Previous studies have shown that the fracture toughness of ceramics can be determined from the fractal dimensions (D) of their fracture surfaces and that the surface should be leveled to obtain an accurate D measurement. This study was to determine the effects of leveling operations and distance from the failure origin on the D values.
Twelve clinically failed zirconia implants from four different manufacturers: Axis Biodental ( n = 7), Z-Systems ( n = 3), Straumann ( n = 1), and Swiss Dental Solutions ( n = 1) were obtained from one of the authors and thoroughly cleaned. Epoxy replicas were made of three locations along the crack path in the center region of each fracture surface (near origin (O), hackle (H), and near compression curl (CC)) using a light body polyvinyl siloxane impression material. Surfaces were scanned in ScanAsyst mode with a scan size of 5 μm × 5 μm and a scan rate of 0.592 Hz using the atomic force microscope. The surface scans were then leveled using 1st order flattening operation in the AFM analysis software. The height data before and after the operation were imported into a custom MathCAD script, and FRACTALS software was used to determine the D value by Minkowski Cover algorithm, which was shown previously to be the algorithm with the highest precision. A Wilcoxon signed-rank test, two-way repeated-measures ANOVA, and one-way repeated-measures ANOVA were performed as detailed below.
The data were not normally distributed (S-W p ≤ 0.05), so a non-parametric repeated measures test (Wilcoxon signed-rank test) was selected. The median D values before and after leveling were 2.161 and 2.174, respectively. There was a significant difference before and after leveling ( p < 0.001). The two-way repeated-measures ANOVA showed no significant difference among the D values for different implant brands ( p = 0.66) and scanning locations on the fracture surface ( p = 0.83). After eliminating the implant brand as a factor, the data passed normality and equal variance tests (S-W p = 0.88, BF p = 0.15). The mean D values and standard deviations from the three locations (O, H, CC) were 2.183 ± 0.031, 2.179 ± 0.024, and 2.175 ± 0.018, respectively. One-way repeated measures ANOVA showed no significant effect of scanning location ( p = 0.74).
The leveling operation successfully removed the tilt without decreasing surface tortuosity, as it increased the D values significantly. The fractal dimension was the same at the three locations on the fracture surfaces. This means that hackle and compression curl regions can be used to determine fracture toughness when the failure origin has been lost.
The growing demand of better esthetics and non-metallic materials has brought zirconia as an alternative to titanium implants due to its inert nature, excellent biocompatibility, and transformation toughening mechanism to prevent crack propagation . On comparing the mechanical aspect, titanium used for dental implants has about 20–30 times higher fracture toughness and is also more ductile than zirconia . The literature is still too young to conclude if zirconia implants can replace the traditional titanium ones in the clinic . One of the ways of improving the materials lifetime is studying the factors that led to its failure. Fractal geometry can provide insights about the failure from the fracture mechanics perspective by estimating the fracture toughness using its empirical relationship with the fractal dimensional increment. Previously, it was not possible to determine the fracture toughness of clinically failed specimens because traditional fractographic methods require knowledge of the failure stress, but in clinical specimens the failure stress is not known . However, the fractal geometry methods explored in this study do not require knowledge of the failure stress.
Fractographic analysis is a widely used technique to study the fracture surfaces and identify the fracture origin or region of crack origin along with factors responsible for the failure . It can provide information about the conditions that were present at the time of failure thereby assisting in improving the design of the restoration or the processing of the material. The use of quantitative fractography for clinically failed dental ceramics dates back to as early as 1989, with an aim of locating the source of fracture and calculating the failure stress by Kelly et al. .
Current fractographic techniques comprise both qualitative and quantitative evaluation of the fracture surface. Qualitative techniques include the use of optical instruments for analyzing the fracture surface to (1) locate the origin of the failure, (2) identify the flaw limiting the strength of the specimen, and (3) determine the direction of progression of fracture . On the other hand, the quantitative techniques include the calculation of (1) fracture toughness of the material using Griffith’s relationship of fracture toughness and critical flaw dimensions and (2) thermally induced residual stresses based on the mirror to flaw size ratio . Traditional quantitative techniques require the fracture origin for analysis. The failure origin can either be lost because of continuous loading resulting in further damage to the fracture surface due to friction between the two broken halves still in situ or during the retrieval process, thus limiting the applicability of quantitative fractography for clinically failed specimens. However, fractal geometry may allow determination of fracture toughness of ceramic without the failure origin. Mecholsky and his team developed the relationship between the fracture toughness of ceramics and the fractal dimensional increment of their fracture surfaces as, <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='KIc=Ea0D*’>𝐾𝐼𝑐=𝐸𝑎0𝐷∗‾‾‾‾‾√KIc=Ea0D*
K I c = E a 0 D *
, where K Ic is the critical stress intensity factor (fracture toughness) in mode I , E is the Young’s modulus of elasticity, a 0 is the characteristic length, and D * is the fractal dimensional increment . Hill et al. observed that ceramics can be divided into three material classes (namely polycrystalline, glass-ceramic, and coarse-grain ceramic) each having a different relationship between fracture toughness and D * values . Further, Della Bona et al. reported that the measured D * decreases with increasing angle of inclination of the fracture surface . Therefore, fracture surfaces must be leveled for accurate fractal analysis. Over the years, researchers have developed different algorithms to calculate the fractal dimensional increment ( D *) for fractal surfaces . Russ compiled some of these techniques (Kolmogorov–Box, Slit-Island Richardson, Minkowski Cover, etc.) in an easy to use software application . McMurphy et al. showed that all of the techniques described by Russ for measuring the D * value are biased and are sensitive to the angle of inclination to varying degrees. They further reported that Minkowski Cover is the most precise algorithm for calculating D * and that the fracture surface should be leveled to get an accurate D * value when using this algorithm .
The objective of this study was to test the hypothesis that: (1) leveling affects the measured D * value and (2) distance of the measurement site from the failure origin does not affect D * values.
Materials and methods
Twelve clinically failed 3Y-TZP monotype dental implants with their all-ceramic crowns cemented on top were obtained from a previous study . The recovered broken implant-crown parts were from four different manufacturers and placed at various intra-oral locations. The implant-crown system had a wide range of clinical service lasting from 2 weeks to 108 months as described in Table 1 . Following retrieval, the implants were thoroughly cleaned to remove any biological residue . The fracture surfaces were analyzed using microscopy as shown in Fig. 1 to detect the fracture origin and fracture features such as hackle and compression curl, allowing the mapping of the direction of crack propagation (dcp). A cotton pellet and 190 proof ethyl alcohol were used to remove any surface impurities followed by air drying. Two impressions of the fracture surface were taken using a light body polyvinylsiloxane impression material (Extrude Base, Kerr Corporation, Orange, CA) as shown in Fig. 2 . After discarding the first impression , a second impression at three different locations on the fracture surface along the crack path was taken; near origin (O) (left), hackle region (H) (middle), and near compression curl (CC) (right) as shown in Fig. 3 . A low viscosity, low shrinkage epoxy resin (EpoxySet, Allied High Tech Products Inc., Rancho Dominguez, CA) was poured on the impressions after an hour and was allowed to cure for 8 h. The epoxy replicas were then carefully placed on polymeric clay (Sculpey III, Polyform Products Company, Elk Grove Village, IL) ensuring that the fracture surface was facing upward and macroscopically leveled for fractal analysis.