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Influence of resin cement polymerization shrinkage on stresses in porcelain crowns
d e n t a l m a t e r i a l s 2 9 ( 2 0 1 3 ) 1073–1079
Available online at www.sciencedirect.com
journal homepage: www.intl.elsevierhealth.com/journals/dema
Influence of resin cement polymerization shrinkage on stresses in porcelain crowns Liliana G. May a,∗ , J. Robert Kelly b a b
Department of Restorative Dentistry, Federal University of Santa Maria, Santa Maria, RS, Brazil Reconstructive Sciences, University of Connecticut Health Center, Farmington, CT, USA
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objective. The aim of this study was to analyze the influence of polymerization shrinkage
Received 26 October 2012
of the cement layer on stresses within feldspathic ceramic crowns, using experimentally
Received in revised form 5 May 2013
validated FEA models for (1) increasing occlusal cement thickness; and, (2) bonded versus
Accepted 24 July 2013
non-bonded ceramic-cement interfaces. Methods. 2-D axial symmetric models simulated stylized feldspathic crowns (1.5 mm occlusal thickness) cemented with resin-cement layers of 50–500 m on dentin preparations, being
Keywords:
loaded (500 N) or not. Ceramic–cement interface was either bonded or not. Cement was
Polymerization shrinkage
bonded to the dentin in all models. Maximum axial shrinkage of 0%, 1%, 2%, 3%, 4% and
Cement thickness
4.65% were simulated. The first principal stresses developing in the cementation surface at
Tensile stress
the center and at the occluso-axial line-angle of the crown were registered.
FEA
Results. Polymerization shrinkage of the cement increased tensile stresses in the ceramic,
Ceramic crowns
especially in loaded non-bonded crowns for thicker cement layers. Stresses in loaded nonbonded crowns increased as much as 87% when cement shrinkage increased from 0% to 4.65% (100–187 MPa), for a 500 m-thick cement. Increasing polymerization shrinkage strain raised the tensile stresses, especially at the internal occlusal-axial line-angle, for bonded crowns. Significance. Changes in the polymerization shrinkage strain (from 0% to 4.65%) have little effect on the tensile stresses generated at the cementation surface of the ceramic crowns, when the occlusal cement thickness is thin (approx. 50 m for bonded crowns). However, as the cement becomes thicker stresses within the ceramic become significant. © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Bonding between the ceramic surface and the cement has become a fundamental practice in restorative dentistry, largely due to two clinical studies of crowns and inlays
[1,2]. Some in vitro studies have suggested that adhesive composite cements can improve not only the bond strength but also the fracture strength of ceramic restorations [3–5]. One of the main concerns about composite cements is their volumetric shrinkage, which can lead to stress generation
∗ Corresponding author at: Department of Restorative Dentistry, Prosthodontics Division, School of Dentistry, Federal University of Santa Maria, Marechal Floriano Peixoto St, 1184, 97015-372, Santa Maria, RS, Brazil. Tel.: +55 55 3220 9276; fax: +55 55 3220 9272. E-mail addresses: [email protected], [email protected] (L.G. May). 0109-5641/$ – see front matter © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.dental.2013.07.018
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d e n t a l m a t e r i a l s 2 9 ( 2 0 1 3 ) 1073–1079
Fig. 1 – Sketch lines and dimensions for the axial-symmetric models prepared in SolidWorks® 2009 for the cement thicknesses of (a) 50 m (0.05 mm) and (b) 500 m (0.5 mm).
within restorative cavities, materials and can lead to bonding failures. The volumetric shrinkage of four chemically cured resin cements dental cements has been reported to vary from 1.69% to 4.62% [6]. For six dual resin cements, the shrinkage strain ranged from 1.77% to 5.28% when the cements were selfcured and from 4.10% to 5.29% when they were dual-cured [7]. Residual stress developing during polymerization is a multi-factorial phenomenon, determined by their volumetric shrinkage, visco-elastic behavior and by restrictions imposed to polymerization shrinkage [8]. These factors are often described by the bonded/free surfaces ratio (c-factor) [9], bonding strength to the substrate walls [10] and hardening vs. time-dependent viscosity of the composite [11]. High C-factor values (>25) may be of concern as shrinkage can cause the development of significant polymerization stresses and can lead to “spontaneous” cohesive failures [11]. Small plastic deformations [12] and low shrinkage stresses [9] have been observed in very thin layers of resin cement. However, the cement mass also plays a dominant role in the shrinkage stresses within luting gaps [9,13]. The greater mass of material (or the thicker the cement layer), the higher the polymerization stresses [13]. Recently, an study showed the importance of polymerization shrinkage being included in FEA models with increasing occlusal cement thickness; bonded and nonbonded ceramic–cement interface [14]. Based on the available literature it is hypothesized that the amount of cement shrinkage, depending on the percentage of
contraction and on the cement mass, plays a role in the tensile stresses generated within ceramic crowns. Therefore, the aim of this study was to analyze the influence increasing percentage of cement shrinkage on the stresses within feldspathic ceramic crowns, for a range of occlusal cement thickness (50–500 m) having bonded and non-bonded ceramic-cement interfaces, using experimentally validated FEA models.
2.
Materials and methods
Axial-symmetric drawings (dentin preparation, cement layer, crown and truncated-conical indenter) for cement thicknesses of 50 m, 100 m, 300 m and 500 m, were created (Fig. 1), using Solidworks® 2009 (Dassault Systèmes Solidworks Corp., Vélizy-Villacoublay, France). The *.dxf drawing files were imported as CAD files to COMSOL Multiphysics® (Comsol Inc, Burlington, MA, USA). COMSOL Multiphysics® was used for stress analyses of 2-D axial symmetric models simulating stylized feldspathic crowns (1.5 mm occlusal thickness) with different occlusal cement thickness, under 0 N or 500 N loading (2 mm diameter piston). Ceramic–cement interfaces were either bonded or not. Cement was bonded to the dentin in all models. The cement–ceramic interface was considered either “bonded” (nodes coupled for displacement) or “non-bonded” (independent nodes at the interface). Contact pairs were created for piston-ceramic and “non-bonded” ceramic–cement interface boundaries, with no gap and no friction. The
d e n t a l m a t e r i a l s 2 9 ( 2 0 1 3 ) 1073–1079
Table 1 – Material elastic properties used in the FEA models (E = elastic modulus and = Poisson’s ratio). Material Piston/preparation Resin cement Feldspathic ceramic a b c
Elastic modulus, E (GPa) 14.9a 6.3b 64c
Poisson’s ratio, 0.31* 0.35* 0.25*
Digital library (Solidworks Corp., Lowell, MA, USA). Binmahfooz and Nathanson [29]. Fischer et al. [30].
constraints of displacement were: the bottom boundary of the dentin preparation was set to “fixed” in the three axis of displacement; boundaries in r = 0 (central axis) were set to “axial symmetry”; compressive distributed loading was applied on the top boundary of the indenter (500 N), for loaded models. The other object boundaries had free displacement. The material properties were defined according to Table 1. For shrinkage, the sub-domain “cement” was set to include thermal expansion, in which the final and initial temperature resulted in a negative temperature gradient (T). Maximum axial shrinkage-strain of 4.65%, observed for the resin cement Multilink Automix® [7], was used as a reference for finding the T necessary to shrink the cement. A disk with the same dimensions used for this study (∅ = 8 mm; h = 1 mm) and the same elastic properties of the cement layer (Table 1) were
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modeled in COMSOL Multiphysics® . The maximum shrinkage of 1%, 2%, 3%, 4% and 4.65% (in the center of the cement disk) was obtained by T of −72 K, −144 K, −214 K, −280 K, and −327 K, for a thermal expansion coefficient, ˛, set at 70 × 10−6 ). Then, the different T, necessary for obtaining the different shrinkages, where applied to the cement layer under crowns (see above described models). For those models without cement shrinkage, the thermal expansion option was not included. Triangular second order elements were used. Maximum element sizes for the cement varied from 0.025 mm to 0.20 mm, in order to obtain 3 layers of elements for each cement thickness. Meshing was controlled through free mesh parameters and the final mesh size was determined by convergence testing, testing gradually finer meshes. Maximum element size of 0.1 mm for ceramic was chosen since FEA presented reasonable solution times and all analyzed models had reached convergence (less than 3% solution change for a maximum element size of 0.05 mm). The first principal stresses were analyzed in the cementation surface of the ceramic crowns (at the central site, where the crowns are expected to fail from, when axially loaded, and at the internal occlusal axial angle, where the stresses concentrate due to shrinkage polymerization). Fig. 2 illustrates two FEA solutions. FEA models used in this study were experimentally validated in a former study [14], using the cement Multilink
Fig. 2 – FEA solution for the 1st principal stresses (MPa) generated in loaded bonded ceramic crowns: (a) no cement shrinkage and (b) cement shrinkage of 4.65%.
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Table 2 – 1st principal stresses (MPa) generated at the cementation surface of bonded crowns (center and occlusal-axial line-angle), for different cement thicknesses and maximum axial shrinkage (%). Thickness (m)
Site
Center 50 Line-angle
Center 100 Line-angle
Center 300 Line-angle
Center 500 Line-angle
0%
1%
2%
3%
4%
4.65%
Loaded Unloaded Loaded Unloaded
57 0 0.1 0
57.8 1.0 11.6 11.9
58.7 2.0 23.5 23.9
59.6 3.0 35.0 35.5
60.3 3.8 45.9 46.3
62.3 4.5 53.6 54.2
Loaded Unloaded Loaded Unloaded
60.5 0 −0.1 0
62.3 1.4 15.4 15.9
62.9 2.8 31.3 31.8
64.7 4.2 46.8 47.3
65.1 5.4 61.4 61.9
67.4 6.7 71.8 72.4
Loaded Unloaded Loaded Unloaded
69.8 0 −0.3 0
73.4 3.9 31.1 31.6
78 7.8 66.0 63.1
80.1 11.6 97.1 94.0
84.5 15.6 126.8 123.1
87.6 17.8 148.0 143.9
Loaded Unloaded Loaded Unloaded
75.4 0 −0.4 0
82.8 7.6 39.8 40.9
91.7 14.9 80.5 81.8
98.6 22.8 120.1 121.5
104.3 29.5 157.3 158.8
110.4 34.1 183.8 185.4
Automix® (Ivoclar Vivadent, Liechtenstein) (4.65% of maximum shrinkage) for bonded and non-bonded crowns and cement thickness range of 50 m to 500 m, as it is shown in Fig. 3. Stress data were analyzed by linear regression (Minitab® , State College, PA, USA) and tensile stresses vs. shrinkage slopes for bonded and non-bonded crowns were compared by the F-test.
3.
1st principal stresses (MPa)
Loading condition
Results
First principal stresses due to cement shrinkage at the cementation surface of bonded and non-bonded crowns are presented at Tables 2 and 3 and Figs. 4 and 5. Increasing polymerization shrinkage from 0% to 4.65% raised the tensile stresses, especially at the internal occlusal-axial line-angle. The stresses also increased with the cement thickness.
Fig. 3 – Experimental and predicted failure loads in CAD/CAM ceramic crowns. Used with permission from May et al. [14].
Table 3 – 1st principal stresses (MPa) generated at the center of the cementation surface of non-bonded loaded crowns, for different cement thicknesses and maximum axial shrinkage (%). 1st principal stresses (MPa)
Thickness (m)
50 100 300 500
0%
1%
2%
3%
4%
88.5 92.7 92.8 100
89.4 95.9 103.6 118.5
89.6 99.1 116.5 141.9
90.5 103.4 130.7 171.3
91.8 106.6 147.8 186.8
4.65% 93.7 107.8 159.4 187.6
For bonded crowns (Table 2), the shrinkage caused an increase in the tensile stresses from 0 to 34 MPa, in the center of the ceramic crown, when the cement was 500 m thick (unloaded row, Table 2). At the internal occlusal-axial lineangle, the stresses increased from 0 to 185.4 MPa for the same cement thickness (unloaded row, Table 2). Looking at the internal occlusal-axial line-angle of bonded crowns, for a maximum axial strain of 4.65%, stresses became
Fig. 4 – FEA tensile stresses (MPa) at the center of the cementation surface of bonded and non-bonded feldspathic crowns with different cement thicknesses, due to increasing axial shrinkage % and loading (500 N).
d e n t a l m a t e r i a l s 2 9 ( 2 0 1 3 ) 1073–1079
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Fig. 5 – FEA tensile stresses (MPa) at the center of the cementation surface in ceramic crowns due to the increasing axial shrinkage % and loading: comparison between slopes for bonded (B) and non-bonded (NB) crowns with 50 m, 100 m, 300 m and 500 m of occlusal resin cement thickness. r = Pearson’s coefficient; P-value = significance level.
critical (>76.5 MPa [15]) when the occlusal cement layer reaches thickness values between 100 and 300 m. In other words, when the cement layer was shifted to 500 m, a small shrinkage of 2% caused tensile stresses (81.8 MPa) high enough for failure. The tensile stresses generated due to the cement shrinkage variation were more pronounced for loaded non-bonded ceramic crowns with thicker cement layers (Table 3). Increasing tensile stresses in the central cementation surface, from 100 MPa to 187 MPa (Table 3), occurred when the shrinkage in a cement layer of 500 m was increased from 0% to 4.65%. When the loading effect was considered in addition to the effect of polymerization shrinkage, bonded crowns with a 500 m-thick cement layer, shrinking 4.65%, presented higher stresses (110 MPa), than non-bonded crowns with the same thickness of cement, without shrinkage (100 MPa) (Fig. 4). For cement layers thicker than 100 m, the stress versus shrinkage slope was statistically steeper for non-bonded crowns than for bonded crowns (Fig. 5).
4.
Discussion
It has been recently demonstrated that shrinkage stresses can influence bonded porcelain resistance-to-fracture due to tensile stresses exerted on the porcelain surface during cement contraction; and/or due to gaps associated with debonding between cement and ceramic surfaces [14]. In the present study, an axial shrinkage of 4.65%, which was reported by Spinell et al. [7] for a dual resin cement, was compared to
hypothetically smaller shrinkages (1%, 2%, 3% and 4%) and to no shrinkage (0%), in order to measure their potential effect on the stresses in feldspathic ceramic crowns. The maximum axial shrinkage strain was chosen as the parameter for shrinkage simulation, since previous studies show that in thin layers, nearly all-volumetric contraction is directed in only one direction, perpendicular to the walls [10,16]. The misfit range of 50–500 m, investigated in the current study was based in literature reports, showing that the internal occlusal misfits of milled crowns can vary enormously both within a single system and among different CAD/CAM systems. An average occlusal space centered on 100–200 m is quite common [17–20], but wide ranging occlusal misfits of 24 m and 634 m can occur beneath cusp tips and central fossa [21] and misfits as large as 1316 m [22] have also been reported. Mean occlusal misfits values of 215–300 m; with standard deviations of 50–100 m, were observed depending on marginal preparation design for one ceramic milled by a popular CAD/CAM machine [23]. FEA is a powerful tool that can help dental and materials scientists to model and predict clinical and experimental situations. However, it is important that these mathematical models have experimental validation. This study uses FEA models validated in a previous work [14]. Increasing polymerization shrinkage produced increasing tensile stresses in the cementation surface of the ceramic crowns. For bonded crowns (Table 2), in which the stresses are resisted by the crown’s internal surface, increasing shrinkage from 0% to 4.65% caused an increase in the tensile stresses from 0 MPa to 34 MPa when the cement was 500-m-thick.
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For crowns bonded to thinner cement layers of 50 m, the polymerization shrinkage variation had a small influence in developing tensile stress in the center of the cementation surface (0–4.5 MPa). However, when the occlusal-axial line-angle is analyzed in bonded crowns, the tensile stresses rose greatly, reaching 72 MPa for 4.65% of shrinkage for a cement thickness of 100 m and 143 MPa for a 300 m thick cement. Considering that the critical tensile stress for a feldspathic ceramic under a 2 mm diameter piston is 76.5 MPa [15], an occlusal cement thicker than 100 m could cause tensile stresses high enough for failure from the internal line-angle. However, it must be noted that no stress reliving mechanisms were included in the FEA modeling. These high tensile stresses due to cement shrinkage beneath ceramic crowns are influenced by two main factors: 1) volume of the cement, which is related to the varying occlusal cement thickness and 2) cavity configuration or bonded/free surface ratio (c-factor). When a composite polymerizes and is free to shrink, a greater volume will result in greater amount of shrinkage, measured either volumetrically or linearly. The cavity configuration or bonded/free surface ratio (c-factor) can restrict the free cement flowing during polymerization [9,11]. A greater restriction implies that the volume diminution or linear reduction will be smaller during the polymerization, but higher stresses will be generated [9,10,16]. These stresses are transmitted along the bonded surfaces and depending on the restoration compliance and cavity walls, a certain amount of stresses can be compensated [11,16,24]. If the cavity walls compliance is not enough to compensate theses stresses, loss of bonding between cement and restoration or between cement and cavity core can occur or tensile stresses will be transmitted to these walls. In the current study, the highest tensile stresses in bonded crowns were caused by 4.65% shrinkage of a 500 m thick cement. According to Watts and Satterthwaite [9], gap formation is influenced by shrinkage percentage and cement volume. Their observation is consistent with our results. The thicker the layer the larger the stress concentration at the periphery of the adhesive interface, making thicker layers more liable to fail adhesively [25]. According De Jager et al. [26], hindering of the transverse contraction has to be taken into account in studying the mechanical properties of luting cements, because they can develop severe shear forces at the adhesive interfaces when they are loaded in tensile or compression, increasing the probability of bonding failure. Gaps between feldspathic crowns and cement were observed by SEM, for cement layers of 300 and 500 m [14], and at dentin-cement interfaces at the cavity floors under ceramic inlays [27]. When the shrinkage is constrained by bonding to crown materials having limited compliance, shrinkage stresses are generated. According to Davidson and Feilzer [24], in this kind of situation, some kind of fracture may occur to compensate the volume reduction of the shrinking material. Therefore, the tensile stresses caused by polymerization shrinkage can also be potentially harmful to the structural durability of bonded ceramic restorations, especially for crack initiation at the internal line-angles. Cracks originating from the internal line-angle of feldspathic crowns were
experimentally observed for occlusal cement thicknesses of 500 m [14]. The effect of the shrinkage was more pronounced for loaded non-bonded ceramic crowns with thicker cement layers. When the cement shrinkage was increased from 0% to 4.65% in a cement layer of 500 m, the tensile stresses in the center of the cementation surface of loaded, nonbonded crowns increased from 100 MPa to 187 MPa (Table 3). For cement layers thicker than 100 m, stress vs. shrinkage slopes were statistically steeper for non-bonded crowns than for bonded crowns (Fig. 5). If there is no bond between the cement and ceramic, shrinkage is unconstrained in the direction of the cavity wall, creating a gap, leading to a lack of support and consequently higher tensile stresses in loaded non-bonded crowns (Table 2). This finding possibly indicates one factor behind the increased clinical success of “bonded” crowns. For the cement thickness of 500 m, when loading was added to the effect of 4.65% shrinkage, tensile stress below the piston at the internal surface of bonded crowns was 110 MPa; while for no cement shrinkage non-bonded crowns presented 100 MPa at the same site (Fig. 2). This indicates that the increasing ceramic stresses due to polymerization shrinkage of thick layers of cement, such as 500 m, may overcome the protective effect of bonding. Once the cement thickness under machined ceramic crowns reach values close to or higher than 500 m (see e.g., [17,21,22]), this study shows that the research and development of low shrinkage composites for ceramic crowns luting are very relevant, in order to contribute to their structural performance. Overall, this analysis reinforces the modeling and physical testing of May et al. [14] finding that the most durable all-ceramic crown is one that (1) is bonded (cement–ceramic) and (2) the cement layer is thin (approx. 50 m). Such a thin cement layer is much less influential in developing tensile stresses in ceramic crowns as the cement shrinkage is increased. These findings have implications both for clinicians as well as those in the International Standards Organization Technical Committee 106 (Dentistry) who are attempting to develop standards for CAD/CAM processes and prostheses. These findings also raise the issue of transitioning away from cements with polymerization shrinkage and to those having higher elastic modulus. Interestingly, the protective ability (i.e. “bonding”) of zinc phosphate cement was recently reported to equal that of a resin-based cement in fatigue testing of an alumina-based crown having a specific surface treatment [28]. This indicates that nonshrinking cements can structurally protect crowns during loading via a mechanism that will be the subject of future study.
5.
Conclusion
Increasing polymerization shrinkage influences the tensile stresses in the cementation surface of ceramic crowns. The effect is more pronounced for thicker cement layers and for loaded, non-bonded crowns.
d e n t a l m a t e r i a l s 2 9 ( 2 0 1 3 ) 1073–1079
The polymerization shrinkage has a little effect on the tensile stresses generated at the cementation surface of the ceramic crowns, when the occlusal cement thickness is 50 m for non-bonded crowns and 50 or 100 m for bonded crowns. However, it becomes important for the stresses generation as the cement becomes thicker. Increasing polymerization shrinkage from 0 to 4.65% raised the tensile stresses, especially at the internal occlusal axial angle, for bonded crowns. When the cement under ceramic crowns is equal to or thicker than 100 m, tensile stresses due to loading are more influenced by the polymerization shrinkage in non-bonded crowns than in bonded crowns.
references
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Available online at www.sciencedirect.com
journal homepage: www.intl.elsevierhealth.com/journals/dema
Influence of resin cement polymerization shrinkage on stresses in porcelain crowns Liliana G. May a,∗ , J. Robert Kelly b a b
Department of Restorative Dentistry, Federal University of Santa Maria, Santa Maria, RS, Brazil Reconstructive Sciences, University of Connecticut Health Center, Farmington, CT, USA
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objective. The aim of this study was to analyze the influence of polymerization shrinkage
Received 26 October 2012
of the cement layer on stresses within feldspathic ceramic crowns, using experimentally
Received in revised form 5 May 2013
validated FEA models for (1) increasing occlusal cement thickness; and, (2) bonded versus
Accepted 24 July 2013
non-bonded ceramic-cement interfaces. Methods. 2-D axial symmetric models simulated stylized feldspathic crowns (1.5 mm occlusal thickness) cemented with resin-cement layers of 50–500 m on dentin preparations, being
Keywords:
loaded (500 N) or not. Ceramic–cement interface was either bonded or not. Cement was
Polymerization shrinkage
bonded to the dentin in all models. Maximum axial shrinkage of 0%, 1%, 2%, 3%, 4% and
Cement thickness
4.65% were simulated. The first principal stresses developing in the cementation surface at
Tensile stress
the center and at the occluso-axial line-angle of the crown were registered.
FEA
Results. Polymerization shrinkage of the cement increased tensile stresses in the ceramic,
Ceramic crowns
especially in loaded non-bonded crowns for thicker cement layers. Stresses in loaded nonbonded crowns increased as much as 87% when cement shrinkage increased from 0% to 4.65% (100–187 MPa), for a 500 m-thick cement. Increasing polymerization shrinkage strain raised the tensile stresses, especially at the internal occlusal-axial line-angle, for bonded crowns. Significance. Changes in the polymerization shrinkage strain (from 0% to 4.65%) have little effect on the tensile stresses generated at the cementation surface of the ceramic crowns, when the occlusal cement thickness is thin (approx. 50 m for bonded crowns). However, as the cement becomes thicker stresses within the ceramic become significant. © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Bonding between the ceramic surface and the cement has become a fundamental practice in restorative dentistry, largely due to two clinical studies of crowns and inlays
[1,2]. Some in vitro studies have suggested that adhesive composite cements can improve not only the bond strength but also the fracture strength of ceramic restorations [3–5]. One of the main concerns about composite cements is their volumetric shrinkage, which can lead to stress generation
∗ Corresponding author at: Department of Restorative Dentistry, Prosthodontics Division, School of Dentistry, Federal University of Santa Maria, Marechal Floriano Peixoto St, 1184, 97015-372, Santa Maria, RS, Brazil. Tel.: +55 55 3220 9276; fax: +55 55 3220 9272. E-mail addresses: [email protected], [email protected] (L.G. May). 0109-5641/$ – see front matter © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.dental.2013.07.018
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Fig. 1 – Sketch lines and dimensions for the axial-symmetric models prepared in SolidWorks® 2009 for the cement thicknesses of (a) 50 m (0.05 mm) and (b) 500 m (0.5 mm).
within restorative cavities, materials and can lead to bonding failures. The volumetric shrinkage of four chemically cured resin cements dental cements has been reported to vary from 1.69% to 4.62% [6]. For six dual resin cements, the shrinkage strain ranged from 1.77% to 5.28% when the cements were selfcured and from 4.10% to 5.29% when they were dual-cured [7]. Residual stress developing during polymerization is a multi-factorial phenomenon, determined by their volumetric shrinkage, visco-elastic behavior and by restrictions imposed to polymerization shrinkage [8]. These factors are often described by the bonded/free surfaces ratio (c-factor) [9], bonding strength to the substrate walls [10] and hardening vs. time-dependent viscosity of the composite [11]. High C-factor values (>25) may be of concern as shrinkage can cause the development of significant polymerization stresses and can lead to “spontaneous” cohesive failures [11]. Small plastic deformations [12] and low shrinkage stresses [9] have been observed in very thin layers of resin cement. However, the cement mass also plays a dominant role in the shrinkage stresses within luting gaps [9,13]. The greater mass of material (or the thicker the cement layer), the higher the polymerization stresses [13]. Recently, an study showed the importance of polymerization shrinkage being included in FEA models with increasing occlusal cement thickness; bonded and nonbonded ceramic–cement interface [14]. Based on the available literature it is hypothesized that the amount of cement shrinkage, depending on the percentage of
contraction and on the cement mass, plays a role in the tensile stresses generated within ceramic crowns. Therefore, the aim of this study was to analyze the influence increasing percentage of cement shrinkage on the stresses within feldspathic ceramic crowns, for a range of occlusal cement thickness (50–500 m) having bonded and non-bonded ceramic-cement interfaces, using experimentally validated FEA models.
2.
Materials and methods
Axial-symmetric drawings (dentin preparation, cement layer, crown and truncated-conical indenter) for cement thicknesses of 50 m, 100 m, 300 m and 500 m, were created (Fig. 1), using Solidworks® 2009 (Dassault Systèmes Solidworks Corp., Vélizy-Villacoublay, France). The *.dxf drawing files were imported as CAD files to COMSOL Multiphysics® (Comsol Inc, Burlington, MA, USA). COMSOL Multiphysics® was used for stress analyses of 2-D axial symmetric models simulating stylized feldspathic crowns (1.5 mm occlusal thickness) with different occlusal cement thickness, under 0 N or 500 N loading (2 mm diameter piston). Ceramic–cement interfaces were either bonded or not. Cement was bonded to the dentin in all models. The cement–ceramic interface was considered either “bonded” (nodes coupled for displacement) or “non-bonded” (independent nodes at the interface). Contact pairs were created for piston-ceramic and “non-bonded” ceramic–cement interface boundaries, with no gap and no friction. The
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Table 1 – Material elastic properties used in the FEA models (E = elastic modulus and = Poisson’s ratio). Material Piston/preparation Resin cement Feldspathic ceramic a b c
Elastic modulus, E (GPa) 14.9a 6.3b 64c
Poisson’s ratio, 0.31* 0.35* 0.25*
Digital library (Solidworks Corp., Lowell, MA, USA). Binmahfooz and Nathanson [29]. Fischer et al. [30].
constraints of displacement were: the bottom boundary of the dentin preparation was set to “fixed” in the three axis of displacement; boundaries in r = 0 (central axis) were set to “axial symmetry”; compressive distributed loading was applied on the top boundary of the indenter (500 N), for loaded models. The other object boundaries had free displacement. The material properties were defined according to Table 1. For shrinkage, the sub-domain “cement” was set to include thermal expansion, in which the final and initial temperature resulted in a negative temperature gradient (T). Maximum axial shrinkage-strain of 4.65%, observed for the resin cement Multilink Automix® [7], was used as a reference for finding the T necessary to shrink the cement. A disk with the same dimensions used for this study (∅ = 8 mm; h = 1 mm) and the same elastic properties of the cement layer (Table 1) were
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modeled in COMSOL Multiphysics® . The maximum shrinkage of 1%, 2%, 3%, 4% and 4.65% (in the center of the cement disk) was obtained by T of −72 K, −144 K, −214 K, −280 K, and −327 K, for a thermal expansion coefficient, ˛, set at 70 × 10−6 ). Then, the different T, necessary for obtaining the different shrinkages, where applied to the cement layer under crowns (see above described models). For those models without cement shrinkage, the thermal expansion option was not included. Triangular second order elements were used. Maximum element sizes for the cement varied from 0.025 mm to 0.20 mm, in order to obtain 3 layers of elements for each cement thickness. Meshing was controlled through free mesh parameters and the final mesh size was determined by convergence testing, testing gradually finer meshes. Maximum element size of 0.1 mm for ceramic was chosen since FEA presented reasonable solution times and all analyzed models had reached convergence (less than 3% solution change for a maximum element size of 0.05 mm). The first principal stresses were analyzed in the cementation surface of the ceramic crowns (at the central site, where the crowns are expected to fail from, when axially loaded, and at the internal occlusal axial angle, where the stresses concentrate due to shrinkage polymerization). Fig. 2 illustrates two FEA solutions. FEA models used in this study were experimentally validated in a former study [14], using the cement Multilink
Fig. 2 – FEA solution for the 1st principal stresses (MPa) generated in loaded bonded ceramic crowns: (a) no cement shrinkage and (b) cement shrinkage of 4.65%.
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Table 2 – 1st principal stresses (MPa) generated at the cementation surface of bonded crowns (center and occlusal-axial line-angle), for different cement thicknesses and maximum axial shrinkage (%). Thickness (m)
Site
Center 50 Line-angle
Center 100 Line-angle
Center 300 Line-angle
Center 500 Line-angle
0%
1%
2%
3%
4%
4.65%
Loaded Unloaded Loaded Unloaded
57 0 0.1 0
57.8 1.0 11.6 11.9
58.7 2.0 23.5 23.9
59.6 3.0 35.0 35.5
60.3 3.8 45.9 46.3
62.3 4.5 53.6 54.2
Loaded Unloaded Loaded Unloaded
60.5 0 −0.1 0
62.3 1.4 15.4 15.9
62.9 2.8 31.3 31.8
64.7 4.2 46.8 47.3
65.1 5.4 61.4 61.9
67.4 6.7 71.8 72.4
Loaded Unloaded Loaded Unloaded
69.8 0 −0.3 0
73.4 3.9 31.1 31.6
78 7.8 66.0 63.1
80.1 11.6 97.1 94.0
84.5 15.6 126.8 123.1
87.6 17.8 148.0 143.9
Loaded Unloaded Loaded Unloaded
75.4 0 −0.4 0
82.8 7.6 39.8 40.9
91.7 14.9 80.5 81.8
98.6 22.8 120.1 121.5
104.3 29.5 157.3 158.8
110.4 34.1 183.8 185.4
Automix® (Ivoclar Vivadent, Liechtenstein) (4.65% of maximum shrinkage) for bonded and non-bonded crowns and cement thickness range of 50 m to 500 m, as it is shown in Fig. 3. Stress data were analyzed by linear regression (Minitab® , State College, PA, USA) and tensile stresses vs. shrinkage slopes for bonded and non-bonded crowns were compared by the F-test.
3.
1st principal stresses (MPa)
Loading condition
Results
First principal stresses due to cement shrinkage at the cementation surface of bonded and non-bonded crowns are presented at Tables 2 and 3 and Figs. 4 and 5. Increasing polymerization shrinkage from 0% to 4.65% raised the tensile stresses, especially at the internal occlusal-axial line-angle. The stresses also increased with the cement thickness.
Fig. 3 – Experimental and predicted failure loads in CAD/CAM ceramic crowns. Used with permission from May et al. [14].
Table 3 – 1st principal stresses (MPa) generated at the center of the cementation surface of non-bonded loaded crowns, for different cement thicknesses and maximum axial shrinkage (%). 1st principal stresses (MPa)
Thickness (m)
50 100 300 500
0%
1%
2%
3%
4%
88.5 92.7 92.8 100
89.4 95.9 103.6 118.5
89.6 99.1 116.5 141.9
90.5 103.4 130.7 171.3
91.8 106.6 147.8 186.8
4.65% 93.7 107.8 159.4 187.6
For bonded crowns (Table 2), the shrinkage caused an increase in the tensile stresses from 0 to 34 MPa, in the center of the ceramic crown, when the cement was 500 m thick (unloaded row, Table 2). At the internal occlusal-axial lineangle, the stresses increased from 0 to 185.4 MPa for the same cement thickness (unloaded row, Table 2). Looking at the internal occlusal-axial line-angle of bonded crowns, for a maximum axial strain of 4.65%, stresses became
Fig. 4 – FEA tensile stresses (MPa) at the center of the cementation surface of bonded and non-bonded feldspathic crowns with different cement thicknesses, due to increasing axial shrinkage % and loading (500 N).
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Fig. 5 – FEA tensile stresses (MPa) at the center of the cementation surface in ceramic crowns due to the increasing axial shrinkage % and loading: comparison between slopes for bonded (B) and non-bonded (NB) crowns with 50 m, 100 m, 300 m and 500 m of occlusal resin cement thickness. r = Pearson’s coefficient; P-value = significance level.
critical (>76.5 MPa [15]) when the occlusal cement layer reaches thickness values between 100 and 300 m. In other words, when the cement layer was shifted to 500 m, a small shrinkage of 2% caused tensile stresses (81.8 MPa) high enough for failure. The tensile stresses generated due to the cement shrinkage variation were more pronounced for loaded non-bonded ceramic crowns with thicker cement layers (Table 3). Increasing tensile stresses in the central cementation surface, from 100 MPa to 187 MPa (Table 3), occurred when the shrinkage in a cement layer of 500 m was increased from 0% to 4.65%. When the loading effect was considered in addition to the effect of polymerization shrinkage, bonded crowns with a 500 m-thick cement layer, shrinking 4.65%, presented higher stresses (110 MPa), than non-bonded crowns with the same thickness of cement, without shrinkage (100 MPa) (Fig. 4). For cement layers thicker than 100 m, the stress versus shrinkage slope was statistically steeper for non-bonded crowns than for bonded crowns (Fig. 5).
4.
Discussion
It has been recently demonstrated that shrinkage stresses can influence bonded porcelain resistance-to-fracture due to tensile stresses exerted on the porcelain surface during cement contraction; and/or due to gaps associated with debonding between cement and ceramic surfaces [14]. In the present study, an axial shrinkage of 4.65%, which was reported by Spinell et al. [7] for a dual resin cement, was compared to
hypothetically smaller shrinkages (1%, 2%, 3% and 4%) and to no shrinkage (0%), in order to measure their potential effect on the stresses in feldspathic ceramic crowns. The maximum axial shrinkage strain was chosen as the parameter for shrinkage simulation, since previous studies show that in thin layers, nearly all-volumetric contraction is directed in only one direction, perpendicular to the walls [10,16]. The misfit range of 50–500 m, investigated in the current study was based in literature reports, showing that the internal occlusal misfits of milled crowns can vary enormously both within a single system and among different CAD/CAM systems. An average occlusal space centered on 100–200 m is quite common [17–20], but wide ranging occlusal misfits of 24 m and 634 m can occur beneath cusp tips and central fossa [21] and misfits as large as 1316 m [22] have also been reported. Mean occlusal misfits values of 215–300 m; with standard deviations of 50–100 m, were observed depending on marginal preparation design for one ceramic milled by a popular CAD/CAM machine [23]. FEA is a powerful tool that can help dental and materials scientists to model and predict clinical and experimental situations. However, it is important that these mathematical models have experimental validation. This study uses FEA models validated in a previous work [14]. Increasing polymerization shrinkage produced increasing tensile stresses in the cementation surface of the ceramic crowns. For bonded crowns (Table 2), in which the stresses are resisted by the crown’s internal surface, increasing shrinkage from 0% to 4.65% caused an increase in the tensile stresses from 0 MPa to 34 MPa when the cement was 500-m-thick.
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For crowns bonded to thinner cement layers of 50 m, the polymerization shrinkage variation had a small influence in developing tensile stress in the center of the cementation surface (0–4.5 MPa). However, when the occlusal-axial line-angle is analyzed in bonded crowns, the tensile stresses rose greatly, reaching 72 MPa for 4.65% of shrinkage for a cement thickness of 100 m and 143 MPa for a 300 m thick cement. Considering that the critical tensile stress for a feldspathic ceramic under a 2 mm diameter piston is 76.5 MPa [15], an occlusal cement thicker than 100 m could cause tensile stresses high enough for failure from the internal line-angle. However, it must be noted that no stress reliving mechanisms were included in the FEA modeling. These high tensile stresses due to cement shrinkage beneath ceramic crowns are influenced by two main factors: 1) volume of the cement, which is related to the varying occlusal cement thickness and 2) cavity configuration or bonded/free surface ratio (c-factor). When a composite polymerizes and is free to shrink, a greater volume will result in greater amount of shrinkage, measured either volumetrically or linearly. The cavity configuration or bonded/free surface ratio (c-factor) can restrict the free cement flowing during polymerization [9,11]. A greater restriction implies that the volume diminution or linear reduction will be smaller during the polymerization, but higher stresses will be generated [9,10,16]. These stresses are transmitted along the bonded surfaces and depending on the restoration compliance and cavity walls, a certain amount of stresses can be compensated [11,16,24]. If the cavity walls compliance is not enough to compensate theses stresses, loss of bonding between cement and restoration or between cement and cavity core can occur or tensile stresses will be transmitted to these walls. In the current study, the highest tensile stresses in bonded crowns were caused by 4.65% shrinkage of a 500 m thick cement. According to Watts and Satterthwaite [9], gap formation is influenced by shrinkage percentage and cement volume. Their observation is consistent with our results. The thicker the layer the larger the stress concentration at the periphery of the adhesive interface, making thicker layers more liable to fail adhesively [25]. According De Jager et al. [26], hindering of the transverse contraction has to be taken into account in studying the mechanical properties of luting cements, because they can develop severe shear forces at the adhesive interfaces when they are loaded in tensile or compression, increasing the probability of bonding failure. Gaps between feldspathic crowns and cement were observed by SEM, for cement layers of 300 and 500 m [14], and at dentin-cement interfaces at the cavity floors under ceramic inlays [27]. When the shrinkage is constrained by bonding to crown materials having limited compliance, shrinkage stresses are generated. According to Davidson and Feilzer [24], in this kind of situation, some kind of fracture may occur to compensate the volume reduction of the shrinking material. Therefore, the tensile stresses caused by polymerization shrinkage can also be potentially harmful to the structural durability of bonded ceramic restorations, especially for crack initiation at the internal line-angles. Cracks originating from the internal line-angle of feldspathic crowns were
experimentally observed for occlusal cement thicknesses of 500 m [14]. The effect of the shrinkage was more pronounced for loaded non-bonded ceramic crowns with thicker cement layers. When the cement shrinkage was increased from 0% to 4.65% in a cement layer of 500 m, the tensile stresses in the center of the cementation surface of loaded, nonbonded crowns increased from 100 MPa to 187 MPa (Table 3). For cement layers thicker than 100 m, stress vs. shrinkage slopes were statistically steeper for non-bonded crowns than for bonded crowns (Fig. 5). If there is no bond between the cement and ceramic, shrinkage is unconstrained in the direction of the cavity wall, creating a gap, leading to a lack of support and consequently higher tensile stresses in loaded non-bonded crowns (Table 2). This finding possibly indicates one factor behind the increased clinical success of “bonded” crowns. For the cement thickness of 500 m, when loading was added to the effect of 4.65% shrinkage, tensile stress below the piston at the internal surface of bonded crowns was 110 MPa; while for no cement shrinkage non-bonded crowns presented 100 MPa at the same site (Fig. 2). This indicates that the increasing ceramic stresses due to polymerization shrinkage of thick layers of cement, such as 500 m, may overcome the protective effect of bonding. Once the cement thickness under machined ceramic crowns reach values close to or higher than 500 m (see e.g., [17,21,22]), this study shows that the research and development of low shrinkage composites for ceramic crowns luting are very relevant, in order to contribute to their structural performance. Overall, this analysis reinforces the modeling and physical testing of May et al. [14] finding that the most durable all-ceramic crown is one that (1) is bonded (cement–ceramic) and (2) the cement layer is thin (approx. 50 m). Such a thin cement layer is much less influential in developing tensile stresses in ceramic crowns as the cement shrinkage is increased. These findings have implications both for clinicians as well as those in the International Standards Organization Technical Committee 106 (Dentistry) who are attempting to develop standards for CAD/CAM processes and prostheses. These findings also raise the issue of transitioning away from cements with polymerization shrinkage and to those having higher elastic modulus. Interestingly, the protective ability (i.e. “bonding”) of zinc phosphate cement was recently reported to equal that of a resin-based cement in fatigue testing of an alumina-based crown having a specific surface treatment [28]. This indicates that nonshrinking cements can structurally protect crowns during loading via a mechanism that will be the subject of future study.
5.
Conclusion
Increasing polymerization shrinkage influences the tensile stresses in the cementation surface of ceramic crowns. The effect is more pronounced for thicker cement layers and for loaded, non-bonded crowns.
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The polymerization shrinkage has a little effect on the tensile stresses generated at the cementation surface of the ceramic crowns, when the occlusal cement thickness is 50 m for non-bonded crowns and 50 or 100 m for bonded crowns. However, it becomes important for the stresses generation as the cement becomes thicker. Increasing polymerization shrinkage from 0 to 4.65% raised the tensile stresses, especially at the internal occlusal axial angle, for bonded crowns. When the cement under ceramic crowns is equal to or thicker than 100 m, tensile stresses due to loading are more influenced by the polymerization shrinkage in non-bonded crowns than in bonded crowns.
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