JJOD 2411 1–8 journal of dentistry xxx (2015) xxx–xxx
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.intl.elsevierhealth.com/journals/jden 1 2 3
Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite
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Q1
Yuanyuan Duan, Jason A. Griggs * Department of Biomedical Materials Science, University of Mississippi Medical Center, MS, USA
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article info
abstract
Article history:
Objectives: Further investigations are required to evaluate the mechanical behaviour of
Received 14 August 2014
newly developed polymer–matrix composite (PMC) blocks for computer-aided design/com-
Received in revised form
puter-aided manufacturing (CAD/CAM) applications. The purpose of this study was to
14 January 2015
investigate the effect of elasticity on the stress distribution in dental crowns made of
Accepted 16 January 2015
glass–ceramic and PMC materials using finite element (FE) analysis.
Available online xxx
Methods: Elastic constants of two materials were determined by ultrasonic pulse velocity using an acoustic thickness gauge. Three-dimensional solid models of a full-coverage dental
Keywords:
crown on a first mandibular molar were generated based on X-ray micro-CT scanning
Dental crowns
images. A variety of load case-material property combinations were simulated and con-
Dental ceramics
ducted using FE analysis. The first principal stress distribution in the crown and luting agent
CAD/CAM
was plotted and analyzed.
Finite element method
Results: The glass–ceramic crown had stress concentrations on the occlusal surface surrounding the area of loading and the cemented surface underneath the area of loading, while the PMC crown had only stress concentration on the occlusal surface. The PMC crown had lower maximum stress than the glass–ceramic crown in all load cases, but this difference was not substantial when the loading had a lateral component. Eccentric loading did not substantially increase the maximum stress in the prosthesis. Conclusions: Both materials are resistant to fracture with physiological occlusal load. The PMC crown had lower maximum stress than the glass–ceramic crown, but the effect of a lateral loading component was more pronounced for a PMC crown than for a glass–ceramic crown. Clinical significance: Knowledge of the stress distribution in dental crowns with low modulus of elasticity will aid clinicians in planning treatments that include such restorations. # 2015 Published by Elsevier Ltd.
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* Corresponding author at: Department of Biomedical Materials Science, University of Mississippi Medical Center, 2500N State Street, Q2 Jackson, MS 39216, USA. Tel.: ++1 601 984 6170; fax: +1 601 984 6087.
E-mail address: [email protected] (J.A. Griggs). http://dx.doi.org/10.1016/j.jdent.2015.01.008 0300-5712/# 2015 Published by Elsevier Ltd.
Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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1.
Introduction
Q3 CAD/CAM technology has been increasingly used to fabricate
dental prostheses in recent years. It resulted in new restorative materials that would otherwise have been infeasible to use in the dental market where every part must be custom fitted. These materials, such as zirconia, glass–ceramic and heat-cured resin-based composites, usually requires a very long processing time in a well-controlled environment. In addition to the ceramic blocks, which are more frequently used for CAD/CAM applications, composite resinbased blocks have been developed. There are several advantages of fabricating resin composites as CAD/CAM blocks compared to traditional resin composites that are polymerized in situ. Firstly, a greater filler volume fraction can be achieved, which results in greater mechanical durability.1 A smaller filler particle size can be used without adversely affecting the filler volume fraction. Smaller particle size decreases undesirable opacity and the roughness of polished surfaces.2 Secondly, a greater degree of cure can be achieved, which decreases elution of toxic or estrogenic unreacted ingredients and increases mechanical durability.3 The curing shrinkage that provides an obstacle to the dimensional accuracy of direct restorations is not present for indirect restorations. There are also some advantages of resin composite blocks over conventional ceramic blocks. They are more easily adjusted, milled and repaired. Micro-tensile bond strength testing showed that resin composite has higher bond strength to resin-based adhesive materials than to glass–ceramics.4 It was also been found that resin composite caused a significantly lower volume loss on antagonist enamel than ceramics did in two-body wear testing, which may help to preserve the functional balance of dentition.5 In light of these advantages, it is not surprising that attempts would be made to substitute highly filled composite CAD/CAM blocks for ceramic blocks in fabricating fullcoverage prostheses. Lava Ultimate (3M ESPE) is one example, and other similar products are soon expected on the market.6 It has a variety of indications for permanent single-tooth restorations such as inlays, onlays, veneers and crowns supported either by natural tooth or dental implant. In vitro testing compared Lava Ultimate to CAD/CAM ceramics favourably in terms of monotonic failure load7–9 and showed performance similar to veneering ceramics in fatigue loading.10 However, dental composites have a discontinuous ceramic phase, and so are limited to much lower elastic modulus values than glass–ceramic materials. It has been found that thin-walled crowns made of low elastic modulus material (composite resin) are more prone to debonding than those made of stiffer materials such as ceramics and gold alloy.11 While thin-walled crowns of stiffer materials can protect tooth structures from damage better than composite resin ones. This lack of stiffness may result in increased stress levels under the same bite force compared to glass–ceramic restorations, eventually leading to a compromised long-term clinical performance. In the absence of long-term clinical data or a reasonable in vitro simulation of clinical conditions, manufacturers must be
cautious in specifying the indications for their new products. Unfortunately, the first simulation of fatigue loading for Lava Ultimate crowns employed a hard indenter and high loading levels, which resulted in a failure mode that is rarely observed in the clinic.12 Failure originated adjacent to the point of loading instead of at the cemented surfaces of the crowns. Two subsequent simulations had stiff substrates that did not simulate the clinical case.13,14 Further investigations are still needed to analyze and evaluate the biomechanical behaviour of this new type of CAD/CAM composite material over ceramic ones. Finite element analysis (FEA) is a powerful and flexible computational tool to model dental structures and devices, simulate the occlusal loading conditions and predict the stress and strain distribution. It has been widely used in the dental and medical fields since the 1970s and has been proven to be accurate and efficient for finding solutions for complex geometry problems.15,16 Therefore, the present study was aimed at constructing FE models for a full-coverage dental crown, comparing the stress distribution between one CAD/ CAM composite material and glass–ceramic under various loading scenarios, and revealing the effect of material stiffness on the biomechanical performance of the dental crown. The following hypotheses were tested: (1) when a dental crown with the elastic modulus of a highly cured nano-filled resin composite is loaded vertically and centrally with an average human bite force, it will develop similar first principal stress compared to a prosthesis with the elastic modulus of a glass–ceramic material; (2) when the applied load has a lateral component, the maximum stress in the prosthesis will be similar to that for a vertical load; and (3) when the applied load is eccentric, the maximum stress in the prosthesis will be similar to that for a centric load.
2.
Methods
2.1.
Material selection
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In this study, IPS e.max CAD (Ivoclar-Vivadent) was selected as the model material for the glass–ceramic crown. It is a lithium disilicate glass–ceramic block for CAD/CAM use. Partially crystalized IPS e.max CAD contains of 40% lithium metasilicate crystals. The grain size of the crystals is in the range of 0.2–1.0 mm. The microstructure of end-crystalized IPS e.max CAD consists of approximately 70% lithium disilicate crystals (Li2Si2O5), which are embedded in a glassy matrix. Lava Ultimate (3M ESPE) was selected as the model material for the polymer–matrix composite (PMC) crown. It is a composite block for CAD/CAM use containing silica particles of 20 nm diameter and zirconia particles of 4–11 nm diameter.
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2.2.
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Determination of elastic constants
The Young’s modulus of elasticity and the Poisson’s ratio for the two materials were determined by ultrasonic pulse velocity using an acoustic thickness gauge (25-DL Plus, Panametrics) according to ASTM E494 (n = 4). The following equations were used to calculate Poisson’s ratio (m) and Young’s modulus (E) for each material:
Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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m¼
1 2ðvs =vl Þ2 2 2ðvs =vl Þ2
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E¼
rv2s ð3v2l 4v2s Þ v2l v2s
where r is the bulk density, vl is the velocity of longitudinal wave pulses passing through the material, and vs is the velocity of shear wave pulses passing through the material. The bulk density was determined by Archimedes’ method using the following equation: Wdry ðrwater rair Þ þ rair r¼ 0:99983ðWdry Wsusp Þ
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where Wdry is the dry weight of the specimen, Wsusp is the weight of the specimen measured while suspended in deionized water, rwater is the density of deionized water at the temperature measured during the experiment, rair is the density of air (0.0012 g/mL), and the constant 0.99983 is a correction factor to account for the buoyancy of the apparatus.
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2.3.
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A stone model of a mandibular first molar was prepared for a full-coverage crown according to the guidelines of the prosthetic material manufacturers. The preparation included a 1.5-mm occlusal reduction, a 1.0-mm axial reduction, a 6degree angle of taper, a 1-mm circular shoulder, and a 100-mm thick cement layer. The crown preparation was captured in 3D using an in-EOS scanner (Sirona), and a crown was milled from an IPS e.max CAD block (Ivoclar-Vivadent) using a CEREC MCXL milling unit (Sirona) and crystalized in a Multimat Touch and Press furnace (Dentsply) by following the manufacturer’s instructions.
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The crown specimen was scanned using micro-CT (Skyscan 1172, Microphotonics) with an image pixel size of 18.7 mm and
Preparation of test specimen
Solid modelling
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an operating voltage of 70 kV. The raw projection images were then reconstructed using Nrecon software (Microphotonics). The reconstruction was exported as transverse sections in a stack of bitmap files, which were imported to ScanIP software (Simpleware). Segmentation of different materials was carried out in ScanIP by thresholding based on radiolucency (Fig. 1, left). The cement layer was created by Boolean subtraction instead of thresholding to ensure a uniform 100 mm thickness. The solid model was meshed in the +FE module (Simpleware) using 10-node tetrahedral (C3D10) elements (Fig. 1, right), and the model was exported to Abaqus software for FE calculation (Simulia).
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2.5.
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FE analysis
The finite element model was solved in Abaqus under a variety of load case-material property combinations. The nodes on the bottom surface of the abutment tooth were constrained with displacement of zero in three directions. The two crown materials were assigned using the values determined by the method mentioned above. The dentine was assigned a Young’s modulus of 14.5 GPa and a Poisson’s ratio of 0.30. The luting agent was assigned a Young’s modulus of 8.3 GPa and a Poisson’s ratio of 0.24.17 All materials were modelled as a homogeneous, linearly elastic and isotropic to reduce the work load in this study. The following loading situations were examined respectively: (1) Load applied at average human bite force (100 N) or maximum human bite force (600 N); (2) Load applied at an angle of 08 or 308 to the long axis of the tooth; (3) Load applied in the central fossa or on the slope of the distal– Q4 buccal cusp (Fig. 2). For each combination of experimental factor levels, the distribution of the first principal stress and the maximum stress value were determined. Subsequent iterations of mesh refinement were conducted to ensure that the solution converged on a limiting value for each case. The simulated bite force was distributed across 1114–1311 nodes. The number of nodes varied because of mesh refinement for the
Fig. 1 – (Left) Isometric view of solid model prepared using ScanIP. (Right) Cross-sectional view of finite element mesh prepared using ScanIP for export to Abaqus. Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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Fig. 2 – Isometric view of solid model showing location of load application on the distal–buccal cusp for eccentric loading.
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convergence test, but the nodes were the same for both crown materials in each load case.
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2.6.
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Student’s t-test (a = 0.05) was used to compare the glass– ceramic material and the resin composite material in terms of density and elastic constants.
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Table 1 summarizes the estimates of bulk density and elastic constants that were determined for the CAD and the PMC materials. The measurements were precise, having less than 5% coefficient of variation (standard deviation/mean) in all cases and less than 1% CV in most cases. Student’s t-tests showed that the PMC material had significantly lower density (p < 0.001), significantly lower Young’s modulus (p < 0.001), and significantly higher Poisson’s ratio (p < 0.001) compared with the CAD material.
Statistical analysis
Results and discussion
Successive iterations of mesh refinement (from 172 K elements to 2.2 M elements) were used to test independence of the solution from the meshing algorithm as demonstrated by convergence of the first principal stress at the location of maximum stress. The graph in Fig. 3 shows that the solution was convergent for both crown materials. Fig. 4 uses contour plots to illustrate the stress distributions resulting from a 600 N vertical centric load in a CAD (left) and a PMC crown (right). The distributions differ substantially. The CAD crown has stress concentration in two locations: (1) the occlusal surface surrounding the area of loading and (2) the cemented surface underneath the area of loading. The PMC crown has only one location of stress concentration (the occlusal surface). The stress is concentrated into a smaller volume for the CAD crown compared with the PMC crown in the axial loading case. However, the stress concentration occurs within a similar volume for both crown materials in the oblique centric loading case. Fig. 5 uses contour plots to illustrate the case of a 600 N oblique load (308 angle to the long axis of the tooth). For oblique loading, the stress concentration shifted towards the occlusal surface for both crown materials. Table 2 summarizes the maximum stress for each of eight combinations of experimental factors, except for load location. There is a linear relationship between load level and maximum stress across the range of loads studied (100–600 N) for every combination of loading direction and crown material. This indicates that the maximum stress at any intermediate load level can be obtained accurately by interpolation without the need for constructing and solving additional finite element load cases. Compared to the flexural strength data of the two materials provided by manufacturers, which are 204 MPa for Lava Ultimate and 360 MPa for e.max CAD, both materials had a maximum stress lower than their strength with physiological occlusal loads.5,18 This suggests that both materials are resistant to fracture under normal mastication. The maximum stress in the PMC crown is lower than that in the CAD crown for each load case. Therefore, the first hypothesis was rejected. This is probably caused by the low stiffness of the PMC material acting to reduce the maximum stress level in two ways: (1) the stiffness of the PMC crown more closely matches those of the dentine substrate and the
Table 1 – Mean (standard deviation) of results obtained from measuring ultrasonic pulse velocity.
Bulk density, r (g/mL) Poisson’s ratio, l Young’s modulus, E (GPa)
CAD
PMC
2.450 (0.010) 0.213 (0.002) 101.9 (0.6)
1.963 (0.004) 0.257 (0.012) 19.45 (0.29)
Fig. 3 – Convergence test for the first principal stress at the location of maximum stress resulting from a 100 N centric vertical load.
Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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Q9 Fig. 4 – Contour plots illustrating the distribution of first
principal stress for a 600 N centric vertical load applied to a CAD crown (top) and a PMC crown (bottom). ‘Hot colours’ represent high stress, and ‘cold colours’ represent low stress. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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luting agent. This would be expected to lead to less stress concentration at the interface between the materials. (2) The compliance of the PMC crown would be expected to distribute loads over a large volume of crown material. However, the stress in the PMC crown is a much greater proportion of the modulus of rupture (MOR) compared with the stress-to-MOR proportion for the CAD crown. This suggests that the glass– ceramic crown would have longer fatigue lifetime, but it is not possible to draw such a conclusion without conducting a fatigue study. There was an interactive effect of crown material with direction of load application. Loading with a lateral component resulted in higher maximum stress for both crown materials. Therefore, the second hypothesis was accepted. This indicates that the crown may be more susceptible to fracture from lateral occlusal forces, possibly due to lack of support from supporting tissues and bone. It is interesting to note that the effect of a lateral component was much smaller for the CAD crown (16% increase in stress for a 308 angle) compared with the PMC crown (81% increase in stress). Moving the location of loading from the central fossa to the distal–buccal cusp did not substantially alter the magnitude of the maximum stress (Table 3). Therefore, the third hypothesis was rejected. The maximum stress in the CAD crown increased slightly from the centric loading case to the eccentric loading case. The stress distribution and location
Fig. 5 – Contour plots illustrating the distribution of first principal stress for a 600 N centric oblique load applied to a CAD crown (top) and a PMC crown (bottom). ‘Hot colours’ represent high stress, and ‘cold colours’ represent low stress. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 2 – First principal stress (MPa) at the location of maximum stress for each combination of three experimental factors (bite force, loading direction, crown material) that were studied. Total load
100 N 600 N
Centric vertical loading
Centric oblique loading
CAD
PMC
CAD
PMC
18.85 113.1
11.48 68.9
21.78 130.7
20.75 124.5
Table 3 – First principal stress (MPa) at the location of maximum stress in the prosthesis for each combination of three experimental factors (loading location, crown material). Total load
100 N
Centric vertical loading
Eccentric vertical loading
CAD
PMC
CAD
PMC
18.85
11.48
22.59
7.92
of maximum stress – the intaglio (cemented) surface – were the same regardless of the location of load application. The maximum stress in the PMC crown decreased slightly from
Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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Fig. 6 – Convergence test for the first principal stress at the location of maximum stress resulting from a 100 N eccentric vertical load.
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the centric loading case to the eccentric loading case. The stress distribution and location of maximum stress, which is the occlusal surface adjacent to the region of load application, were the same regardless of the location of load application. The maximum stress in the PMC crown was less than that in the CAD crown for both load cases. This finding supports previous in vitro studies that showed PMC specimens to have higher or equal failure load compared to CAD/CAM ceramic specimens when tested under monotonic loading.7–9
Fig. 7 – Contour plots illustrating the distribution of first principal stress for a 100 N eccentric vertical load applied to a CAD crown (top) and a PMC crown (bottom). ‘Hot colours’ represent high stress, and ‘cold colours’ represent low stress. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6 shows that the maximum stress converged with successive iterations of mesh refinement, which indicates that magnitude of maximum stress is numerically accurate, given that all modelling assumptions were valid (Figs. 7 and 8, Q5 and Table 4). One assumption made was that the dentine substrate and the restorative materials were homogeneous. Since the inhomogeneity of the material nano/micro-structure is several orders of magnitude smaller than the features of the crown preparation, the assumption of homogeneity likely did not affect the results of this study. Another assumption was that the materials were isotropic. However, dentine is known to be anisotropic with the long axis of the dentinal tubules being approximately perpendicular to the interface with the prosthesis. It is conceivable that the assumption of isotropy may have affected the results. One might speculate that modelling the dentine substrate with greater stiffness perpendicular and less stiffness parallel to the cemented surface would have resulted in greater stress in the prosthesis for cases of oblique loading. A third assumption was that the materials were linearly elastic. This is probably a valid assumption for the synthetic materials because they do not contain continuous fibres/crystals, but dentine contains continuous tubules and thus may be nonlinearly elastic. If
Fig. 8 – Contour plots illustrating the distribution of first principal stress on the surface of the prosthesis for a 100 N eccentric vertical load applied to a CAD crown. (Top) The location of maximum stress (intaglio surface) of CAD crown. (Bottom) The location of maximum stress (occlusal surface) of PMC crown. ‘Hot colours’ represent high stress, and ‘cold colours’ represent low stress. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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Table 4 – First principal stress (MPa) at the location of maximum stress in the luting agent. Total load
100 N
Eccentric vertical loading CAD
PMC
4.13
6.98
Fig. 9 – Convergence test for the first principal stress at the location of maximum stress in the luting agent resulting from a 100 N eccentric vertical load.
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the stiffness of dentine increases with increasing strain, then one might speculate that this would result in lower stress in both prosthetic materials than predicted by the linearly elastic model. The maximum stress in the luting agent underneath the crown was not substantially affected by the stiffness of the crown when the location of load application was on the distal– buccal cusp and the loading direction was vertical. Fig. 9 shows that the magnitude of maximum stress converged for successive iterations of mesh refinement. However, the assumptions that are made in modelling a luting agent are more numerous and more likely to be invalid than the assumptions made in modelling the prosthesis. The FE model assumes that the dentine underneath the luting agent is homogeneous and has no voids between it and the luting agent. Another assumption about the model is that the luting agent does not plastically deform. In light of these numerous assumptions, testing any hypothesis regarding a luting agent Q6 based solely on FEA is not advisable (Fig. 10).
4.
Conclusions
Within the confines of the experimental factors investigated and the assumptions that were made in modelling, the following conclusions can be drawn:
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(1) The distribution of stress was not dependent on the bite force. (2) Introducing a lateral component to the load increased the maximum stress. (3) The effect of a lateral loading component was more pronounced for a polymer-matrix composite crown than for a glass–ceramic crown. (4) Eccentric loading did not substantially increase the maximum stress in the prosthesis. (5) The PMC crown had lower maximum stress than the glass– ceramic crown, but this difference was not substantial when the loading had a lateral component. Based on the increased stress that the PMC material developed under lateral loading, dental crowns made from this material would probably not be indicated for patients known to exhibit bruxism.
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This study was funded by a research grant from Ivoclar Q8 Q7 Vivadent, Inc..
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Acknowledgement
Fig. 10 – Contour plots illustrating the distribution of first principal stress on the surface of the luting agent for a 100 N eccentric vertical load applied to a (top) CAD crown and (bottom) PMC crown. ‘Hot colours’ represent high stress, and ‘cold colours’ represent low stress. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
references
1. Anusavice KJ. Phillips’ science of dental materials. St. Louis, MO: Saunders; 2003. 2. Marghalani HY. Effect of filler particles on surface roughness of experimental composite series. Journal of Applied Oral Science 2010;18:59–67.
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3. Nandini S. Indirect resin composites. Journal of Conservative Dentistry 2010;13:184–94. 4. El Zohairy AA, De Gee AJ, Mohsen MM, Feilzer AJ. Microtensile bond strength testing of luting cements to prefabricated CAD/CAM ceramic and composite blocks. Dental Materials 2003;19:575–83. 5. Lava Ultimate technical product profile. 2011. 6. Personal communication. 2012. 7. Chen C, Trindade FZ, de Jager N, Kleverlaan CJ, Feilzer AJ. The fracture resistance of a CAD/CAM resin nano ceramic (RNC) and a CAD ceramic at different thicknesses. Dental Materials 2014;30:954–62. 8. El-Damanhoury H, Haj-Ali R, Platt J. Fracture resistance and microleakage of endocrowns utilizing three CAD-CAM [sic] blocks. Operative Dentistry 2014. http://dx.doi.org/10.2341/13-143-L. 9. Ilgenstein I, Zitzmann NU, Bu¨hler J, Wegehaupt FJ, Attin T, Weiger R, et al. Influence of proximal box elevation on the marginal quality and fracture behavior of root-filled molars restored with CAD/CAM ceramic or composite onlays. Clinical Oral Investigations 2014. http://dx.doi.org/10.1007/ s00784-014-1325-z. 10. Belli R, Geinzer E, Muschweck A, Petschelt A, Lohbauer U. Mechanical fatigue degradation of ceramics versus resin composites for dental restorations. Dental Materials 2014;30:424–32. 11. Dejak B, Mlotkowski A, Langot C. Three-dimensional finite element analysis of molars with thin-walled prosthetic
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crowns made of various materials. Dental Materials 2012;28:433–41. Suzuki M, Bonfante EA, Silva NRFA, Thompson V, Coelho PG. Indirect composites as single implant restorations: ultimate strength and reliability. Journal of Dental Research 2012;91:2425. Bonfante EA, Suzuki M, Witek L, Carvalho RM, Marin C, Giro G, et al. Reliability of resin nano ceramic and metal ceramic implant-supported crowns. Journal of Dental Research 2012;91:3246. Carneiro LC, Varpavaara P, Heikinheimo T, Lassila L. Evaluation of onlay fracture load; resin nano ceramic and IPS e.max. Journal of Dental Materials 2012;91:676. Savoldelli C, Tillier Y, Bouchard PO, Odin G. Contribution of the finite element method in maxillofacial surgery. Revuede Stomatologie et de Chirurgie Maxillo-faciale 2009;110:27–33. Van Staden RC, Guan H, Loo YC. Application of the finite element method in dental implant research. Computational Methods in Biomechanics and Biomedical Engineering 2006;9: 257–70. Magne P, Perakis N, Belser UC, Krejci I. Stress distribution of inlay-anchored adhesive fixed partial dentures: a finite element analysis of the influence of restorative materials and abutment preparation design. Journal of Prosthetic Dentistry 2002;87:516–27. IPS emax CAD scientific document. 2005.
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Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.intl.elsevierhealth.com/journals/jden 1 2 3
Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite
4 5
6 7
Q1
Yuanyuan Duan, Jason A. Griggs * Department of Biomedical Materials Science, University of Mississippi Medical Center, MS, USA
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article info
abstract
Article history:
Objectives: Further investigations are required to evaluate the mechanical behaviour of
Received 14 August 2014
newly developed polymer–matrix composite (PMC) blocks for computer-aided design/com-
Received in revised form
puter-aided manufacturing (CAD/CAM) applications. The purpose of this study was to
14 January 2015
investigate the effect of elasticity on the stress distribution in dental crowns made of
Accepted 16 January 2015
glass–ceramic and PMC materials using finite element (FE) analysis.
Available online xxx
Methods: Elastic constants of two materials were determined by ultrasonic pulse velocity using an acoustic thickness gauge. Three-dimensional solid models of a full-coverage dental
Keywords:
crown on a first mandibular molar were generated based on X-ray micro-CT scanning
Dental crowns
images. A variety of load case-material property combinations were simulated and con-
Dental ceramics
ducted using FE analysis. The first principal stress distribution in the crown and luting agent
CAD/CAM
was plotted and analyzed.
Finite element method
Results: The glass–ceramic crown had stress concentrations on the occlusal surface surrounding the area of loading and the cemented surface underneath the area of loading, while the PMC crown had only stress concentration on the occlusal surface. The PMC crown had lower maximum stress than the glass–ceramic crown in all load cases, but this difference was not substantial when the loading had a lateral component. Eccentric loading did not substantially increase the maximum stress in the prosthesis. Conclusions: Both materials are resistant to fracture with physiological occlusal load. The PMC crown had lower maximum stress than the glass–ceramic crown, but the effect of a lateral loading component was more pronounced for a PMC crown than for a glass–ceramic crown. Clinical significance: Knowledge of the stress distribution in dental crowns with low modulus of elasticity will aid clinicians in planning treatments that include such restorations. # 2015 Published by Elsevier Ltd.
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* Corresponding author at: Department of Biomedical Materials Science, University of Mississippi Medical Center, 2500N State Street, Q2 Jackson, MS 39216, USA. Tel.: ++1 601 984 6170; fax: +1 601 984 6087.
E-mail address: [email protected] (J.A. Griggs). http://dx.doi.org/10.1016/j.jdent.2015.01.008 0300-5712/# 2015 Published by Elsevier Ltd.
Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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1.
Introduction
Q3 CAD/CAM technology has been increasingly used to fabricate
dental prostheses in recent years. It resulted in new restorative materials that would otherwise have been infeasible to use in the dental market where every part must be custom fitted. These materials, such as zirconia, glass–ceramic and heat-cured resin-based composites, usually requires a very long processing time in a well-controlled environment. In addition to the ceramic blocks, which are more frequently used for CAD/CAM applications, composite resinbased blocks have been developed. There are several advantages of fabricating resin composites as CAD/CAM blocks compared to traditional resin composites that are polymerized in situ. Firstly, a greater filler volume fraction can be achieved, which results in greater mechanical durability.1 A smaller filler particle size can be used without adversely affecting the filler volume fraction. Smaller particle size decreases undesirable opacity and the roughness of polished surfaces.2 Secondly, a greater degree of cure can be achieved, which decreases elution of toxic or estrogenic unreacted ingredients and increases mechanical durability.3 The curing shrinkage that provides an obstacle to the dimensional accuracy of direct restorations is not present for indirect restorations. There are also some advantages of resin composite blocks over conventional ceramic blocks. They are more easily adjusted, milled and repaired. Micro-tensile bond strength testing showed that resin composite has higher bond strength to resin-based adhesive materials than to glass–ceramics.4 It was also been found that resin composite caused a significantly lower volume loss on antagonist enamel than ceramics did in two-body wear testing, which may help to preserve the functional balance of dentition.5 In light of these advantages, it is not surprising that attempts would be made to substitute highly filled composite CAD/CAM blocks for ceramic blocks in fabricating fullcoverage prostheses. Lava Ultimate (3M ESPE) is one example, and other similar products are soon expected on the market.6 It has a variety of indications for permanent single-tooth restorations such as inlays, onlays, veneers and crowns supported either by natural tooth or dental implant. In vitro testing compared Lava Ultimate to CAD/CAM ceramics favourably in terms of monotonic failure load7–9 and showed performance similar to veneering ceramics in fatigue loading.10 However, dental composites have a discontinuous ceramic phase, and so are limited to much lower elastic modulus values than glass–ceramic materials. It has been found that thin-walled crowns made of low elastic modulus material (composite resin) are more prone to debonding than those made of stiffer materials such as ceramics and gold alloy.11 While thin-walled crowns of stiffer materials can protect tooth structures from damage better than composite resin ones. This lack of stiffness may result in increased stress levels under the same bite force compared to glass–ceramic restorations, eventually leading to a compromised long-term clinical performance. In the absence of long-term clinical data or a reasonable in vitro simulation of clinical conditions, manufacturers must be
cautious in specifying the indications for their new products. Unfortunately, the first simulation of fatigue loading for Lava Ultimate crowns employed a hard indenter and high loading levels, which resulted in a failure mode that is rarely observed in the clinic.12 Failure originated adjacent to the point of loading instead of at the cemented surfaces of the crowns. Two subsequent simulations had stiff substrates that did not simulate the clinical case.13,14 Further investigations are still needed to analyze and evaluate the biomechanical behaviour of this new type of CAD/CAM composite material over ceramic ones. Finite element analysis (FEA) is a powerful and flexible computational tool to model dental structures and devices, simulate the occlusal loading conditions and predict the stress and strain distribution. It has been widely used in the dental and medical fields since the 1970s and has been proven to be accurate and efficient for finding solutions for complex geometry problems.15,16 Therefore, the present study was aimed at constructing FE models for a full-coverage dental crown, comparing the stress distribution between one CAD/ CAM composite material and glass–ceramic under various loading scenarios, and revealing the effect of material stiffness on the biomechanical performance of the dental crown. The following hypotheses were tested: (1) when a dental crown with the elastic modulus of a highly cured nano-filled resin composite is loaded vertically and centrally with an average human bite force, it will develop similar first principal stress compared to a prosthesis with the elastic modulus of a glass–ceramic material; (2) when the applied load has a lateral component, the maximum stress in the prosthesis will be similar to that for a vertical load; and (3) when the applied load is eccentric, the maximum stress in the prosthesis will be similar to that for a centric load.
2.
Methods
2.1.
Material selection
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In this study, IPS e.max CAD (Ivoclar-Vivadent) was selected as the model material for the glass–ceramic crown. It is a lithium disilicate glass–ceramic block for CAD/CAM use. Partially crystalized IPS e.max CAD contains of 40% lithium metasilicate crystals. The grain size of the crystals is in the range of 0.2–1.0 mm. The microstructure of end-crystalized IPS e.max CAD consists of approximately 70% lithium disilicate crystals (Li2Si2O5), which are embedded in a glassy matrix. Lava Ultimate (3M ESPE) was selected as the model material for the polymer–matrix composite (PMC) crown. It is a composite block for CAD/CAM use containing silica particles of 20 nm diameter and zirconia particles of 4–11 nm diameter.
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2.2.
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Determination of elastic constants
The Young’s modulus of elasticity and the Poisson’s ratio for the two materials were determined by ultrasonic pulse velocity using an acoustic thickness gauge (25-DL Plus, Panametrics) according to ASTM E494 (n = 4). The following equations were used to calculate Poisson’s ratio (m) and Young’s modulus (E) for each material:
Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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m¼
1 2ðvs =vl Þ2 2 2ðvs =vl Þ2
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E¼
rv2s ð3v2l 4v2s Þ v2l v2s
where r is the bulk density, vl is the velocity of longitudinal wave pulses passing through the material, and vs is the velocity of shear wave pulses passing through the material. The bulk density was determined by Archimedes’ method using the following equation: Wdry ðrwater rair Þ þ rair r¼ 0:99983ðWdry Wsusp Þ
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where Wdry is the dry weight of the specimen, Wsusp is the weight of the specimen measured while suspended in deionized water, rwater is the density of deionized water at the temperature measured during the experiment, rair is the density of air (0.0012 g/mL), and the constant 0.99983 is a correction factor to account for the buoyancy of the apparatus.
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2.3.
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A stone model of a mandibular first molar was prepared for a full-coverage crown according to the guidelines of the prosthetic material manufacturers. The preparation included a 1.5-mm occlusal reduction, a 1.0-mm axial reduction, a 6degree angle of taper, a 1-mm circular shoulder, and a 100-mm thick cement layer. The crown preparation was captured in 3D using an in-EOS scanner (Sirona), and a crown was milled from an IPS e.max CAD block (Ivoclar-Vivadent) using a CEREC MCXL milling unit (Sirona) and crystalized in a Multimat Touch and Press furnace (Dentsply) by following the manufacturer’s instructions.
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2.4.
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The crown specimen was scanned using micro-CT (Skyscan 1172, Microphotonics) with an image pixel size of 18.7 mm and
Preparation of test specimen
Solid modelling
3
an operating voltage of 70 kV. The raw projection images were then reconstructed using Nrecon software (Microphotonics). The reconstruction was exported as transverse sections in a stack of bitmap files, which were imported to ScanIP software (Simpleware). Segmentation of different materials was carried out in ScanIP by thresholding based on radiolucency (Fig. 1, left). The cement layer was created by Boolean subtraction instead of thresholding to ensure a uniform 100 mm thickness. The solid model was meshed in the +FE module (Simpleware) using 10-node tetrahedral (C3D10) elements (Fig. 1, right), and the model was exported to Abaqus software for FE calculation (Simulia).
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2.5.
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FE analysis
The finite element model was solved in Abaqus under a variety of load case-material property combinations. The nodes on the bottom surface of the abutment tooth were constrained with displacement of zero in three directions. The two crown materials were assigned using the values determined by the method mentioned above. The dentine was assigned a Young’s modulus of 14.5 GPa and a Poisson’s ratio of 0.30. The luting agent was assigned a Young’s modulus of 8.3 GPa and a Poisson’s ratio of 0.24.17 All materials were modelled as a homogeneous, linearly elastic and isotropic to reduce the work load in this study. The following loading situations were examined respectively: (1) Load applied at average human bite force (100 N) or maximum human bite force (600 N); (2) Load applied at an angle of 08 or 308 to the long axis of the tooth; (3) Load applied in the central fossa or on the slope of the distal– Q4 buccal cusp (Fig. 2). For each combination of experimental factor levels, the distribution of the first principal stress and the maximum stress value were determined. Subsequent iterations of mesh refinement were conducted to ensure that the solution converged on a limiting value for each case. The simulated bite force was distributed across 1114–1311 nodes. The number of nodes varied because of mesh refinement for the
Fig. 1 – (Left) Isometric view of solid model prepared using ScanIP. (Right) Cross-sectional view of finite element mesh prepared using ScanIP for export to Abaqus. Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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Fig. 2 – Isometric view of solid model showing location of load application on the distal–buccal cusp for eccentric loading.
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convergence test, but the nodes were the same for both crown materials in each load case.
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2.6.
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Student’s t-test (a = 0.05) was used to compare the glass– ceramic material and the resin composite material in terms of density and elastic constants.
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3.
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Table 1 summarizes the estimates of bulk density and elastic constants that were determined for the CAD and the PMC materials. The measurements were precise, having less than 5% coefficient of variation (standard deviation/mean) in all cases and less than 1% CV in most cases. Student’s t-tests showed that the PMC material had significantly lower density (p < 0.001), significantly lower Young’s modulus (p < 0.001), and significantly higher Poisson’s ratio (p < 0.001) compared with the CAD material.
Statistical analysis
Results and discussion
Successive iterations of mesh refinement (from 172 K elements to 2.2 M elements) were used to test independence of the solution from the meshing algorithm as demonstrated by convergence of the first principal stress at the location of maximum stress. The graph in Fig. 3 shows that the solution was convergent for both crown materials. Fig. 4 uses contour plots to illustrate the stress distributions resulting from a 600 N vertical centric load in a CAD (left) and a PMC crown (right). The distributions differ substantially. The CAD crown has stress concentration in two locations: (1) the occlusal surface surrounding the area of loading and (2) the cemented surface underneath the area of loading. The PMC crown has only one location of stress concentration (the occlusal surface). The stress is concentrated into a smaller volume for the CAD crown compared with the PMC crown in the axial loading case. However, the stress concentration occurs within a similar volume for both crown materials in the oblique centric loading case. Fig. 5 uses contour plots to illustrate the case of a 600 N oblique load (308 angle to the long axis of the tooth). For oblique loading, the stress concentration shifted towards the occlusal surface for both crown materials. Table 2 summarizes the maximum stress for each of eight combinations of experimental factors, except for load location. There is a linear relationship between load level and maximum stress across the range of loads studied (100–600 N) for every combination of loading direction and crown material. This indicates that the maximum stress at any intermediate load level can be obtained accurately by interpolation without the need for constructing and solving additional finite element load cases. Compared to the flexural strength data of the two materials provided by manufacturers, which are 204 MPa for Lava Ultimate and 360 MPa for e.max CAD, both materials had a maximum stress lower than their strength with physiological occlusal loads.5,18 This suggests that both materials are resistant to fracture under normal mastication. The maximum stress in the PMC crown is lower than that in the CAD crown for each load case. Therefore, the first hypothesis was rejected. This is probably caused by the low stiffness of the PMC material acting to reduce the maximum stress level in two ways: (1) the stiffness of the PMC crown more closely matches those of the dentine substrate and the
Table 1 – Mean (standard deviation) of results obtained from measuring ultrasonic pulse velocity.
Bulk density, r (g/mL) Poisson’s ratio, l Young’s modulus, E (GPa)
CAD
PMC
2.450 (0.010) 0.213 (0.002) 101.9 (0.6)
1.963 (0.004) 0.257 (0.012) 19.45 (0.29)
Fig. 3 – Convergence test for the first principal stress at the location of maximum stress resulting from a 100 N centric vertical load.
Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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Q9 Fig. 4 – Contour plots illustrating the distribution of first
principal stress for a 600 N centric vertical load applied to a CAD crown (top) and a PMC crown (bottom). ‘Hot colours’ represent high stress, and ‘cold colours’ represent low stress. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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luting agent. This would be expected to lead to less stress concentration at the interface between the materials. (2) The compliance of the PMC crown would be expected to distribute loads over a large volume of crown material. However, the stress in the PMC crown is a much greater proportion of the modulus of rupture (MOR) compared with the stress-to-MOR proportion for the CAD crown. This suggests that the glass– ceramic crown would have longer fatigue lifetime, but it is not possible to draw such a conclusion without conducting a fatigue study. There was an interactive effect of crown material with direction of load application. Loading with a lateral component resulted in higher maximum stress for both crown materials. Therefore, the second hypothesis was accepted. This indicates that the crown may be more susceptible to fracture from lateral occlusal forces, possibly due to lack of support from supporting tissues and bone. It is interesting to note that the effect of a lateral component was much smaller for the CAD crown (16% increase in stress for a 308 angle) compared with the PMC crown (81% increase in stress). Moving the location of loading from the central fossa to the distal–buccal cusp did not substantially alter the magnitude of the maximum stress (Table 3). Therefore, the third hypothesis was rejected. The maximum stress in the CAD crown increased slightly from the centric loading case to the eccentric loading case. The stress distribution and location
Fig. 5 – Contour plots illustrating the distribution of first principal stress for a 600 N centric oblique load applied to a CAD crown (top) and a PMC crown (bottom). ‘Hot colours’ represent high stress, and ‘cold colours’ represent low stress. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 2 – First principal stress (MPa) at the location of maximum stress for each combination of three experimental factors (bite force, loading direction, crown material) that were studied. Total load
100 N 600 N
Centric vertical loading
Centric oblique loading
CAD
PMC
CAD
PMC
18.85 113.1
11.48 68.9
21.78 130.7
20.75 124.5
Table 3 – First principal stress (MPa) at the location of maximum stress in the prosthesis for each combination of three experimental factors (loading location, crown material). Total load
100 N
Centric vertical loading
Eccentric vertical loading
CAD
PMC
CAD
PMC
18.85
11.48
22.59
7.92
of maximum stress – the intaglio (cemented) surface – were the same regardless of the location of load application. The maximum stress in the PMC crown decreased slightly from
Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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Fig. 6 – Convergence test for the first principal stress at the location of maximum stress resulting from a 100 N eccentric vertical load.
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the centric loading case to the eccentric loading case. The stress distribution and location of maximum stress, which is the occlusal surface adjacent to the region of load application, were the same regardless of the location of load application. The maximum stress in the PMC crown was less than that in the CAD crown for both load cases. This finding supports previous in vitro studies that showed PMC specimens to have higher or equal failure load compared to CAD/CAM ceramic specimens when tested under monotonic loading.7–9
Fig. 7 – Contour plots illustrating the distribution of first principal stress for a 100 N eccentric vertical load applied to a CAD crown (top) and a PMC crown (bottom). ‘Hot colours’ represent high stress, and ‘cold colours’ represent low stress. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6 shows that the maximum stress converged with successive iterations of mesh refinement, which indicates that magnitude of maximum stress is numerically accurate, given that all modelling assumptions were valid (Figs. 7 and 8, Q5 and Table 4). One assumption made was that the dentine substrate and the restorative materials were homogeneous. Since the inhomogeneity of the material nano/micro-structure is several orders of magnitude smaller than the features of the crown preparation, the assumption of homogeneity likely did not affect the results of this study. Another assumption was that the materials were isotropic. However, dentine is known to be anisotropic with the long axis of the dentinal tubules being approximately perpendicular to the interface with the prosthesis. It is conceivable that the assumption of isotropy may have affected the results. One might speculate that modelling the dentine substrate with greater stiffness perpendicular and less stiffness parallel to the cemented surface would have resulted in greater stress in the prosthesis for cases of oblique loading. A third assumption was that the materials were linearly elastic. This is probably a valid assumption for the synthetic materials because they do not contain continuous fibres/crystals, but dentine contains continuous tubules and thus may be nonlinearly elastic. If
Fig. 8 – Contour plots illustrating the distribution of first principal stress on the surface of the prosthesis for a 100 N eccentric vertical load applied to a CAD crown. (Top) The location of maximum stress (intaglio surface) of CAD crown. (Bottom) The location of maximum stress (occlusal surface) of PMC crown. ‘Hot colours’ represent high stress, and ‘cold colours’ represent low stress. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: Duan Y, Griggs JA. Effect of elasticity on stress distribution in CAD/CAM dental crowns: Glass ceramic vs. polymer–matrix composite. Journal of Dentistry (2015), http://dx.doi.org/10.1016/j.jdent.2015.01.008
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Table 4 – First principal stress (MPa) at the location of maximum stress in the luting agent. Total load
100 N
Eccentric vertical loading CAD
PMC
4.13
6.98
Fig. 9 – Convergence test for the first principal stress at the location of maximum stress in the luting agent resulting from a 100 N eccentric vertical load.
7
the stiffness of dentine increases with increasing strain, then one might speculate that this would result in lower stress in both prosthetic materials than predicted by the linearly elastic model. The maximum stress in the luting agent underneath the crown was not substantially affected by the stiffness of the crown when the location of load application was on the distal– buccal cusp and the loading direction was vertical. Fig. 9 shows that the magnitude of maximum stress converged for successive iterations of mesh refinement. However, the assumptions that are made in modelling a luting agent are more numerous and more likely to be invalid than the assumptions made in modelling the prosthesis. The FE model assumes that the dentine underneath the luting agent is homogeneous and has no voids between it and the luting agent. Another assumption about the model is that the luting agent does not plastically deform. In light of these numerous assumptions, testing any hypothesis regarding a luting agent Q6 based solely on FEA is not advisable (Fig. 10).
4.
Conclusions
Within the confines of the experimental factors investigated and the assumptions that were made in modelling, the following conclusions can be drawn:
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(1) The distribution of stress was not dependent on the bite force. (2) Introducing a lateral component to the load increased the maximum stress. (3) The effect of a lateral loading component was more pronounced for a polymer-matrix composite crown than for a glass–ceramic crown. (4) Eccentric loading did not substantially increase the maximum stress in the prosthesis. (5) The PMC crown had lower maximum stress than the glass– ceramic crown, but this difference was not substantial when the loading had a lateral component. Based on the increased stress that the PMC material developed under lateral loading, dental crowns made from this material would probably not be indicated for patients known to exhibit bruxism.
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This study was funded by a research grant from Ivoclar Q8 Q7 Vivadent, Inc..
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Acknowledgement
Fig. 10 – Contour plots illustrating the distribution of first principal stress on the surface of the luting agent for a 100 N eccentric vertical load applied to a (top) CAD crown and (bottom) PMC crown. ‘Hot colours’ represent high stress, and ‘cold colours’ represent low stress. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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