A Bilayer Method for Measuring Toughness and Strength of Dental Ceramics

Abstract

The ever-increasing usage of ceramic materials in restorative dentistry necessitates a simple and effective method to evaluate flexural strength σ_F and fracture toughness K_C. We propose a novel method to determine these quantities using a bilayer specimen composed of a brittle plate adhesively bonded onto a transparent polycarbonate substrate. When this bilayer structure is placed under spherical indentation, tunneling radial cracks initiate and propagate in the lower surface of the brittle layer. The failure analysis is based on previous theoretical relationships, which correlate σ_F with the indentation force P and layer thickness d, and K_C with P and mean length of radial cracks. This work examines the accuracy and limitations of this approach using a wide range of contemporary dental ceramic materials. The effect of layer thickness, indenter radius, load level, and length and number of radial cracks are carefully examined. The accuracy of the predicted σ_F and K_C is similar to those obtained with other concurrent test methods, such as biaxial flexure and 3-point bending (σ_F), and bending specimens with crack-initiation flaws (K_C). The benefits of the present approach include treatment for small and thin plates, elimination of the need to introduce a precrack, and avoidance of dealing with local material nonlinearity effects for the K_C measurements. Finally, the bilayer configuration resembles occlusal loading of a ceramic restoration (brittle layer) bonded to a posterior tooth (compliant substrate).

Introduction

Hard ceramic layers constitute a basic building block in natural, biological, and synthetic structures. The layer’s flexural strength σ_F and mode I fracture toughness K_C are primary material properties that dictate the fracture resistance of the whole structure. Of special interest in this work are lithia-based glass ceramics and zirconia, which are used for restoring function and esthetics while providing protection to the underlying tooth structure (Zhang, Sailer, and Lawn 2013). Such materials are widely used in restorative dentistry, with new products rapidly emerging (Zhang and Lawn 2018; Lubauer et al. 2022; Phark and Duarte 2022; Zhang et al. 2023). Thus, there is a need to develop a simple and effective method for rapid evaluations of flexural strength σ_F and fracture toughness K_C of dental ceramics.

The failure stress σ_F of thin ceramic plates is generally evaluated using biaxial flexure-type specimens for ease of specimen preparation and avoidance of fracture from specimen edges (Sen and Us 2018; Alves et al. 2019; Demirel et al. 2023). Measuring K_C is more involved due to the need to introduce a sharp precrack. The most popular specimens used are the 3-point bending flexure and compact tension specimens with a Chevron notch or local precrack (Alkadi and Ruse 2016; Elsaka and Elnaghy 2016; Alves et al. 2019; Jodha et al. 2022) and Vickers indentation on a flat surface (Villas-Boas et al. 2020; Čokić et al. 2022). The Vickers test avoids the need to introduce a sharp precrack, but its data reduction is marred by plastic deformation and residual stresses at the indentation site (Anstis et al. 1981). Belli et al. (2018) performed a comparative study using various test methods and data reduction schemes to calculate K_C. The error among these tests was generally less than 10%. As discussed later in this work, the scatter in some of the reported σ_F and K_C may be even larger.

The layer thickness d used in the aforementioned tests typically exceeds 1.2 mm. Available fracture toughness tests for thinner layers include direct tension (Sharpe et al. 1997; Espinosa and Peng 2005; Ando et al. 2011), micro-cantilever bending (Xiao et al. 2019), and, as discussed in other studies (Chai and Lawn 2004; Zhang et al. 2005; Jaya et al. 2015; Chai et al. 2019), bending, buckling, micro- or nano-indentation, and wedging. However, many of these tests are difficult to implement and require tedious preparations, sophisticated test apparatuses, and complex data interpretation schemes. Chai (2009) developed a method for measuring K_C of thin layers using a bilayer indentation (BI) test, which is based on spherical indentation of a brittle layer bonded onto a compliant polycarbonate substrate. The values of K_C were determined from an analysis of radial cracks that form in the lower surface of the brittle layer. The results for 3Y-PSZ (3 mol.% yttria partially stabilized zirconia), alumina, porcelain, and (001) single crystal silicon layers were comparable to those obtained using other fracture mechanics approaches.

This work focuses on the merit of the bilayer subsurface cracking (BSC) test for determining σ_F and K_C in thin brittle materials. Tests are conducted on a wide range of current dental ceramic materials. Special attention is given to geometric nonlinearity, load level, and number and length of the subsurface cracks. For the purposes of clarity, the analyses used for biaxial flexural strength and fracture toughness are reviewed in the Materials and Methods section.

Materials and Methods

The BSC test is used to evaluate the biaxial flexural strength σ_F and mode I fracture toughness K_C. Figure 1 describes figuratively the test specimen and theoretical analysis used.

Figure 1.

The bilayer specimen. (A) Nomenclature; c is the mean length of the n subsurface radial cracks. (B) Three video frames showing growth of a tunneling radial crack due to indentation by a hard sphere (Chai 2009). (C) Function g versus k as defined in the failure analysis below; the solid-line curve is a possible fit to the data. (D) Distribution of tensile stress along the layer subsurface from the 2-dimensional finite element method (FEM) analysis (Chai 2009); the solid-line curves are possible fits to the FEM data for x/d > 1.

Materials and Testing

The biaxial flexural strength and fracture toughness tests were carried out independently using the same bilayer configuration. As shown in Figure 1A, the bilayer consists of a thin, hard layer of thickness d bonded onto a 12.5-mm-thick polycarbonate block by a room temperature (RT) structural adhesive (“double/bubble epoxy”; Element Specialties). The adhesive, ≈50 µm thick, provides a strong bond with minimal curing stresses. As seen from the Table, the Young’s modulus and Poisson’s ratio of the adhesive are similar to that of polycarbonate, which practically renders the specimen as a bilayer. The following pertinent ceramic materials were used: 3 lithia-based glass ceramics (IPS e.max CAD by Ivoclar Vivadent; CEREC Tessera by Dentsply Sirona; Initial LiSi Block by GC America) and 3 compositions of yttria partially stabilized zirconia (3Y-PSZ, 4Y-PSZ, and 5Y-PSZ, all by Tosoh Corporation).

Table.

System Parameters.

Material	E	ν	σF	K C
Polycarbonate	2.35	0.35	NA
Adhesive	2.03	0.32	NA
Soda-lime glass	70	0.22	NA	0.67 (0.09)
IPS e.max CAD (A2, HT)	102.5	0.22	462 (34)	1.80 (0.21)
CEREC Tessera (A2, HT)	103.1	0.23	367 (57)	1.24 (0.15)
GC LiSi (A2, HT)	95.6	0.20	396 (34)	1.27 (0.12)
3Y-PSZ (with 0.05 wt.% Al2O3)	205	0.32	1,467 (85)	3.56 (0.35)
4Y-PSZ (with 0.05 wt.% Al2O3)	205	0.32	1,208 (112)	3.27 (0.39)
5Y-PSZ (with 0.05 wt.% Al2O3)	205	0.32	1,022 (112)	2.33 (0.20)
IPS e.max CAD			415 (26)(A2, HT) a ; 418 (58)(A2, HT) b 296 (49)(A2, HT) c ; 424 (52)(A2, HT) d ; 421 (57)(A2, HT) e ; 561 (48)(A2, HT) f	1.62 (0.05) g ; 2.01 (0.13) h 1.79 (0.26) i ; 1.62 (0.07) j ; 2.04 (0.10) k
CEREC Tessera			374 (30)(A2, HT) d ; 285 (55)(A2, HT) e	1.45 (0.10) k
GC LiSi			459 (16)(A2, HT) f	1.50 (0.04) k
3Y-PSZ (with 0.35 wt.% Al2O3)			1,556 (264) l	4.2 (0.2) l
3Y-PSZ (with 0.11 wt.% Al2O3)			1,439 (146) l	3.7 (0.2) l
3Y-PSZ (with 0.05 wt.% Al2O3)			1,348 (115) m	3.7 (0.1) l
4Y-PSZ			952 (112) l ; 928 (87) l ; 1,396 (71) m	3.7 (0.1) l ; 3.4 (0.2) l
5Y-PSZ			680 (163) l ; 702 (127) l ; 1,026 (70) m ; 1,212 (144) n ; 1,124 (161) n ; 1,047 (162) n ; 1,034 (187) n ; 989 (201) n ; 952 (205) n ; 908 (205) n ; 877 (190) n	2.6 (0.1) l ; 2.4 (0.2) l

Data for present and literature (superscripted) values. E [GPa], ν, σ_F [MPa], and K_C [MPa m^1/2] denote Young’s modulus, Poisson’s ratio, biaxial flexural failure stress, and mode I fracture toughness. The values are presented as mean (standard deviation). The present σ_F values correspond to d = 1 mm.

^aSen and Us (2018).

^bStawarczyk et al. (2021).

^cWang et al. (2020).

^dDemirel et al. (2023).

^eAl-Johani et al. (2023).

^fDiken Türksayar et al. (2022).

^gAlves et al. (2019).

^hElsaka and Elnaghy (2016).

ⁱAlkadi and Ruse (2016).

^jJodha et al. (2022).

^kLubauer et al. (2022).

^lČokić et al. (2022).

^mToo et al. (2021).

ⁿSpintzyk et al. (2021).

The Table lists the material properties and layer thickness used, where E and ν denote Young’s modulus and Poisson’s ratio, respectively. As shown, the thickness for the flexural strength specimens was 1 mm while that for the fracture toughness was either 0.25 mm (Y-PSZ) or 0.41 mm for the other materials.

The lithia-based glass-ceramic CAD/CAM blocks (size C14, HT, A2 shade) were obtained from respective manufacturers: IPS e.max CAD (Ivoclar Vivadent), Cerec Tessera (Dentsply Sirona), and GC LiSi (GC America). Disc-shaped specimens 12 mm in diameter were cut from these CAD/CAM blocks. Specimens from IPS e.max CAD and CEREC Tessera were further heat treated according to the manufacturers’ instructions. The PSZ specimens were disc shaped with 13 mm in diameter and 1 mm in thickness. The disks were prepared from presintered 3Y-PSZ (Zpex), 4Y-PSZ (Zpex 4), and 5Y-PSZ (Zpex Smile) zirconia rods (Tosoh Corporation). The zirconia samples were sintered at 1,500°C for 1 min followed by dwelling at 1,150°C for 10 h. A constant heating and cooling rate of 5°C per minute was used. Building on a previous study (Lim et al. 2022), we conducted extensive sintering studies, which revealed that these sintering conditions produced the best combination of strength and translucency for these zirconia compositions. Detailed sintering mechanisms and property optimization approaches for the zirconia materials used will be addressed in a separate study.

The ceramic discs were ground and polished to the given thickness with a 0.5-µm diamond grit finish using an automatic polishing machine (Ecomet 4; Buehler). The polished sample was ultrasonically cleaned and bonded to the polycarbonate slab. The bonded specimens were stored at RT for 24 h to aid in polymerization prior to testing. The tests were performed at RT (21°C) with 40% humidity using a universal testing machine (68TM-5; Instron Corporation). The crosshead speed was 0.1 mm/min, which is fast enough to prevent significant slow crack growth in these material classes (Zhang and Lawn 2004). The indenter was a 3Y-PSZ zirconia with 0.25 wt.% Al₂O₃ (Tosoh Corporation) ball of radius r = 3.17 mm. After unloading, the length of all subsurface cracks was measured through the transparent polycarbonate slab using a reflection optical microscope (ZEISS USA).

In addition to the ceramics, tests were performed on soda-lime glass layers. The goal of these tests was to follow the evolution of the subsurface cracks and explore the effect of evolving crack length c on the fracture toughness. The layers are standard microscope glass slides of dimension 20 × 50 × 0.153 mm. The glass slides were first etched with 10% hydrofluoric acid solution for 1 min to produce a pristine surface (under this etching condition, approximately 20 µm surface material has been removed). The bonding surface was then abraded with 600-grit SiC particles to provide a uniform flaw distribution. After bonding to the polycarbonate slab, the bilayers were indented by a tungsten carbide (WC) sphere of radius r = 3.17 mm using a universal testing machine. The loading rate was 0.05 mm/min. The failure process in the glass was recorded in situ from underneath the specimen using a half-mirror to redirect the incoming light (Chai et al. 1999). The recording was done using a video camera (Canon EOS Mark 5) equipped with a high-power zoom lens (Optem). The loading was terminated after several radial cracks evolved from the layer subsurface. The length of each crack was measured from the video record. This was done each time a new crack emerged.

Failure Analysis

Referring to Figure 1A for notation, the subsurface radial stress under the load, σ₀, is given by Chai (2009).

$${\sigma }_0=BP/d^2,B\equiv (1-2{\nu }_c)/4\pi +A_{0}logk$$ (1)

$$k\equiv E_c(1-{{\nu }_s}^2)/E_s(1-{{\nu }_c}^2),A_0=0.72,$$

where d is the layer thickness, subscripts c and s indicate layer and substrate, and P is the applied load. The biaxial flexural strength of the layer, σ_F, is obtained from equation (1) using the load at onset of subsurface radial cracks, P_F.

Once initiated, the subsurface cracks grow as tunneling radial cracks under a diminishing tensile stress field (Fig. 1B). Building on this behavior, Chai (2009) obtained a simple and economical approach to measure K_C based on crack initiation load P and mean length of radial cracks c (Fig. 1A):

$$K_C=a_{0}B{g}^{1/2}P/c^{3/2},a_0=0.165,$$ (2)

where g is a function of the elastic moduli of the layer and substrate that was obtained as follows. The stress intensity factor K for a steady-state channel or tunnel crack under uniform tensile stress σ is given as (Beuth 1992)

$$K=\sigma {(\pi dg/2)}^{1/2},$$ (3)

where g = g(α, β) and

$$\begin{array}{l}a\equiv \left(k-1\right)/\left(k+1\right),\\ \beta \equiv 0.5[(1-2{\nu }_s)/(1-{\nu }_s)-\left(1/k\right)(1-2{\nu }_c)/(1-{\nu }_c)]/\left(1+1/k\right)\end{array}$$ (4)

Beuth (1992) determined g for a wide range of α and β using a FEM analysis. The results are given in tabulated forms. Using these tables, the following values of g were obtained for porcelain, glass, (001) single crystal silicon, 3Y-PSZ, and alumina layers: 7.3, 7.5, 15.8, 17.7, and 22.8, in that order (Chai 2009). These g values are plotted versus k in Figure 1C. The solid-line curve corresponds to the following fit to these data

$$g=0.304k-1.062k^2/{10}^3+309.1k^3/{10}^9$$ (5)

For simplicity, equation (5) will be used to obtain g for any value of k.

The stress σ in equation (3) was evaluated as follows. Because analytical solutions for tunneling radial cracks under varying stress field are difficult to obtain, calculations were made using the finite-element analysis in (Chai 2009). Figure 1D plots normalized radial stress σ(x)/σ₀ versus radial coordinate x for d = 1 mm, P = 1 N, and k = 30 (glass/polycarbonate) or 157 (alumina/polycarbonate). The solid-line curves are the following empirical fits to x/d > 1:

$$\sigma \left(x\right)/{\sigma }_0=\delta {\left(d/x\right)}^{3/2},$$ (6)

where δ is some constant. As shown in Figure 1D, equation (6) approximates well σ(x) over the range 1 < d/x < 4. Equation (2) is obtained by combining equations (1), (3), and (6) with x taken as c.

The fracture toughness K_C was obtained from equations (2) and (5) using the mean crack length c and crack initiation (ceramics) or concurrent load (glass).

Results

Soda-Lime Glass

Figure 2A shows select images from a typical video sequence. Radial cracks propagate and proliferate with increasing load, starting with 2 and ending with 6 cracks. Figure 2B plots the calculated K_C versus c/d or number of cracks n for the 6 different tests conducted, each with up to 6 different video frames. Notwithstanding the scatter, K_C seems little affected by c/d or n up to c/d ≈4. Note from Figure 1D that the corresponding solid-line curve (k = 30) departs from the FEM data for c/d > ≈4. The mean and standard deviation (SD) values for c/d < 4 are 0.67(0.09) MPa m^1/2, which is close to the 0.65 value obtained in Chai (2009).

Figure 2.

Results for soda-lime glass. (A) Select video frames from specimen 6 showing the evolution of subsurface radial cracks with load. (B) Fracture toughness K_C versus c/d or number of radial cracks n; the solid-line curve is mean value for c/d < 4.

Ceramics

The tests for the dental ceramic layers were automatically terminated once a load drop occurred, an event accompanied by rapid growth and arrest of the subsurface radial cracks. The biaxial failure stress σ_F was determined from equation (1) with P corresponding to the incident of load drop.

After unloading, the cracked specimens were observed with a reflection optical microscope. Figure 3A shows typical fracture morphologies for each of the 6 materials studied. The cracks in the upper row are nearly uniform in length while those in the lower row exhibit complex patterns, with small cracks trapped between large ones. This behavior reflects the large dynamic release of stored strain energy due to cracking in the polished subsurface. In calculating K_C, only simple crack patterns like those in the upper row of Figure 3A were used. Figure 3B plots K_C versus c/d or n for the 6 layers studied. No structural dependence of K_C on c/d or n is apparent. The horizontal lines are the best fits.

Figure 3.

Ceramic layer data. (A) Postmortem fracture morphology for the 6 layers studied; the upper and lower rows represent acceptable and unacceptable fracture pattern for data reduction. (B) Calculated fracture toughness K_C versus c/d or number of cracks n. The horizontal lines are mean values.

The Table lists the mean and standard deviation values of σ_F and K_C for the ceramic layers while Figure 4 depicts these values in an increasing order. The FEM stress analysis of the bilayer showed that case d = 1 mm yields the true value of σ_F (Chai et al. 1999; Lawn et al. 2002; Kim et al. 2006; Zhang, Lee, Srikanth, and Lawn 2013; Yan et al. 2018). On the other hand, for d = 0.25 and 0.41, the calculated σ_F is marred by geometric nonlinearity effects (see Discussion section), and thus it is not included in Figure 4. Also shown in Figure 4B are the K_C values for alumina, porcelain, and (001) single crystal silicon from (Chai 2009). Included in Figure 4 are the literature data for σ_F and K_C given in the Table; all these σ_F values are associated with a biaxial stress field, layer thickness of ≈1.2 mm or more, and polished surface. The literature toughness data include precracked bending or compact tension-type specimens as well as Vickers indentation specimens. A significant scatter is evident for some of the present and literature data.

Figure 4.

Material data from the present work and literature as detailed in the Table. (A) Biaxial flexural failure stress σ_F. (B) Fracture toughness K_C. Note that the data for 3Y-TZP in the Table (Čokić et al. 2022) are here prescribed to 3Y-PSZ.

Discussion

The biaxial flexural strength σ_F and fracture toughness K_C of a range of dental ceramics were determined using the BSC test. Under spherical indentation, tunneling radial cracks initiate on the subsurface of the ceramic layer and propagate dynamically to some length before being arrested. σ_F and K_C were computed from equations (1) and (2), respectively, using the failure initiation force and, for K_C, also the mean length of the arrested cracks (Fig. 1A). In calculating K_C, complex crack profiles as in the lower row in Figure 3A and crack length c exceeding ≈4d were avoided. The literature data for σ_F and K_C exhibit considerable scatter in a given test or among authors testing the same ceramic material (Fig. 4). The scatters in the present tests are in the same order of magnitude as that in literature.

Flexural Strength

The large scatter seen in Figure 4A is somewhat perplexing given that all the data were obtained using biaxial flexure specimens, similar composition (e.g., all glass ceramics were A2 shade and HT grade; zirconias were primarily Tosoh grades), layer thickness d (i.e., 1 mm here and around 1.2 mm in the literature), and mirror-like surface quality. The scatter in a given source is attributable to such factors as geometric misalignments and presence of a large surface flaw. In the present bilayer test, the stress is maximized over a small region around the loading axis, which limits the flaw size effect. The effect of surface quality is clearly seen for the case of soda-lime glass (Chai et al. 1999), where the failure stress for a chemically etched surface was nearly 10 times that due to abrasion by a slurry of 600-grit SiC particles.

The present test has several useful traits, including ability to accommodate very thin layers and perform a number of indents in a single specimen. However, some limitations on the thinnest layer exist. To demonstrate this, we calculated the ratio ρ = σ_F(d)/σ_F (d = 1 mm) for all our d values using equation (1). The results are ρ = (1.51, 1.53, 1.35) for (3Y, 4Y, 5Y)PSZ (d = 0.25 mm), and ρ = (2.1, 1.53, 1.31) for (IPS e.max CAD, CEREC Tessera, GC LiSi) (d = 0.41 mm). Thus, the calculated flexural strength for the thin layers greatly exceeds the true value due to d = 1 mm. This departure is attributed to geometric nonlinear effects. As shown in Chai and Lawn (2004), to maintain the required linearity between P and d² in equation (1), the ratio d/a should exceed ≈2 or d > ≈20σ_Fr/E_c, where a is the contact radius. To exemplify this, consider indentation by a 3.17-mm radius ball. For a 3Y-PSZ layer with σ_F = 1.47 GPa, d/r should exceed 0.143 or d > 0.46 mm. This value is nearly twice that used in this work (0.25 mm). In the case of glass, with σF = 1,000 MPa for a polished surface and 110 MPa for a surface abraded with 600-grit slurry of SiC particles (Chai et al. 1999), the limiting value of d is 0.91 and 0.10 mm, respectively.

Fracture Toughness

An insight into the data scatter seen in Figure 4B can be gained from the work of Belli et al. (2018), who evaluated K_C using a variety of test specimens, including ball-on-3-balls biaxial flexure with indentation notch and compact tension with sawed or Chevron notches. K_C for IPS e.max CAD varies from 1.92 to 2.29 MPa m^1/2 while the data from the other 7 references given in this source ranged from 1.23 to 2.37 MPa m^1/2 (Table). These values compare with the 1.80 (0.21) figure in the present test. The data scatter is also influenced by crack velocity. As shown in Zhang et al. (2019), the K_C value for 3Y-PSZ varies from 2.6 for a slow growth to 4.8 MPa m^1/2 for a rapid one.

The BSC test has several useful traits. First, the values of K_C for layer thickness d as small as 0.15 mm for soda-lime glass, 0.25 mm for zirconias, and 0.41 mm for the other ceramics were comparable to literature values. (Note that for K_C, the geometric nonlinearity effects are muted owing to the remoteness of crack tip from the contact axis.) Second, it is only necessary to measure the mean crack length c after unloading. Third, there is no requirement on the layer surface quality or a need to introduce an initial crack (and analyze its effect). As in other bending tests, radial or cone cracking from the indented surface should be avoided. This can be achieved using relatively large indenters; as shown in Chai (2014), the load needed to initiate such cracks increases with ball radius.

Conclusions

A simple bilayer subsurface cracking test for determining biaxial flexural failure stress σ_F and fracture toughness K_C in brittle layers is proposed. The BSC test is especially suitable for dental glass-ceramic materials available in small sizes and quantities. Such materials are hard to shape into a desired test specimen. The proposed test eliminates the need to introduce a precrack for toughness evaluation and deal with material nonlinearity effects as in Vickers indentation tests. To validate the method, a number of dental lithia glass-ceramic and zirconia materials were tested. As shown in Figure 4, the values of σ_F and K_C obtained using the BSC test are within the range obtained in commonly used testing approaches. Finally, the explicit relations presented enable simple, direct estimates of critical failure loads in dental prostheses. The BSC test thus emerges as a viable testing methodology in restorative dentistry.

Author Contributions

H. Chai, Y. Zhang, contributed to conception, design, data acquisition, analysis, and interpretation, drafted and critically revised the manuscript; J. Russ, S. Vardhaman, contributed to data acquisition, analysis, and interpretation, critically revised the manuscript; C.H. Lim, contributed to data acquisition, critically revised the manuscript. All authors gave final approval and agree to be accountable for all aspects of the work.