| Sign In to gain access to subscriptions and/or personal tools. |
Sliding Contact Fatigue Damage in Layered Ceramic StructuresDepartment of Biomaterials and Biomimetics, New York University College of Dentistry, 345 E. 24th St., Room 813C, New York, NY 10010, USA Correspondence: * corresponding author, yz21{at}nyu.edu
Porcelain-veneered restorations often chip and fracture from repeated occlusal loading, making fatigue studies relevant. Most fatigue studies are limited to uni-axial loading without sliding motion. We hypothesized that bi-axial loading (contact-load-slide-liftoff, simulating a masticatory cycle), as compared with uni-axial loading, accelerates the fatigue of layered ceramics. Monolithic glass plates were epoxy-joined to polycarbonate substrates as a transparent model for an all-ceramic crown on dentin. Uni-and bi-axial cyclic contact was applied through a hard sphere in water, by means of a mouth-motion simulator apparatus. The uni-axial (contact-load-hold-liftoff) and traditional R-ratio fatigue (indenter never leaves the specimen surface) produced similar lifespans, while bi-axial fatigue was more severe. The accelerated crack growth rate in bi-axial fatigue is attributed to enhanced tensile stresses at the trailing edges of a moving indenter. Fracture mechanics descriptions for damage evolution in brittle materials loaded repeatedly with a sliding sphere are provided. Clinical relevance is addressed.
Key Words: fatigue • load-slide contact • partial cone cracks • layered structures • ceramics
One of the emerging causes of fracture of all-ceramic dental restorations is the generation of microcracks due to occlusal contact and wear. To improve the contact damage resistance of dental ceramics, one must understand the damage mechanisms involved.
A three-phase model of a chewing cycle has been proposed by DeLong and Douglas (1983): a preparatory phase, during which the mandible is positioned; a crushing phase, which starts from tooth contact with the food bolus until it comes into contact with the opposing tooth; and a final grinding or sliding phase, where the 2 opposing teeth slide against each other under the masticatory force. The sliding phase for the molar teeth begins with an eccentric contact of the mandibular buccal cusps with the inner inclines of the maxillary buccal cusps, followed by a sliding movement through centric occlusion, and then lifting off (Fig. 1a
The above contact-slide action is most pertinent to porcelain occlusal damage and wear. Yet most contact fatigue studies use uni-axial loading without the critical sliding action. This study sought to address this by using mouth-motion-like fatigue loading (contact-load-slide-liftoff) on crack evolution in ceramics with uni-axial and R-ratio controls.
Materials Systems Soda-lime glass was used as a model material, because its physical properties are similar to those of dental porcelains, and its transparency allows for in situ observation of the entire evolution of fracture. Glass plates (25 x 25 x 1 mm, Daigger, Wheeling, IL, USA) were polished on side surfaces for in situ viewing during testing. The top surfaces of the glass plates were lightly abraded with 600-grit SiC to provide an adequate density of flaws for cone crack initiation, for the introduction of flaws comparable in scale (~ 10 – 20 µm) with those associated with crystallites in the porcelain and glass-ceramic interior. The bottom surfaces of the plates were etched with 9.5% hydrofluoric acid for 5 min to remove surface flaws and to avoid flexure-induced bulk fracture from the cementation interface. Plates were then joined to the polycarbonate substrates (12.5 mm thick, AlN Plastics, Norfolk, VA, USA) with a thin layer (~ 10–20 µm) of epoxy adhesive, which was allowed to cure for 48 hrs. Since the elastic modulus of epoxy (3.5 GPa) is similar to that of polycarbonate (2.3 GPa), the structure was effectively a glass/polycarbonate bilayer. For reference, porcelain-veneered (LAVA Ceram, 3M/ESPE, St. Paul, MN, USA) (  20 x 1 mm), fully sintered CAD/CAM zirconia plates ( 20 x 0.5 mm) (LAVA Frame, 3M/ESPE) were cemented (Rely X, ARC, 3M/ESPE) to composite blocks (Z100, 3M/ESPE) (Kim et al., 2007).
Fatigue Tests
Crack Morphology In all instances, cone cracks were the dominant mode of fracture, but differed in evolution, with R-ratio and uni-axial fatigue most similar (see sequence in Fig. 2a  , Pm = 120 N). In both R-ratio and uni-axial fatigue, the outer cone initiated first and propagated downward and outward at a slow but steady pace. The angle of the cone crack,  , relative to the free surface was typically 22 ± 5°. Subsequently, an inner cone formed within the contact region from the occlusal surface and extended downward at a relatively high rate and steep angle (55 ± 15°). Intrusion of water into the inner cone crack was evident, especially during the loading cycle. When inner cones propagated approximately halfway through the glass thickness, they began to experience the plate flexure-induced tensile stresses and surged abruptly to the glass polycarbonate interface. In all tests, failure of the glass layer resulted from the deep-penetrating inner cones.
In bi-axial fatigue at the same load ( Pm = 120 N, Fig. 2b  ), a comparable sequence of observations revealed a series of partial cone cracks forming in the first sliding cycle (distorted outer cones of uni-axial loading; see APPENDIX). The trailing edges of the partial cones had an inclination angle ' = 52 ± 10°, which was much steeper than for classic Hertzian outer cones in uni-axial loading ( = 22 ± 5°). Water intrusion was observed from the second sliding cycle onward. These partial cones became increasingly unstable as they approached the mid-thickness of the glass plate, and ultimately jumped to the glass polycarbonate interface. The final crack configuration had a tilted aspect, somewhat like the schematic in the APPENDIX (APPENDIX Fig., b). The main difference between the bi-axial fatigue and uni-axial or R-ratio fatigue was propagation of the partial cones to the glass polycarbonate interface, rather than the inner cones in the latter.
Similar sliding damage features, a series of partial cones, were observed in surface-view optical micrographs of glass/polycarbonate and porcelain/zirconia/composite structures subjected to single-cycle bi-axial loading ( Pm = 120 N, WC indenter, r = 1.5 mm) in water (Figs. 2c, 2d ).
Crack Evolution
During the first sliding cycle of bi-axial fatigue (Fig. 3c ), a series of partial cone cracks formed, at a much greater depth (~ 200  m) and a steeper angle to the classic outer cone cracks of uni-axial loading. Under the subsequent sliding contacts, one of the partial cone cracks, usually the second or the third one from the initial contact point, began to dominate. This dominant crack extended downward dramatically to the half-thickness of the glass plate, followed by a rapid jump to the glass polycarbonate interface. The number of cycles required for cracks to penetrate the entire glass layer was over 2 orders of magnitude less for partial cones as compared with inner cones in both uni-axial and R-ratio fatigue (vertical dashed lines in Fig. 3). A one-sample t test showed this difference to be significant (p < 0.001).
This report has considered the influence of bi-axial fatigue on crack modes in brittle-layer structures using a hard sphere in water, with data on model glass/polycarbonate bilayers as a case study. For a glass thickness of 1 mm used here, the dominant stresses are the near-contact Hertzian stresses. The corresponding mode of fracture is occlusal surface cone cracking. Definitive experiments have been conducted to identify the effect of the initial quasi-impact contact and sliding action (analogous to tooth contact during mastication) on the damage modes and fatigue life of brittle layers on compliant substrates. Our findings showed that an initial quasi-impact contact had little influence on either damage modes or fatigue life of glass/polycarbonate bilayers. However, sliding motion under masticatory force was highly deleterious to the layers’ lifetime. Therefore, sliding action must be considered in any laboratory simulation of the clinical environment intended to establish the longevity of all-ceramic crowns.
Friction associated with sliding action intensified the tensile stresses at the trailing edges of the contact, generating a series of partial cone cracks. Both theory (APPENDIX) and experiments indicate that, for a given load, partial cone cracks penetrate deeper into the material relative to uni-axial outer cone cracks. The uni-axial outer cones experience tensile stresses throughout the entire load-unload cycle, while partial cones experience both compressive (shaded grey) and tensile stresses as the indenter slides across the surface (Fig. 4
We have not considered internal radial cracks, originating from the cementation surfaces. These far-field flexural-stress-induced cracks are not sensitive to loading conditions, uni-axial or bi-axial (Lee et al., 2001). Radial cracks can become dangerous in thin ceramic crowns, since they propagate rapidly and the load for initiation falls off rapidly with diminishing thickness. Radial fracture will not be an immediate threat to ceramic thickness > 1 mm. For dental crowns, the norm is a thickness of 1.5 mm, but geometric constraints imposed by tooth position and the opposing dentition may limit thickness. Our studies found that cone cracks ceased at the glass/polycarbonate interface, neither propagating into the polycarbonate base nor extending along the interface. Although the incidence of occlusal cone cracks may not result in catastrophic failure of the ceramic crowns, as may cementation radial fractures (i.e., bulk fracture), they may nevertheless provide pathways for external elements to the interior of the layer system. In the case of weak interfaces, cone cracks can promote interlayer delamination. We acknowledge that occlusion involves enamel-porcelain or porcelain-porcelain antagonistic contacts with various cuspal radii. The question arises: How do the choices of indenter material and radius influence the mechanics? A recent study has shown that the critical loads and numbers of cycles to penetrate an occlusal surface cone crack through a glass layer are insensitive to either the indenter material (WC or glass) or the indenter radius (r = 1.6–12.5 mm) (Bhowmick et al., 2007). The choice of a hard WC indenter is simply to enable multiple testing to be conducted without the need for test-by-test replacement of the indenter. Our results might be modified in saliva, which is known to reduce the friction coefficient between the slider and the ceramic surface (Koran et al., 1972). Further investigation into the effect of saliva is warranted. In summary, occlusal-like bi-axial loading of brittle crown-like structures can trigger a series of partial cone cracks, capable of causing failure by propagation to the intervening interface. Fracture mechanics descriptions (APPENDIX) have been developed for the evolution of partial cones in brittle materials loaded repeatedly with a sliding sphere. In aqueous environments, the friction-activated partial cone cracks are much more deleterious than the outer and inner cone cracks associated with uni-axial fatigue loading.
FRACTURE MECHANICS ANALYSIS OF HERTZIAN CONTACT The stress fields associated with frictionless elastic contacts (µ = 0) between a rigid spherical indenter and a flat brittle specimen have been solved by Hertz (Hertz, 1882). The semi-ellipsoidal distribution of contact pressure gives rise to a region of compression of the surface in the center of the contact, surrounded by a region of tension with the maximum tensile stresses in the specimen occurring at the edge of the contact circle. Hamilton and Goodman (Hamilton and Goodman, 1966; Hamilton, 1983) have extended the analysis to the case where the indenter is moved across the specimen surface at a constant velocity. Their main conclusions were that: (1) the friction between the sliding sphere and the specimen added a compressive stress at the front edge of the contact and enhanced the tensile stress at the trailing edge of the contact; and (2) greater friction yielded higher tensile stresses. These findings indicate that cone cracks would initiate at a lower load in the sliding contact compared with normal loading.
A complete analysis of crack initiation and propagation under the action of Hertzian contact requires a knowledge of fracture mechanics. It is now well-appreciated that cone cracks start from small flaws on the specimen surface just outside the contact circle, where the tensile stresses are greatest (Frank and Lawn, 1967). Embryonic cracks, initially in the form of shallow surface ring cracks, will, at a critical load, propagate downward and flare outward into a truncated cone configuration (Lawn, 1998). A detailed analysis of cone crack initiation at the small-flaw stage has been described (Frank and Lawn, 1967). Here, we focus on the classic cone crack in its well-developed state, i.e., cone cracks enter the tensile far-field, where the crack length C >> R0 (R0 is the contact radius) (APPENDIX Fig., a
where Kc is the stress-intensity factor, and
With the actual penetration depth of a virtual cone h = C sin
When the indenting sphere is laterally translated across a brittle surface, friction at the contact intensifies the tensile stresses at the trailing edges of the contact circles, resulting in the generation of a series of distorted classic cone cracks, i.e., partial cone cracks (APPENDIX Fig., b
The inclination angle
where
Explicit equations (A2–A4) quantitatively predict the penetration depth and inclination angle of cone cracks for biaxial (contact-load-slide-liftoff) loading. For a given normal load Pn, a larger friction results in a larger cone crack (C'), with a steeper inclination angle ( APPENDIX REFERENCES Frank FC, Lawn BR (1967). On the theory of Hertzian fracture. Proc R Soc London Series A Math Phys Sci 299(1458):291–306. Hamilton GM (1983). Explicit equations for the stresses beneath a sliding spherical contact. Proc Inst Mech Eng 197(C):53–59. Hamilton GM, Goodman LE (1966). The stress field created by a circular sliding contact. J Appl Mechanics 33:371–376. Hertz H (1882). On the contact of elastic solids. J Reine und Angewandte Mathematik 92:156–171. Kocer C, Collins RE (1998). Angle of Hertzian cone cracks. J Am Ceram Soc 81:1736–1742. Lawn BR (1967). Partial cone crack formation in a brittle material loaded with a sliding spherical indenter. Proc R Soc Lond Series A Math Phys Sci 299:307–316. Lawn BR (1993). Fracture of brittle solids. 2nd ed. Cambridge: Cambridge University Press. Lawn BR (1998). Indentation of ceramics with spheres: a century after Hertz. J Am Ceram Soc 81:1977–1994. Lawn BR, Wiederhorn SM, Roberts DE (1984). Effect of sliding friction forces on the strength of brittle materials. J Mater Sci 19:2561–2569.
Valuable discussions with Dr. Brian R. Lawn are appreciated. This work is supported by the New York University Research Challenge Fund.
A supplemental appendix to this article is published electronically only at http://www.dentalresearch.org. Received for publication February 22, 2007. Revision received June 5, 2007. Accepted for publication June 12, 2007.
Journal of Dental Research, Vol. 86, No. 11,
1046-1050 (2007) This article has been cited by other articles:
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
 |
|
|
 |
|
Sign In to gain access to subscriptions and/or personal tools.
TOP
ABSTRACT
INTRODUCTION
0.58. It was estimated according to Eq. A4 (APPENDIX), with a measured value of 
, 
, or 
.
= arctan µ. 
