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Three-dimensional characterization and distribution of fabrication defects in bilayered lithium disilicate glass-ceramic molar crowns Yutao Jian a,1 , Zi-hua He b,1 , Li Dao c,1 , Michael V. Swain d , Xin-ping Zhang e , Ke Zhao c,∗ a
Institute of Stomatological Research, Guangdong Provincial Key Laboratory of Stomatology, Sun Yat-sen University, Guangzhou, China b Department of Prosthodontics, Guangdong Provincial Stomatological Hospital, The Affiliated Stomatological Hospital of Southern Medical University, Guangzhou, China c Department of Prosthodontics, Guanghua School of Stomatology, Sun Yat-sen University, Guangdong Provincial Key Laboratory of Stomatology, Guangzhou, China d Dental Materials, Bio-clinical Sciences, Faculty of Dentistry, Kuwait University, Kuwait City, Kuwait e School of Materials Science and Engineering, South China University of Technology, Guangzhou, China
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objective. To investigate and characterize the distribution of fabrication defects in bilayered
Received 25 August 2016
lithium disilicate glass-ceramic (LDG) crowns using micro-CT and 3D reconstruction.
Received in revised form
Methods. Ten standardized molar crowns (IPS e.max Press; Ivoclar Vivadent) were fabricated
17 January 2017
by heat-pressing on a core and subsequent manual veneering. All crowns were scanned by
Accepted 17 January 2017
micro-CT and 3D reconstructed. Volume, position and sphericity of each defect was measured in every crown. Each crown was divided into four regions—central fossa (CF), occlusal fossa (OF), cusp (C) and axial wall (AW). Porosity and number density of each region were
Keywords:
calculated. Statistical analyses were performed using Welch two sample t-test, Friedman
Micro-CT
one-way rank sum test and Nemenyi post-hoc test. The defect volume distribution type
Porosity
was determined based on Akaike information criterion (AIC).
Fabrication defect
Results. The core ceramic contained fewer defects (p < 0.001) than the veneer layer. The size
3D characterization
of smaller defects, which were 95% of the total, obeyed a logarithmic normal distribution.
Glass-ceramics
Region CF showed higher porosity (p < 0.001) than the other regions. Defect number density of region CF was higher than region C (p < 0.001) and region AW (p = 0.029), but no difference was found between region CF and OF (p > 0.05). Four of ten specimens contained the largest pores in region CF, while for the remaining six specimens the largest pore was in region OF. Significance. LDG core ceramic contained fewer defects than the veneer ceramic. LDG strength estimated from pore size was comparable to literature values. Large defects were more likely to appear at the core–veneer interface of occlusal fossa, while small defects also distributed in every region of the crowns but tended to aggregate in the central fossa region. Size distribution of small defects in veneer obeyed a logarithmic normal distribution. © 2017 Published by Elsevier Ltd on behalf of The Academy of Dental Materials.
∗ Corresponding author at: Guanghua School of Stomatology, Hospital of Stomatology, Sun Yat-sen University, Guangdong Provincial Key Laboratory of Stomatology, 510055 Guangzhou, China. E-mail address:
[email protected] (K. Zhao). 1 Contributed equally to this work. http://dx.doi.org/10.1016/j.dental.2017.01.009 0109-5641/© 2017 Published by Elsevier Ltd on behalf of The Academy of Dental Materials.
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1.
Introduction
Bilayered lithium disilicate glass-ceramic (LDG) fixed restorative materials have become popular because of their biocompatibility and esthetics. LDG core material, such as IPS e.max Press (Ivoclar Vivadent, Schaan, Liechtenstein) with high flexural strength of approximately 400 MPa and a fracture toughness of approximately 3.0 MPa m1/2 , in its bilayered application form has become a viable treatment of choice for fixed dental prostheses [1,2]. However, fracture of the framework material and chipping of the veneering porcelain from the underlying ceramic substrate have been reported for bilayered LDG restorations [3,4]. LDG crowns tend to have more chippings of the veneer resulting in a 5-year failure rate of 1.2%, while for metal-ceramic crowns, the incidence of veneer chipping was 0.4% after 5 years [5]. Several factors have been suggested to explain the failure in all-ceramic restorations: (i) defects [6], (ii) mechanical residual stresses [7], (iii) thermal residual stresses [8] and (iv) contact cracks [9]. However for all these factors, defects have been suggested to be the major cause of failure [10]. Under the combined effect of mechanical and thermal stresses, clinically observed failure was noted to initiate at the core–veneer interface or from surface defects, leading to chipping or fracture of restorations [11]. Defects such as pores, inclusion and small cracks may cause stress concentration and become the site of subcritical crack growth. As a consequence, ceramic materials may fracture at a stress far less than their original fracture strength under cyclic loading [12]. Thus, defects inside or on the surface of ceramic restoration are deemed to be critical for initiating clinical catastrophic fracture and chipping. Defects are found to be present inevitably in most allceramic restorations originating during fabrication, regardless of fabrication technique or ceramic type [13]. However not all defects lead to failure of all-ceramic restorations. When a fracture initiating defect has a critical size, which is dependent upon the tensile stress prevailing, catastrophic crack propagation in ceramic materials is likely to occur [14]. Defect sizes of 30–40 m equate very well with defects observed at the primary fracture origin of LDG materials [15]. Research results have shown that chipping mostly initiates from defects at the core–veneer interface [16]. Chipping and fracture are also observed to initiate from the defects in the marginal areas [17,18]. Since the clinical fabrication of glass ceramics may bring about both intrinsic and processing defects, the failure of LDG restorations has been suggested to be related to the size and location of such defects [19,20]. Clarifying the characteristics and distribution of defects in bi-layered LDG crowns should provide deep understanding of the relationship between defects and crown failure. In the literature, defect size measurement and calculation are generally based upon scanning electron microscopy 2D images and fractographic analyses. Defect distribution and associated shape complexity, however, are somewhat inhomogeneous. 2D analysis from polished cross-sections may underestimate the quantity and size of defects. In comparison, 3D analysis is deemed to be suitable to authentically acquire the entire data-set of the larger defects. Micro-CT provides the possibility for conducting nondestructive studies on 3D mor-
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phologies of dental material structures [21]. A recent study taking advantage of micro-CT analysis has shown that multiple pores ranging from 50 to 300 m existed within the veneer and core of all-ceramic crowns [22]. The aim of the present study was to elucidate the relationship among the size, shape and distribution of fabrication defects in bi-layered LDG crowns by means of micro-CT, 3D reconstruction and statistical analysis. Bilayered molar crowns will be selected for investigating the characteristic form and distribution of fabrication defects of a more complicated anatomical morphological structure. The information is essential for ongoing mechanical property research [17,23]. The primary null hypothesis of this study is that the tested main parameters of the defects, either in core or in veneer, cannot be describe with any other known statistical model.
2.
Materials and methods
2.1.
Specimen preparation
A typodont maxillary first molar (A5A-500-#16; Nissin) was prepared as a unified die. All undercuts were eliminated by axial reduction of 1.5 mm. The palatal occlusal surface was reduced by 2.0 mm evenly, while the buccal occlusal surface was reduced by 1.5 mm with functional cusp bevels. The deepest point of the central fossa was 2.0 mm. All sharp angles were subsequently rounded to a 1.0 mm deep chamfer finish line and a 6◦ convergence angle between tooth axis and lateral wall was prepared. Another maxillary first molar model tooth (A5A-500-#16; Nissin) was chosen as a unified core die and prepared by occlusal reduction of 1.5 mm, while the axial wall was reduced by 0.7 mm, providing space for veneering. All sharp angles were rounded.
2.2.
Fabrication of crowns
The anatomically corrected cores (n = 10) were fabricated using the lost wax casting technique generated from impressions of the core dies, after which the wax cores were invested (SpeedVest; Ivoclar Vivadent). Wax was removed by heating and the resultant void was filled with pressable materials (IPS e.max Press, LT A1; Ivoclar Vivadent). Following the heat pressing procedure, the crowns were divested and sandblasted with 120 m glass beads at a pressure of 2 bar. The cores were veneered (IPS e.max Ceram; Ivoclar Vivadent) in multilayering/firing steps by an experienced technician following the manufacturer’s instruction. The veneering process was began by conducting a wash firing of Dentin material (IPS e.max Ceram,Dentin; Ivoclar Vivadent) on the core. Then the first layer was then applied onto the core and fired according to the manufacturer’s instruction. Second layering was taken on the thoroughly dry crown after first layering in order to complete any missing areas. The crown was final polished after the second firing.
2.3.
Acquisition of the defect data-set
Acquisition of the defect data-set of LDG was performed using a commercial micro-CT system (CT50, SCANCO, Bassersdorf,
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as crown defects. The core being the matrix material having a lower atomic number elemental composition gives rise to the second peak followed by veneer as the third peak on the right of the gray value histogram, as shown by peak b and peak c in Fig. 1. Defect was defined and analyzed utilizing a defined threshold of the gray values of both core and veneer. Defects were characterized based upon several parameters, namely; volume, surface area, coordinate position and sphericity. The sphericity (s) of a defect was defined as the ratio of the surface area to that of a sphere, which has the same volume (V) as the given defect to the surface area of the defect (S).
s= Fig. 1 – Gray value histogram of the experimental crown by using micro-CT, in which from left to right, the different gray values correspond to distinct crown constituents; namely (a) air/pores (b) core and (c) veneer.
Switzerland). The protocols used in this study were optimized to enable the detail of the defects to be analyzed, and were standardized at 90 kV, 155 A and 14 W with an integration time of 1500 ms for a singe of the two averaged scans per step and a filter of 0.5 mm aluminium. Scanning resolution was set to 2048 × 2048 pixels. Raw data set of each cross-section was converted to dicom format and 3D reconstructed to provide an axial perspective data of the entire ceramic crown. The calculated voxel size for such scanning conditions was estimated to be ca. 405 m3 . Small voxel size can be achieved by increased the tomograms of z-axis in case of fixed pixels. A lower voxel size is more accurate for the data acquisition as well as 3D reconstruction, but will generally exceed the operation capacity of the work station and time consume. Defect has been suggested to be defined by volume equal or greater than 8 voxel [24]. The detectable lowest void volume of 3241 m3 of defects in the present study is a balanced consequence of clinical relevance and calculation.
2.4.
3D reconstruction
VGStudio Max 2.1 (Volume Graphics GmbH, Heidelberg, Germany) was used for 3D reconstruction and visualization of the data-set. Beam artifacts represented themselves as linear dark streaks, and were defined with software function and discounted when subsequently building the defects list. Such artifact correction in the 3D reconstructing by software underwent a reliability verification test compared with micro-CT reconstruction. Veneer, core and air (porosity) were distinguished from each other based upon gray scale values of the histogram of the whole reconstructed volume, as shown in Fig. 1. Air (pores and that surrounding the specimen in the system) was the first peak on the left of the gray value histogram, as indicated by peak a in Fig. 1. Defects were discontinuities and thus indistinguishable from the surrounding air of the specimen by the automatic calculation (Fig. 1). By means of the hyalinise volume rending software option, pores inside the core and veneer could be observed from different perspectives, and identified
3
36V 2 S3
(1)
Sphericity was calculated depending on the shapes changing from 0 as the pore collapsed to a line, and 1 when the pore was a perfect sphere. All the defects were sorted by volume. According to the volume probability cumulative curve [25], the size (volume) of 95% of defects were concentrated in a narrow range from 3241 to 107,785 m3 , which were considered as group A. While the remaining larger, and potentially more significant 5% of defects were scattered over a broad size range from 107,785 to 8.54 × 108 m3 , which were considered as group B. To facilitate the analysis of defects, each crown was divided into four regions—central fossa (CF), occlusal fossa (OF), cusp (C) and axial wall (AW), as shown in Fig. 2. The volume measurements in the region were computed automatically with the 3D analysis tools of VGStudio Max. The porosity and defect number density per mm3 were calculated for the core and veneer of each region. Defect number density per mm3 was defined as the number of defects in 1 mm3 bulk materials. Porosity was defined as the ratio of pore volume (Vp ) to the bulk volume (Vb ) and Vp of pores and solid together. P=
Vp × 100 (%) Vb + Vp
2.5.
Statistics
(2)
Differences in porosity and defect number density between core and veneer were analyzed based upon the Welch two sample t-test [26]. Relative frequency distribution and cumulative frequency of defect volume were calculated on group A. Four distributions (normal, gamma, log-normal and exponential distribution expressions) were fitted to the volume data, and the distribution type was determined according to the Akaike information criterion (AIC) [27]. The parameters of cumulative probability function were subsequently estimated based on the measured pore-size data from the present result. Differences of sphericity between group A and B were analyzed with Welch two sample t-test. Differences among defect number density and volume fraction of different regions were calculated with A Friedman one-way rank sum test. The homogeneity in variance was pairwise compared with Nemenyi post-hoc test for each region. Differences and parameters were considered statistically significant at the level of 0.05.
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Fig. 2 – Top view (a) and side view (b) of a crown consisting of four regions and their dimensions, in which red, gray, light blue and deep blue region represent central fossa, occlusal fossa, cusp and axial wall respectively.
3.
Results
3.1.
Defect analysis from 3D reconstruction
According to the specific contrast in the reconstructed images, the 3D spatial morphologies were visible after reconstruction. Inner defects colored in the rendered transparent crown in 3D reconstruction were displayed in Fig. 3. Defects were detected both in veneer and core in the same manner. 3D data of defects, such as volume, surface area, sphericity and position were collected and subsequently analyzed.
3.2.
Difference between the core and veneer
The porosity and defect number density for core and veneer materials are shown in Table 1. All specimens in the present study contained defects with different number density in the veneer and core. The veneer contained more pores than the core with a significantly higher defect number density
Table 1 – Porosity and defect quantity of in the core and veneer.
0.0121 ± 0.0086 0.4740 ± 0.1840
Core Veneer
1.3606 ± 0.6812 67.7001 ± 31.4033
(p < 0.001) and the porosity of the veneer was also significantly greater than that of core (p < 0.001).
3.3.
Pore size distribution
The total number of defects detected in the 10 crowns was 119,771. The distribution of defect size was extremely broad ranging in volume from 3241.00 m3 to 8.54 × 108 m3 . The number of pores in the core was far smaller by a factor of 50 than in the veneering porcelain. Based upon algorithm fitting of the present data-set, 95% defects (volume ≤ 107,785 m3 ) were divided into group A, while the other 5% (volume > 107,785 m3 ) were group B, since all pores of the specimens were sorted by volume. As the size of defects increased, the number of defects in group A appeared to increase initially and then decrease exponentially peaking in the range 3241–20,000 m3 (Fig. 4a), whereas group B showed no tendency between the number and volume, as the volume of defects in group B was more widely distributed (Fig. 4b). Logarithmic normal distribution function was consistent with the group A data, namely 95% defect size distribution, and the cumulative probability function was given by
f (x) =
Fig. 3 – Top view (a) and side view (b) of reconstructed 3D images of one specimen. The transparency of the ceramic materials to X-rays enables the presence of defects dispersed around the crown to be visualised. Defects were colored yellow in veneer and blue in core.
Number density (per 1 mm3 )
Porosity (%)
1 √
x 2
exp
−(ln x − ) 2 2
2
(3)
where and were the logarithmic mean value and standard deviation respectively, and x for the defects volume. Value of and in Eq. (1) was estimated by measuring the pore-size data from the study (Table 2) and fitting curves are shown in Fig. 5.
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Fig. 4 – Pore size distribution curves of group A (a) with the mono-peak between 3241–20,000 m3 consistently and pore size distribution curves of group B (b) was comparatively flat and the defects size distributed discretely with large disparity.
Table 2 – Parameters of log normal distribution fitting of bi-layer LDG crowns.
Table 3 – Median of volume fraction and number density of four region.
9.15
0.95
Porosity (%) CF OF C AW
0.55 (0.40, 1.15) 0.44 (0.31, 0.60) 0.11 (0.07, 0.19) 0.10 (0.05, 0.16)
Number density per 1 mm3 65.71 (55.85, 92.01) 40.55 (34.80, 60.69) 23.56 (11.60, 31.61) 33.15 (23.06, 67.36)
*CF = central fossa, OF = occlusal fossa, C = cusp, AW = axial wall.
3.6.
Fig. 5 – Density curve and cumulative distribution function (CDF) for 95% smaller defects of specimens.
3.4.
Sphericity of pores
Sphericity of the pores ranged between 0.12 and 0.81, and for 95.78% of the pores their sphericity was larger than 0.5. The sphericity of group A is slightly higher than that of group B with a significant difference (p < 0.001). Most pores of group A were ellipsoidal or rounded with relative smooth surface while some pores of group B were irregular and sharp edged.
3.5.
Difference of pore distribution
The volume fraction and number density of pores in the four regions (CF, OF, C, AW) of specimens are shown in Table 3. Porosity of the four regions differed from each other (p < 0.001), as did the number density of these regions (p < 0.001). Porosity of region CF was higher than that of other regions (p < 0.001) as shown in Fig. 6(a). The number density was higher in region CF than that in region C (p < 0.001) and AW (p = 0.029), and no difference was found between region CF and OF (p > 0.05), as shown in Fig. 6(b).
Characteristics of the largest pore
The largest pores in each specimen were observed to have equivalent diameters ranging from 438 m to 1176 m. The sphericity of the largest pores, ranged from 0.17 to 0.49, which was less than the average level (0.619). These pores were irregular, with an elongated and flattened form. All the largest pores were located at or next to the veneer–core interface. Four of 10 specimens contained the largest pores in region CF, while the other six specimens contained the largest pore in region OF. No large pores (equivalent diameter > 183 m) were found in region C or AW (Fig. 7).
4.
Discussion
In visualizing the data-set, defects in the core were found to be much less in terms of both number and size than in the veneer. The core was produced by a heat-press treatment. During the pressing procedure, the lithium disilicate crystals grow and are aligned along the pressing direction [28]. Heat pressing not only enhances the crystal distribution, but also decreases the number and size of pores. However, defects within the core, such as the development of pores still may be created in the heat-pressing process [13]. Results of this study confirmed the latter finding and clearly demonstrated that small, homogeneous pores existed in the core and could not be eliminated during the heat-pressing process. Yet these defects in the core were dispersed uniformly and had similar smaller size and more regular shape than those defects in the veneer. It is interesting to attempt to determine the range of fracture strengths associated with these defects and compare with typical val-
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Fig. 6 – Box plot of volume fraction (a) and number density (b) of four regions.
ues of strength reported in the literature. If we assume that pores in LDG core have the potential to become the critical flaw and the radius of the volume associated with the defect is an estimate of the flaw size and then from the simple fracture mechanics expression relating strength to fracture toughness, namely [19]. =
KIc √ 1.12 c
(4)
where KIc is the critical stress intensity factor and c is the radius of the defect [29]. Using the values of the volume size of the flaws in the core to determine c, and a fracture toughness (KIc ) value of pressed Emax as 2.9 MPa m1/2 (Guazzato et al.) [29] the strengths for the core material was determined to be 324.7 ± 56.8 MPa. Previous studies by Guazzato et al. [29] measured strengths of 306.4 ± 29.2 MPa while Albakry et al. [28] measured 300.3 ± 35.2 MPa for as pressed and 387.3 ± 34.2 MPa
for as polished specimens. Accordingly, pores present in the LDG core were deemed to provide a critical estimate of its strength. As most strength tests are conducted in flexure the proximity of a defect to the location of the maximum stress, which is highly localized in such tests, will dictate the range of strengths measured. The situation regarding the strength of the veneering porcelain, even with the size of the pores and defects observed, is very difficult to predict. This arises because of the complex stress state within the porcelain because of the thermal expansion mismatch with the underlying core material and also because of possible tempering stresses that develop as a consequence of the cooling rate induced temperature gradient when the specimen is removed from the sintering furnace during the final cooling. What’s more, pores and defects with respect to the pore size in the veneering porcelain may not be the main factor for determining fracture. Other parameters of pores in the veneer such as relative location to the interface
Fig. 7 – The largest pores of each specimen were identified and colored yellow, in which four crowns had the largest pores in region CF, i.e. (a), (d)–(f). Six crowns had the largest pores located in region OF, i.e. (b), (c), (g)–(j).
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of veneer and core, or to the cups of the crown were deemed to be also involved in the fracture strengths. Defects present in the veneering porcelain are more complex and less homogeneously distributed than in the core ceramic. In the present results, the smaller defects were regular in size distribution in each crown and the shape tended to be ellipsoid or more like bubbles. The similarity of size distribution and morphology of the smaller defects might suggest that it may have a common origin and might be attributable to the crown preparation. The layering process during crown fabrication involved several manual steps which essentially controlled the final quality of the prosthetic work, i.e. mixing of porcelain slurry, veneer layering and sintering. It has been reported that the porcelain slurry preparation is closely related to defect generation [30]. In clinical practice, porcelain slurry is prepared by mixing water with porcelain powder together to obtain a desired consistency, which may inevitably entrap air bubbles. In the slurry, the liquid acts as a lubricant for particle movement, occupying small spaces between ceramic particles. When sintering, liquid in the slurry will evaporate, thus micro defects and uniform porosity can form and be homogeneously distributed [31]. The water to powder ratio for this situation is uncertain and any excess may deviate from the manufacturer’s recommendation may result in higher porosity [32]. In a dental laboratory, mechanical vibration and blotting are commonly used to reduce the volume fraction of porosity in layering, but the effect of vibration on defect number reduction is limited [33]. Sintering is also related to defect formation as trapped gases in the slurry tend to increase its size due to pressure balance, when the sintering temperature is increased. Since the viscosity of the porcelain decreases with cooling down, trapped gases escape by diffusion through the matrix [34]. In general, defects formed in this way should be characterized as small, regular and homogenously distributed. Difference of defect quantity but similarity of smaller defects size distribution was deemed to be attributable to empirical factors of dental technicians. Our results clearly visualized the defects in all specimens, in which the defects reached a proportion till 95%, and demonstrated the characters of small defects both in the core and veneer of the crown. The larger defects with higher volume but lower sphericity were quite different. The largest defects in specimens were relatively flat with the central area uplifted along with slumped jagged rims, which were located in the core–veneer interface of fissure regions. It has been suggested that sintering shrinkage of dental porcelain frits is in the range of 13%–17% [33,35]. Due to the feldspar-based dental porcelains, sintering begins primarily by viscous flow, presence of a liquid phase at firing temperatures allows the veneer material to flow toward shrinking centers which are always located in the thicker cuspal regions, in order to compensate for sintering shrinkage. The shrinkage beneath the fossa at the inner surface of the veneering material, especially about the central fossa and if there is any contamination and air bubbles present, may cause uplift of veneer and form a void with central domes and slumped rims at the interface [20]. In addition, manual veneer layering is involved in the formation of larger defects. In practice, the porcelain slurry is applied by a fine brush resulting in a multi-layered structure. The initial build-up of porcelain commences generally at the cusps and is completed in the
fissure with occlusal porcelain. Because of the limited wettability of porcelain slurry and intrinsic surface depression of the framework, finishing such layer in the fissure region may contribute to void formation beneath the occlusal porcelain. This region is particularly vulnerable to a hasty veneering buildup operation. The larger defects formed in this way should be sporadic, irregular in shape, and located in specific regions of the crown. Visualization of the larger defects in the present results demonstrated the character of the larger defects and might suggest its potential formation origin. In the present study, the porosity and number density of the central fossa region were higher than of the others, suggesting that defects were deemed to more likely form in central fossa region. The central fossa is the intrinsic surface depression of the framework. In this region, the difference of shrinkage and the susceptibility of layering are associated with larger defect formation. When vibrating the slurry, liquid flows down the hydraulic gradient from cusp to fossa, and may induce a waterenriched region in the depression area, just as in the central fossa. As a consequence, not only are the larger defects more readily introduced into the occlusal fossa region, but also the general defects tend to gather around the fossa region. Defects in the central areas cause additional stress concentration under primary chewing forces [19]. Though fracture of allceramic crowns is complex, the fracture process is triggered by the magnitude of stress and weakest volume element, which is significantly influenced by the largest flaw it contains [19,20,36]. In this sense, larger defects located in the core–veneer interface of central fossa are critical for restoration failure. In the present results we also found that the larger defects were irregular in shape. The sharp surfaces and edges of the larger defects might induce stress concentration more easily, which would be expected to result in fracture initiating at the tips of such defects [19]. The smaller defects near the fossa towards the occlusal surface are likely to be involved in adjustment and antagonist abrasion during function. During fabrication, cracks are much more easily produced by mechanical polishing in the margin area, a region which has been suggested to be the major fracture initiation site [37]. In the present results, no large pores were found and only small pores aggregated in the margin area. However crack detection requires even higher resolution and phase contrast micro-CT imaging as possible currently with synchrotron based instrument and usually involves miniature specimen [38], which limits such application in brittle dental crown research. Thus, as in the current approach, the microCT resolution possible is unable to adequately address this situation.
5.
Conclusions
LDG core ceramic contained fewer defects than veneer ceramic. The predicted strengths on the basis of a simple fracture mechanics approach are comparable with previously reported values. Large defects were more likely to occur in the core–veneer interface of occlusal fossa, while small defects distributed in every region of the crowns but tended to aggregate in central fossa. Size of 95% small defects in veneer obeyed a logarithmic normal distribution.
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Acknowledgements This investigation was supported by the National Natural Science Foundation of China under grant No. 81470767. Thanks also for the donated materials from IvoclarVivadent.
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