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Materials Design of Ceramic-based Layer Structures for Crowns

¹ Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899-8500;
² Department of Materials and Nuclear Engineering, University of Maryland, College Park, MD 20742-2115; and
³ University of Medicine and Dentistry of New Jersey, Dental School, 110 Bergen Street, Newark, NJ 07103-2400;

*corresponding author, brian.lawn{at}nist.gov

	ABSTRACT

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Radial cracking has been identified as the primary mode of failure in all-ceramic crowns. This study investigates the hypothesis that critical loads for radial cracking in crown-like layers vary explicitly as the square of ceramic layer thickness. Experimental data from tests with spherical indenters on model flat laminates of selected dental ceramics bonded to clear polycarbonate bases (simulating crown/dentin structures) are presented. Damage initiation events are video-recorded in situ during applied loading, and critical loads are measured. The results demonstrate an increase in the resistance to radial cracking for zirconia relative to alumina and for alumina relative to porcelain. The study provides simple a priori predictions of failure in prospective ceramic/substrate bilayers and ranks ceramic materials for best clinical performance.

KEY WORDS: dental ceramics • elastic modulus • hardness • fracture • layer structures • material design • strength • toughness

	INTRODUCTION

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Background
Ceramics are attractive materials for use in dental crowns because of their aesthetics, inertness, and biocompatibility. But all ceramics are brittle, to a greater or lesser extent, and tend to fail beyond a critical load or lifetime (Lawn, 1993). Even all-ceramic crowns fabricated with aesthetic but weak veneer porcelains on strong support alumina cores (InCeram) are subject to premature failure (Kelly, 1999). In the clinical context, we need to understand the fundamental mechanics of failure in dental ceramics on soft dentin-like underlayers under conditions that simulate basic occlusal function, so that a proper foundation can be laid for rational materials design of future multilayer crown structures.

The basic elements of occlusal function can be simulated in the laboratory by controlled contact testing (DeLong and Douglas, 1983). In the last decade, tests on monolithic polycrystalline ceramics (Guiberteau et al., 1993; Lawn, 1998; Peterson et al., 1998a; Rhee et al., 2001a) indicate two modes of damage in the near-contact field: brittle mode—in small-grain, high-strength ceramics, with classic cone-like tensile cracks initiating from the upper surface; and quasi-plastic mode—in coarse-grain, high-toughness ceramics, with distributed shear-microcracks initiating within a subsurface "yield" zone. Analogous contact tests on flat ceramic layers joined to dentin-like soft substrates (Wuttiphan et al., 1996; Chai et al., 1999; Jung et al., 1999; Chai and Lawn, 2000) indicate a third mode, radial cracking at the inner surface (i.e., at the ceramic-layer/substrate interface), driven by undersurface tension from flexure of the ceramic layer on the soft support substrate. This last mode is considered most relevant in the context of failure of all-ceramic crowns, because it can occur at relatively low loads and spread over long lateral distances. Moreover, it may remain entirely subsurface, and therefore pass undetected in opaque materials.

Independent studies in the clinical literature on simulated crown structures, mostly flat-layer ceramics on composite resin bases in various forms of upper-surface contact loading, acknowledge the existence of at least two of the above damage modes (Scherrer and Rijk, 1993; Scherrer et al., 1994; Kelly, 1997; Tsai et al., 1998)—specifically, outer-surface Hertzian-like cracks and inner-surface radial cracks, depending on loading and layer geometry. Kelly and others (Kelly et al., 1990; Thompson et al., 1994; Kelly, 1999; Wakabayashi and Anusavice, 2000) argue that it is the inner-surface cracks that are most likely to lead to clinical crown failures. Those studies, coupled with finite element modeling, noted empirical dependencies of critical fracture loads on ceramic thickness and ceramic/substrate elastic modulus ratio. However, the explicit form of these dependencies and the role of other material parameters (strength, toughness, hardness) were not determined.

Basic Fracture Mechanics Relations
Recently, explicit analytical fracture mechanics relations expressing critical contact loads for each damage mode in terms of basic material and geometrical parameters (elastic modulus, toughness, hardness, strength) and critical geometrical variables (layer thickness, indenter radius) have been developed for bilayer brittle-ceramic/ soft-substrate structures (Lawn et al., 2000; Rhee et al., 2001b). Such relations open the way to rational design of ceramic-based crown structures.

Consider the flat-layer system of Fig. 1, consisting of a single ceramic layer of thickness d and Young's modulus E_c bonded onto a compliant thick substrate of modulus E_S, subjected to contact at load P with a sphere of radius r_i and modulus E_i. From the theory of Hertzian elastic contact, it is convenient to generalize the description by defining an "effective sphere radius" r and "effective ceramic modulus" E (Rhee et al., 2001a):

(1a)

(1b)

View larger version (29K): [in this window] [in a new window]   Figure 1. Schematic of brittle layer of thickness d and modulus EC on a compliant substrate of modulus ES, depicting sphere indenter of radius ri. (Specimen radius rc in general relation Eq. 1a is effectively infinite in the flat layer structure depicted here.) Damage modes: surface cone cracks (C); quasi-plastic yield zone (Y); inner-surface flexural radial cracks (R).

Fig. 1 depicts three basic ceramic-layer damage modes, for which the critical load relations are as follows (Lawn et al., 2000; Rhee et al., 2001a,b):

    (i) Cone cracks (C)
This kind of fracture initiates from the top surface outside the contact circle, where the Hertzian tensile stress is maximum. The crack first grows downward as a stable, shallow surface ring, resisted by the material toughness T (K_Ic), before propagating unstably and arresting in its ultimate cone-like geometry. The critical load for crack pop-in is

(2)

with dimensionless constant A = 8.6 x 10³ from fits to data from monolithic ceramics with known toughness (Rhee et al., 2001a).

    (ii) Quasi-plasticity (Y)
Yield initiates when the maximum shear stress in the Hertzian nearfield exceeds one-half the yield stress for plastic deformation, which in turn is proportional to the material hardness H (load/projected area, Vickers indentation). The critical load is given by

(3)

with dimensionless constant D = 0.85 from fits to data for monolithic ceramics with known hardness (Rhee et al., 2001a).

    (iii) Radial cracks (R)
These cracks initiate spontaneously from a starting flaw in the inner ceramic surface when the maximum tensile stress in this surface equals the bulk flexure strength _F of the ceramic, at critical load

(4)

with dimensionless constant B = 2.0 from data fits to well-characterized bilayer material systems (Rhee et al., 2001b).

In this paper, we examine the hypothesis that the critical loads for dominant flexural radial cracking vary as the square of layer thickness, as predicted by Eq. 4, at ceramic layer thicknesses less than 1 mm.

	MATERIALS & METHODS

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Single-cycle Hertzian contact experiments were conducted on crown-like ceramic layers bonded to dentin-like soft support substrates (Rhee et al., 2001b). The ceramic materials used in this study are listed in the Table, along with commercial sources and pertinent properties. Ceramic materials were supplied by the manufacturers in the form of plates with minimum lateral surface dimension of 15 mm. These were ground flat and parallel, and upper and lower ceramic surfaces were polished with 1 µm diamond paste, to thicknesses in the range 100 µm to 6 mm. The ceramic layers were bonded to thick (12.7 mm) transparent polycarbonate support substrates (previous work indicates that increasing substrate layer thicknesses above 2 mm do not strongly influence Hertzian contact damage [Miranda et al., 2001]). Bonding was effected by means of an epoxy adhesive (Harcos Chemicals, Bellesville, NJ, USA) under light pressure for 24 hrs. The resultant thin (10-20 µm) adhesive interlayer was also transparent, with elastic properties similar to those of the polycarbonate base, so that viewing of subsurface radial cracks would not be impaired (Chai et al., 1999; Chai and Lawn, 2000).

Radial crack initiation and evolution were monitored in situ from below the contact through the transparent adhesive/ polycarbonate sublayer by means of an optical zoom microscope with a video tape recorder (Optem, Santa Clara, CA, USA) (Chai et al., 1999; Chai and Lawn, 2000; Kim et al., 2001). (In polycrystalline ceramics, the microstructures provide an abundance of natural flaw sites for radial crack initiation [Lawn, 1993].) The contact load from the testing machine output was recorded on the tape as a picture-in-picture inset. Means and standard deviations for P_R were determined directly from the videotape, for a minimum of n = 5 indentations on each determination. An alternative procedure was used to determine the onset of cone cracking and quasi-plasticity in the opaque ceramic layers (Peterson et al., 1998a). Rows of indentations were made on each layer surface at incrementally increasing peak loads, and the indented outer surfaces were gold-coated and examined a posteriori in Nomarski illumination. Mean and uncertainty bounds for P_C were determined from the loads over which surface ring cracks first appeared as incipient shallow arcs (lower limit) and were fully formed (upper limit), minimum n = 5. Values for P_Y were similarly determined as the load ranges over which the residual surface impressions were completely undetectable and were clearly visible.

To facilitate data comparisons between any two materials, we made regression analyses on the P_R critical load data as a function of ceramic layer thickness d for each bilayer system, and correlation coefficients were determined.

	RESULTS

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Fig. 2 shows a micrographic sequence of radial crack evolution in one bilayer system, glass-infiltrated-alumina/polycarbonate, video-recorded through the bottom of the transparent substrate during one complete Hertzian loading cycle. The example is for a relatively thin alumina layer, d =155 µm, at a sphere radius r = 3.96 mm, but the observations are quite representative of all thicknesses studied, including those in the clinically relevant region 500 µm to 1.5 mm. The sequence shows how radial cracks initiate (pop-in) at a critical load, multiply, and extend as the indenter load is increased beyond this threshold, and ultimately close up and become almost invisible as the indenter is withdrawn. (Reloading regenerates the same pattern, indicating that the cracks do not heal and therefore remain dangerous.) These cracks have a typically elongate geometry, with lateral dimension d and through-thickness dimension 0.5 d at pop-in. At higher loads, the radial cracks became even more elongate, sometimes propagating to the edge of the specimen (full failure). No delamination occurred at the ceramic/polycarbonate interface in our experiments, despite the weak epoxy bond and the metallized alumina undersurface.

View larger version (152K): [in this window] [in a new window]   Figure 2. Radial crack sequence in glass-infiltrated alumina layer, thickness d = 155 µm, on polycarbonate substrate, from indentation with WC sphere of radius r = 3.96 mm. Sequence during loading cycle at (a) P = 15.1 N (critical), (b) P = 35.1 N (intermediate), (c) P = 56.6 N (peak), and (d) P = 0 N (fully unloaded).

View larger version (24K): [in this window] [in a new window]   Figure 3. Critical load for first damage as function of layer thickness d, for ceramic/polycarbonate bilayers indented with WC spheres. (a) Results for zirconia, alumina, and porcelain specimens, fixed sphere radius r = 3.96 mm. Filled symbols are PR data (R), unfilled symbols are PC data (C) or PY data (Y). Minimum n = 5 indentations each data point, standard deviation limits shown (some less than the size of the symbol). Solid lines are theoretical first-damage predictions for radial and cone cracking or quasi-plasticity. (Regression fits not shown.) (b) Predictions from Eq. 4 for hypothetical Dicor/polycarbonate bilayers, sphere radii r = 4 mm and 2 mm. Inclined lines—radial cracking (R); horizontal lines—cone cracking (C) or quasi-plasticity (Y). Shaded line represents a nominal occlusal load of 100 N, dashed vertical line indicates the corresponding thickness ( 0.3 mm) at which this load will induce flexural radial cracking.

	DISCUSSION

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Fundamental damage modes in flat dental ceramic layers on soft substrates in contact loading that simulates the basic elements of occlusal function have been confirmed for ceramic crown layers with clinically relevant thicknesses. Critical loads to initiate each mode have been measured for selected dental ceramic materials, as a function of layer thickness and contacting sphere radius. In situ observations of the inner ceramic surfaces through the base of the transparent substrate material facilitate determination of critical initiation loads for radial cracks, as well as of subsequent evolution of these cracks to failure. These radial cracks are of primary interest for their clinical relevance (Kelly et al., 1990; Thompson et al., 1994; Tsai et al., 1998)—they can form at relatively low loads in thinner layers and thereafter grow over long distances subsurface. The observations in Fig. 2 suggest that such subsurface radial cracks may be hard to detect in clinical examinations, especially in opaque crowns on dentin substrates. Fig. 3a shows that cone cracking or quasi-plasticity becomes the dominant damage mechanism above a certain threshold thickness for each ceramic. Such a shift in damage mechanism may not always be apparent in routine testing, depending on contact conditions—for instance, no such shift to cone cracking was reported in flexure tests on Dicor/epoxy-resin plates (Tsai et al., 1998), where adhesive tape (thickness, 0.6 mm) on the top surface and a relatively blunt (1.6-mm-diameter flatended punch) indenter were deliberately used to reduce the contact stress concentration.

The critical load data in Fig. 3a have been analyzed in terms of analytical fracture mechanics relations (Eqs. 1-4) for each damage mode. Statistical analysis of the flexural radial crack data (correlation coefficients > 0.98) confirms the hypothesis that these relations have the capacity to account for essential data trends. The relations explicitly identify controlling geometric and material parameters. For the outer-surface cone cracking and quasi-plasticity modes, it is sphere radius r and toughness T or hardness H that control. For the inner-surface flexural radial crack mode, layer thickness d and strength _F are the crucial parameters—modulus mismatch E_c/E_s enters only as a relatively slow logarithmic dependence. In the case of radial cracks, the critical load varies as the square of the ceramic layer thickness, P_R d².

The fracture mechanics relations thereby facilitates a priori predictions of critical loads for ceramic-crown-like bilayer systems. Our experiments have been performed on soft polycarbonate substrates (E_S = 2.35 GPa) for experimental convenience. In real crown systems, the modulus of dentin is substantially higher (E_s =16 GPa) (Xu et al., 1998; Kinney et al., 1999). Recent contact studies for soda-lime glass (E_s = 70 GPa; cf. E_s = 68 GPa for porcelain) on a broad range of compliant substrates (E_s = 2.35-44 GPa) have confirmed the logarithmic E_c/E_s dependence in Eq. 4 (Lee et al., 2000). According to Eq. 4, therefore, replacing E_s for polycarbonate with that for dentin will simply shift the P_R(d) curves upward in Fig. 3a. Also in real crown systems, the cuspal radius r_c of the crown is finite (cf. r_c = for flat-layer systems). From Eqs. 1-3, decreasing r_c from infinity will shift the P_C(d) and P_Y(d) curves downward in Fig. 3a. As an illustrative case study, consider a monolithic glass-ceramic (Dicor) crown on dentin substrate, in occlusal contact with tooth enamel (E_i = 94 GPa), assuming r_i = r_c. Fig. 3b is a design diagram constructed according to Eqs. 1-4, in conjunction with appropriate material parameters from the Table, in analogy to Fig. 3a. Predictions are shown for P_R, P_C, and P_Y at two cuspal radii, r_c = 2 and 4 mm. The horizontal band at P_* = 100 N represents a nominal molar biting force. Minimum conditions to survive dental function are that (i) the ceramic thickness should remain above 1 mm, to avoid radial cracking, and (ii) the cuspal radius should remain above 4 mm, to avoid quasi-plasticity (or cone cracking). While studies of failed Dicor crowns indicate ceramic thicknesses > 1 mm in almost all cases (Malament and Socransky, 1999), the especially high susceptibility of glass ceramics to quasi-plasticity (Peterson et al., 1998b) (attributable to a relatively low hardness) may account for the unacceptably high failure rates of Dicor molar crowns in clinical practice (Malament and Socransky, 1999; Sjogren et al., 1999). In harder ceramics, radial cracking is expected to be the dominant mode of failure.

Of interest is the appearance of strength _F in Eq. 4 for radial cracking. The strength of ceramics varies with the inverse square root of flaw size (Lawn, 1993). In polycrystalline ceramics, especially those with coarser grain structures, such flaws are generally intrinsic to the microstructure (Peterson et al., 1998b). For ceramics with more refined microstructures, dominant flaws may be introduced in surface handling or preparation, e.g., by sandblasting or grinding ("machining flaws"), or from preparation and manufacturing problems (voids). One should therefore take care to avoid large surface flaws in the undersurface of the brittle layer, to prevent the P_R(d) function from shifting downward in Fig. 3. At the same time, P_C in Eq. 2 and P_Y in Eq. 3 are relatively insensitive to starting flaw size (Langitan and Lawn, 1969).

Some restrictions in our analysis are acknowledged. We have considered only flat-surface ceramic monolayers on soft substrates, with virtually no intervening adhesive layer. Real crowns consist of ceramic veneer/core bilayers, with convoluted cuspal/occlusal geometries and complex loading, bonded to dentin with cement layers that may be 100 µm or more thick and contain voids. Recent work on ceramic veneer/core bilayers indicates that the veneer/core thickness ratio can be a crucial variable in failure mechanics, especially for radial cracking (Wakabayashi and Anusavice, 2000; Miranda et al., 2001). The compliance of even the thinnest adhesives (down to 10 µm) can have disproportionately large effects, especially between two adjoining stiff layers (Chai and Lawn, 2000). Cyclic contact loading of monolithic ceramics has been shown to cause cumulative strength degradation in a variety of dental ceramics (Jung et al., 2000)—others have demonstrated analogous degradation in all-ceramic crowns bonded to dentin-like substrates (Chen et al., 1999). These complicating factors may ultimately be best evaluated in artificial mouth-motion machines. Nevertheless, the procedure outlined here affords a simple route to the materials characterization of layered dental ceramics, and provides a sound physical basis for design against lifetime-threatening damage in simulated occlusal conditions.

	ACKNOWLEDGMENTS

 
Thanks are due to H.-W. Kim, I.M. Peterson, Y.-W Rhee, J. Quinn, and H. Xu at NIST for providing some of the data in the Table. Specimen materials were generously supplied by H. Hornberger of Vita Zahnfabrik, Bad Sackingen, Germany, and E. Levadnuk of Norton Desmarquest Fine Ceramics, East Granby, CT, USA. This study was supported by a grant from the US National Institute of Dental and Craniofacial Research, POI DE10976.

Received December 12, 2000; Last revision February 20, 2002; Accepted April 4, 2002

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