indentation load and c is the radial crack length [13]. Eq. (4) may be rewritten, Kc =
˚ c3/2
(5)
where ˚ is P, and the value of ˚ is Kc c3/2 . In the case of the indentation crack experiencing an applied stress, an additional term is added to Eq. (4) [34], Kc =
P c 3/2
+ Ya c
1/2
(6)
where the second term is the stress intensity factor for a crack in a uniform stress field, Y is a geometrical term 1.121/2 as described, a is the applied stress, and c is the new radial crack length. Re-arranging Eq. (6), the value of the stress a can be determined using Eq. (3).
3.
Results
Crack propagation was demonstrated in all groups. Fig. 3 shows representative images of the crack propagation found in Z100/one-step specimen. The top and bottom images are the same crack before and after curing the composite, respectively. White arrows indicate length between the indentation corner (left vertical lines) and the crack end (right vertical line). The length after composite polymerization was longer than that before light activation. The crack propagated about 30 m as an extension of the original indentation crack. The crack lengths after curing (c ) were significantly longer than that before curing (c) in all the groups (p < 0.05) (Table 3). The propagation lengths with the one-step method were equivalent among the three composites and were approximately 37 m. The lengths with the two-step method ranged from 32.3 ± 6.2 m with Heliomolar to 62.4 ± 16.6 m with
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Table 4 – Ratio of contraction gap as percent of total perimeter (%) in each group. Heliomolar One-step Two-step ∗
87.8 ± 17.8 96.3 ± 5.2
Herculite XRV
Z100
100.0 ± 0.0 90.9 ± 8.4*
98.5 ± 3.4 92.1 ± 14.2
Mean of two-step with an asterisk was significantly lower than mean of the corresponding one-step.
Table 5 – Maximum gap width (m) in each group. Heliomolar One-step Two-step
Fig. 3 – Same crack in a Z100/one-step specimen before (top) and after (bottom) curing the composite. White arrows indicate lengths between the indentation corner and crack end.
7.4 ± 1.6 10.6 ± 0.8
Herculite XRV
Z100
9.8 ± 1.9 9.2 ± 2.6
10.5 ± 3.4 8.0 ± 1.4
8.0 ± 1.4 m with Z100 to 10.6 ± 0.8 m with Heliomolar. There were no significant differences between the one- and the twostep methods for the composites.
4.
Z100. The propagation length was independent of the activation method for Heliomolar and Herculite XRV. A significant difference was recognized between the one- and the two-steps with Z100 (p = 0.0128). Within each curing method, there was no significant difference among the propagation lengths of the three composites with the one-step method. However, with the two-step method, Z100 showed the longest propagation among the composites, being significantly longer than the propagation of Heliomolar (p < 0.05). Table 3 also shows the stress values calculated from the propagation lengths in the six groups. Similar to the results of the propagation length, the stress values with the onestep method were equivalent among the three composites and approximated 4.8 MPa. The stresses with the two-step method ranged from 4.2 ± 0.7 MPa with Heliomolar to 7.0 ± 1.5 MPa with Z100. A significant difference was demonstrated between the one- and the two-steps with Z100 (p = 0.0201). Contraction gaps were demonstrated in all groups and the ratios of the gap length to the hole perimeter were more than 85% (Table 4). A significant difference was recognized between the one- and the two-step light activation methods with Herculite XRV only (p = 0.0413). Table 5 shows the maximum gap widths in the groups. The one-step method ranged from 7.4 ± 1.6 m with Heliomolar to 10.5 ± 3.4 m with Z100, and the two-step method ranged from
Discussion
All groups exhibited propagation of the initial crack after polymerization of the composite. In the preliminary study, lengths of the radial cracks were measured to evaluate whether the steps prior to light activation of the composite resulted in propagation of the cracks. It was confirmed that the crack was not propagated by irradiation of the curing light alone, placement and removal of the removable tape, or application of the resin adhesive. Thus, we are confident in concluding that the cracks were propagated by stresses induced in the ceramic by the polymerization contraction of the resin composite. Lim et al. [32] evaluated the influence of light-activation method on polymerization contraction stress of the same composites as those used in the present study. They found that the polymerization contraction stresses of the composites with the two-step activation were smaller than those with one-step activation. In the present study, the propagation length and the stress values had been expected to be lower with two-step activation. However, neither propagation length nor stress decreased significantly with two-step activation. Furthermore, a significant increase was seen for the two-step activation of Z100 (Table 3). The inconsistency between the present study and the previous report [32] might have been
Table 3 – Crack lengths (m) before curing (c), after curing (c ) and propagation length (c − c), and calculated stress (MPa) in each group. Composite Irradiation c c (c − c) a ∗ ∗∗ #
Heliomolar One-step 294.0 333.1 39.1 4.9
± ± ± ±
9.6 18.3* 13.1 1.3
Herculite XRV
Two-step 299.9 332.2 32.3 4.2
± ± ± ±
14.8 17.3* 6.2 0.7
One-step 291.7 329.4 37.7 4.8
± ± ± ±
13.0 21.2* 9.7 0.9
Z100
Two-step 301.7 349.2 47.5 5.5
± ± ± ±
20.8 26.7* 11.5 1.1
Mean of c with an asterisk was significantly higher than mean of the corresponding c. Mean of two-step with an asterisk was significantly higher than mean of the corresponding one-step. Mean of two-step with an asterisk was significantly higher than mean of the corresponding one-step.
One-step 294.5 330.0 35.5 4.6
± ± ± ±
7.6 8.6* 5.5 0.6
Two-step 293.6 356.0 62.4 7.0
± ± ± ±
7.0 15.6* 16.6** 1.5#
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Fig. 4 – Contraction gap in a Heliomolar/two-step specimen. Fragments of the ceramic (*) delaminated from the ceramic body and were incorporated in the adhesive resin.
the result of gaps formed at the ceramic–composite interface observed in all groups (Tables 4 and 5). The relation between stresses at the interface and gap formation is complex. Initially, shrinkage stress develops in the composite, and this generates a radial tensile stress in the surrounding ceramic material and at the composite–ceramic interface when there is good bonding. As the stress builds up, the indentation crack begins to extend. However, when the interfacial stresses reach a critical value, debonding at the composite–ceramic interface occurs. At this time, the stresses within the surrounding ceramic begin to drop and the extending indentation crack arrests. This arises because the interfacial crack at the composite–ceramic interface enables stored strain energy within the composite to be released. On this basis the stresses developed in the ceramic as measured by the current analysis from the extension of the indentation crack are an underestimate because of the interfacial separation. In this study, the contraction gaps were formed not only at the composite–ceramic interface, but in the ceramic itself near the interface. Xu and Jahanmir [35], and Xu et al. [36] reported that subsurface damage was generated in ceramic materials by machining. Subsurface damage is also produced in human enamel when the enamel is machined by diamond burs [37]. Fig. 4 is an SEM image revealing the contraction gap in a Heliomolar/two-step specimen. Some fragments of the ceramic (* in Fig. 4) detached from the ceramic body and incorporated in the adhesive layer, and the gap was formed between the ceramic fragments and the ceramic body. This image indicates that the gap was formed after the application of the adhesive. The ceramic surface bonded to the adhesive delaminated from the rest of the ceramic when contraction stresses were generated by composite polymerization. The tensile strength measured by flexure of the ceramic used in this study is 290 MPa [27] and is much higher than the reported contraction stresses of the composites (5.4–12.5 MPa) [32]. However, in general, the tensile strength of ceramics is dramatically decreased once the ceramics contain critical flaws
in the surface where tensile stress is generated [25]. Consequently, subsurface damage created by drilling the cylindrical hole in the ceramic may serve as the origin of the critical flaws that result in subsequent gap formation. We expected crack propagation magnitudes to be correlated with the contraction force transferred to the ceramic. Z100 was expected to produce greater crack propagation than Herculite XRV, which in turn would be higher than Heliomolar, based on the previously reported contraction stress differences among these materials [32]. This trend was not observed for one-step light activation, but was for the two-step method. It is likely that high stresses caused by the rapid curing in the one-step method resulted in initial stress transfer as described above. Critical stress levels were then reached that led to interfacial gap formation, stress reduction and crack arrest. The two-step method, which was previously shown to yield a reduced rate of stress buildup [32,38], may have reached the critical stress for debonding and gap formation more slowly, thus allowing greater opportunity for force transfer and evidence of the differences in stress production among the three composites. The Z100/two-step group had the greatest force transfer among the six groups. In addition, the irradiance of the light source in the two-step activation mode was lower than that for the one-step mode. Others have shown that light sources with lower irradiance produce slower development of polymerization contraction stress and reduced rates of polymerization [32,38]. Though similar tendencies were shown in the statistical results of the propagation length and the stress, the statistical results of the ratio and the gap width did not coincide with the results of the propagation length and the stress (Tables 3–5). Therefore, there were no apparent relationships between the propagation length and the ratio or the width of the crack in this experimental system. A new method to calculate the contraction stress has been proposed. This method can evaluate two clinical phenomena in resin composite restorations, the formation of contraction gaps [39] and cracking in the surrounding “simulated” enamel material [9,40]. Utilizing the indentation fracture technique, which is essentially non-destructive, it is possible to calculate the stresses at certain points in the surrounding material simultaneously and to understand the stress distribution around the composite restoration. The proposed indentation method has advantages in comparison with other stress analyses such as photoelastic analysis or strain gage methods [41,42]. The photoelastic material is not appropriate for the “simulated” enamel because the elastic modulus of the photoelastic material is much lower than that of enamel. The strain gage requires a gage bonding area that is wider than the dimension of the indentation and the cracks in this method. Thus, the indentation method can measure stress magnitudes over a much smaller area. In addition, the method only requires a conventional hardness tester and a measuring microscope. A limitation of this method is that a prescribed distance between the cavity edge and the indentation is required to avoid chipping of the cavity edge during indentation. The distance is determined by the edge strength of surrounding matrix [43]. In order to simplify the stress distribution around the composite, a ceramic material was used as the surrounding
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substrate in this study. The magnitude of contraction stress in tooth tissue is likely to be different from that in the ceramic because of a difference in elastic modulus and compliance [30]. Further investigations using natural teeth are required to obtain a better understanding of composite resin contraction stress in tooth tissue.
5.
Conclusion
Contraction stresses generated by curing dental resin composites are sufficient to cause propagation of cracks from flaws existing in a surrounding brittle material. The proposed method for the stress calculation using indentation crack extension is a simple technique requiring only a conventional hardness tester and can evaluate two clinical phenomena of the composite restoration, that is, enamel cracking and interfacial contraction gap formation.
references
[1] Park J-W, Ferracane JL. Measuring the residual stress in dental composites using a ring slitting method. Dent Mater 2005;21:882–9. [2] Pearson GJ, Hegarty SM. Cusp movement of molar teeth with composite filling materials in conventional and modified MOD cavities. Br Dent J 1989;166:162–5. [3] Suliman AA, Boyer DB, Lakes RS. Cusp movement in premolars resulting from composite polymerization shrinkage. Dent Mater 1993;9:6–10. [4] Tantbirojn D, Versluis A, Pintado MR, DeLong R, Douglas WH. Tooth deformation patterns in molars after composite restoration. Dent Mater 2004;20:535–42. [5] Asmussen E. Composite restorative resins. Composition versus wall-to-wall polymerization contraction. Acta Odontol Scand 1975;33:337–44. [6] Munksgaard EC, Irie M, Asmussen E. Dentin-polymer bond promoted by Gluma and various resins. J Dent Res 1985;64:1409–11. [7] Irie M, Suzuki K, Watts DC. Marginal gap formation of light-activated restorative materials: effects of immediate setting shrinkage and bond strength. Dent Mater 2002;18:203–10. [8] Kanca J, Suh BI. Pulse activation: reducing resin-based composite contraction stresses at the enamel cavosurface margins. Am J Dent 1999;12:107–12. [9] Jørgensen KD, Asmussen E, Shimokobe H. Enamel damages caused by contracting restorative resins. Scand J Dent Res 1975;83:120–2. [10] Lawn BR, Swain MV. Microfracture beneath point indentations in brittle solids. J Mater Sci 1975;10:113–22. [11] Niihara K, Morena R, Hasselman DPH. Evaluation of K1c of brittle solids by the indentation method with low crack-to-indent ratios. J Mater Sci Lett 1982;1:13–6. [12] Lardner TJ, Ritter JE, Shiao ML, Lin MR. Behavior of indentation cracks near free surfaces and interfaces. Int J Fracture 1990;44:133–43. [13] Anstis GR, Chantikul P, Lawn BR, Marshall DB. A critical evaluation of indentation techniques for measuring fracture toughness. I. Direct crack measurements. J Am Ceram Soc 1981;64:533–8. [14] Maehara S, Fujishima A, Hotta Y, Miyazaki T. Fracture toughness measurement of dental ceramics using the indentation fracture method with different formulas. Dent Mater J 2005;24:328–34.
549
[15] Sakar-Deliormanli A, Güden M. Microhardness and fracture toughness of dental materials by indentation method. J Biomed Mater Res Part B: Appl Biomater 2006;76B:257–64. [16] Quinn GD, Bradt RC. On the Vickers indentation fracture toughness test. J Am Ceram Soc 2007;90:673–80. [17] Marshall DB, Lawn BR. An indentation technique for measuring stresses in tempered glass surfaces. J Am Ceram Soc 1977;60:86–7. [18] Niihara K. Indentation microfracture of ceramics—its application and problems. Ceram Jpn 1985;20:12–8. [19] JSMS-SD-4-01. Residual stress measurement for engineering ceramics by indentation fracture method. The Society of Material Science Japan (JSMS) Committee on Fatigue of Materials, Kyoto, Japan, 2001. [20] Fisher H, Marx R. Fracture toughness of dental ceramics: comparison of bending and indentation method. Dent Mater 2002;18:12–9. [21] Taskonak B, Mecholsky Jr JJ, Anusavice KJ. Residual stress in bilayer dental ceramics. Biomaterials 2005;26:3235–41. [22] Yamamoto T, Nishiura R. Marginal toughness of bonded dental ceramics evaluated by determination of the crack length. J Dent 2006;34:146–54. [23] Lawn BR, Wilshaw TR. Indentation fracture: principles and applications. J Mater Sci 1975;10:1049–81. [24] Marshall DB, Lawn BR. Residual stress effects in sharp contact cracking. Part 1. Indentation fracture mechanics. J Mater Sci 1979;14:2001–12. [25] Anusavice KJ. Dental ceramics. In: Anusavice KJ, editor. Phillips’ science of dental materials. tenth edition Philadelphia: W.B. Saunders Company; 1996. p. 583–618. [26] Darvell BW. Griffith’s law. In: Darvell BW, editor. Material science for dentistry. sixth edition Pokfulam: BW Darvell; 2000. p. 20–1. [27] Hata Y, Suzuki H, Iijima H, Yamazaki H, Iwashita H, Hakamatsuka Y, et al. Preparation and properties of castable ceramics (OCC). J Jpn Prosthodont Soc 1988;32:52–61. [28] Yamamoto T, Takamizu M, Kohno A. Influence of residual surface investment material on crystallization shrinkage of a mica-based glass-ceramic. Dent Mater 2002;18:336–42. [29] Hassan R, Caputo AA, Bunshah RF. Fracture toughness of human enamel. J Dent Res 1981;60:820–7. [30] Xu HHK, Smith DT, Jahanmir S, Romberg E, Kelly JR, Thompson VP, et al. Indentation damage and mechanical properties of human enamel and dentin. J Dent Res 1998;77:472–80. [31] Wuttiphan S, Lawn BR, Padture NP. Crack suppression in strongly bonded homogeneous/heterogeneous laminates: a study on glass/glass-ceramic bilayers. J Am Ceram Soc 1996;79:634–40. [32] Lim B-S, Ferracane JL, Sakaguchi RL, Condon JR. Reduction of polymerization stress for dental composites by two-step light-activation. Dent Mater 2002;18:436–44. [33] de Andrade OS, de Goes MF, Montes MAJR. Marginal adaptation and microtensile bond strength of composite indirect restorations bonded to dentin treated with adhesive and low-viscosity composite. Dent Mater 2007;23:279–87. [34] Lawn BR. Indentation cracks as controlled flaws: inert strength, toughness, and T-curves. In: Davis EA, Ward IM, editors. Fracture of brittle solids. second edition Cambridge: Cambridge University Press; 1993. p. 263–76. [35] Xu HHK, Jahanmir S. Simple technique for observing subsurface damage in machining of ceramics. J Am Ceram Soc 1994;77:1388–90. [36] Xu HHK, Smith DT, Jahanmir S. Influence of microstructure on indentation and machining of dental glass-ceramics. J Mater Res 1996;11:2325–37. [37] Xu HHK, Kelly JR, Jahanmir S, Thompson VP, Rekow ED. Enamel subsurface damage due to tooth preparation with diamonds. J Dent Res 1997;76:1698–706.
550
d e n t a l m a t e r i a l s 2 5 ( 2 0 0 9 ) 543–550
[38] Watts DC, Cash AJ. Determination of polymerization shrinkage kinetics in visible-light-cured materials: methods development. Dent Mater 1991;7:281–7. [39] Davidson CL, de Gee AJ. Relaxation of polymerization contraction stresses by flow in dental composites. J Dent Res 1984;63:146–8. [40] Hilton TJ, Broome JC. Direct posterior esthetic restorations. In: Summitt JB, et al., editors. Fundamentals of operative dentistry: a contemporary approach. third edition Hanover Park: Quintessence Publishing Co., Inc.; 2006. p. 289–339.
[41] Kinomoto Y, Torii M. Photoelastic analysis of polymerization contraction stresses in resin composite restorations. J Dent 1998;26:165–71. [42] Sakaguchi RL, Ferracane JL. Stress transfer from polymerization shrinkage of a chemical-cured composite bonded to a pre-cast composite substrate. Dent Mater 1998;14:106–11. [43] Watts DC, Issa M, Ibrahim A, Wakiaga J, Al-Samadani K, Al-Azraqi M, et al. Edge strength of resin-composite margins. Dent Mater 2008;24:129–33.