Edge chipping patterns in posterior teeth of hominins and apes.

Chip scars in fossil teeth are a lasting evidence that bears on human evolution. Chip dimensions in posterior teeth of hominins, apes and white-lipped peccary (Tayassu pecari) are measured from published occlusal images. The results are plotted as D/Dm vs. h/Dm, where h, D and Dm denote indent distance, chip width and mean tooth crown diameter. The hominin species follow a similar pattern where D/Dm monotonically increases up to h/Dm ≈ 0.3. The behavior for the apes is characterized by two phases. In the first, h/Dm monotonically increases up to h/Dm ≈ 0.26 while in the second (h/Dm ≈ 0.26 to 0.42), D/Dm experiences a drastic change in behavior. The interpretation of chip morphology is assisted by results from controlled spherical indentation tests on extracted human molars. This study shows that in addition to the commonly recognized chipping due to cusp loading, a chip may also initiate from the inner wall of the tooth's central fossa. Accordingly, it is suggested that the chipping in hominins generally initiates from a (worn) cusp while that in apes involves cusp loading up to h/Dm ≈ 0.26 and fossa loading thereafter. The behavior for T. pecari is much similar to that of the apes. The fossa chipping is facilitated by a consumption of hard, large-size diet (e.g., plants, roots, barks and nuts) and presence of broad central fossa, conditions that are met in apes. Finally, a simple expression for the critical chipping force Pch due to fossa loading is developed.

On edge chipping in molar teeth from blunt occlusal contact.

Edge chipping is a leading failure mode in dental teeth. Virtually all chipping studies are limited to Vickers indentation on polished cusps of molar teeth. Such works are here extended to spherical contact. Occlusal loads are applied on the tooth's central fossa or a polished cusp using ball radii ranging from 0.4 to 5.16 mm. The chip dimensions are characterized by h/Dm and D/Dm, where h, D and Dm denote indent distance, chip size and tooth crown diameter. For the fossa loading, h/Dm, D/Dm and the least chipping force Pch are virtually independent of ball radius r for r < ≈ 4 mm. In this range, h/Dm and D/Dm lie between ≈0.30 to 0.36 and 0.51 to 0.69, respectively, while Pch equals ≈1330 N. For r > ≈ 4 mm, the failure occurs by debonding of enamel sectors from the dentin core. In the case of cusp loading, h/Dm < ≈ 0.3 while D/Dm and Pch vary with r. For relatively small h or large r, the failure occurs as soon as radial cracks initiate under the loading point. For a load applied near a cusp tip, the failure occurs by enamel debonding. Finally, the present work is easily extendable to fossil teeth of hominins and apes as well as prosthetic teeth. The morphological features obtained in such studies should provide quantitative means to assess the relationships between chip dimensions, chipping force and diet characteristics.

On the fracture behavior of molar teeth with MOD cavity preparation.

Mesial-occlusal-distal (MOD) cavity preparations are commonly used to restore damaged teeth. While numerous in vitro cavity designs have been devised and tested, no analytical frameworks for assessing their resistance to fracture seem to exist. This concern is addressed here by resorting to a 2D slice specimen cut from restored molar teeth with rectangular-base MOD cavity. The evolution of damage due to axial cylindrical indentation is followed in situ. The failure begins with a rapid debonding along the tooth/filler interface and continues with unstable cracking from the cavity corner. The debonding load qd is fairly fixed while the failure load qf is insensitive to the presence of filler, increasing with cavity wall thickness h and reducing with cavity depth D. The growth of the corner crack is studied using a 2D fracture analysis in conjunction with the FEM technique. The ratio h = h/D emerges as a viable system parameter. A simple expression for qf given in terms of h and dentin toughness KC is developed that predicts well the test data. In vitro studies on full-fledged molar teeth with MOD cavity preparation show that the fracture resistance of filled cavities often exceeds by a large margin that of unfilled ones. Indications are that this may reflect load sharing with the filler. Thus, the fracture resistance of the unfilled cavity provides a lower bound to a compromised MOD filling after long-term aging in the mouth. This bound is well predicted by the slice model. Finally, it is recommended that MOD cavities be prepared, if applicable, such that h > D regardless of the tooth size.

On the evolution of the morphology and resilience of molar cusps in fossil hominid teeth.

Teeth play an important role in evolutionary studies due to their good preservation and direct link to diet. The present work makes use of a previously generated database on molar teeth of fossil hominids which consists of cuspal enamel thickness dc, dentin horn angle φ and section width D, all measured on a given histological tooth section. These data are here interpreted with the aid of "fracture stress" QF = PF/D2 and geological age t, where PF is the occlusal force needed to cause cusp failure as determined from dc and φ. QF is virtually a constant in non-hominins ("apes") while monotonically increasing toward present time in hominins. These two trends intersect at t = ts = 4.5 (0.11) mya, a value similar to other divergence estimates. QF was fitted with a function f(t) which is proportional to (dc/D)2. The monotonic variation of QF and in turn dc/D with t contrasts the more complex behavior generally characterizing other physical entities of fossil hominids. The increase in dc/D in hominins promotes tooth resilience and in turn life span. Finally, it is suggested that PF provides an upper bound to the maximum bite force produced by the jaw structure.

On the morphology and failure of worn human molar cusps.

OBJECTIVES: Enamel wear is a common occurrence that may lead to tooth failure. Beyond reducing enamel thickness, wear exposes different regions of enamel microstructure to various types of stresses. This work was aimed at elucidating the effect of enamel wear on enamel morphology and tooth resilience in human molar teeth undergoing large-scale contact. METHODS: Intact/polished molar cusps were indented with a hard disk/ball. The unloaded specimens were sectioned longitudinally or transversely, and the damage examined by optical and scanning electron microscopy. The onset of cracks at the dentin horn apex was determined by a FEM stress analysis that modeled a cusp as truncated, conical enamel shell supported by dentin. RESULTS: The damage consisted of radial and cylindrical cracks growing under the contact, sparsely distributed radial cracks in the enamel shell region, and cracking from tufts at the dentin horn apex (TA cracks). The damage under the contact circle exhibited shear deformation zones. These zones helped relieve contact stresses, absorb energy, contain damage, and solicit cylindrical cracks in order to avoid growth of wear-sensitive cone cracks. Enamel tufts provided stress shielding while Hunter-Schreger Bands helped maintain this benefit by enforcing a collaborative cracking. The TA cracks were deemed a primary cause for tooth failure. The FEA predicted well the onset of these cracks. Making use of in vivo enamel wear data, the analysis showed that cusp failure might routinely occur at old age. SIGNIFICANCE: The results provided new information on the response of the interior part of enamel to contact loading. This included the resistant effects of the waviness of enamel rods, interrods and tufts. The unique microstructure of enamel gave rise to shear bands under the contact circle that helped relieve contact stresses, absorb energy and contain damage. Enamel interrods solicited cylindrical cracking in order to avoid the wear-sensitive cone cracks. The onset of cracks at the dentin horn apex (TA cracks) was deemed critical to a tooth survival. The FEA showed that this cracking mode might routinely occur at old age due to natural enamel wear. Finally, the occlusal force needed to initiate the TA cracks in intact cusps can help explain the natural design logic involving the maximum bite force of hominid species.

Determining primates bite force from histological tooth sections.

OBJECTIVES: The ability to accurately estimate bite force (BF) in extant and fossil primates is valuable to biological anthropologists. BF is generally evaluated using complex jaw musculature and lever arm analyses employing numerous assumptions and requiring complete cranial morphology. Here, a simple method to determine BF from data measured on histological sections of fossil teeth is proposed. METHODS: Published sections of molar teeth encompassing 27 different extinct and extant primates dating back to as early as 17 million years ago were examined. Focusing on the cusp region, the extracted data include characteristic enamel thickness dc and dentin horn angle φ. The occlusal force needed to fracture a cusp, PF , was determined from these variables with the aid of a finite element stress analysis similarly to a previous study on postcanine human teeth. The bite force was obtained by linking BF to PF using a universal constant. RESULTS: The measured variables dc and φ are conclusively linked. This link produces a virtually constant fracture force PF and in turn bite force BF for all cusps in the molar row. An explicit formula tying BF to dc and φ was derived. For nonhominin taxa the bite force, molar crown area, and body mass are found to be intimately related. The case of hominins is more involved. The so determined BF is gender-averaged, with the bite force of males estimated to be ≈12% greater than that of females. CONCLUSIONS: The use of "fracture mechanics" concepts from mechanics of materials facilitates determination of critical bite force in primates based on characteristic enamel thickness dc and dentin horn angle φ as extracted from histological sections of molar teeth. This novel approach enables quantitative insight into the role played by crown area, body mass and bite force on evolutionary trends. The conclusive link between cuspal enamel thickness and dentin horn angle facilitates optimal food processing without hindering cusp resilience. The proposed approach may be extended to mammals having asymmetric cusp structures.

Probing the interfacial strength of novel multi-layer zirconias.

OBJECTIVES: The rapidly increasing use of zirconia-based CAD/CAM multi-layer structures in dentistry calls for a thorough evaluation of their mechanical integrity. This work examines the effect of the multi-layering architecture as well as variations in composition and inclusion of pigments among the layers on the flexural strength of multi-layer zirconias. METHODS: A modified 4-point bending test, aided by a Finite Element Analysis (FEA), was used to probe the interfacial strength of 3 classes of yttria-partially-stabilized zirconia: Ultra Translucent Multi-Layer (UTML-5Y-PSZ), Super Translucent Multi-Layer (STML-4Y-PSZ), Multi-Layer (ML-3Y-PSZ). In accord with the size limitation (22-mm height) of CAD/CAM pucks, test samples were prepared in the form of "long" (25×2×3mm) and "short" (17.8×1.5×2mm) beams. Homogeneous beams (both long and short) were produced from either the Enamel (the lightest shade) or Dentin (the darkest shade) layer, whereas multi-layer beams (short beam only) were obtained by cutting the pucks along their thickness direction, where the material components of various shades were stacked. RESULTS: The Enamel and Dentin layers exhibited similar flexural strength for a given material class, with ML amassing the highest strength (800-900MPa) followed by STML (560-650MPa) and UTML (470-500MPa). The 3 classes of multi-layer zirconia showed a trade-off between strength and translucency, reflecting different yttria contents in these materials. The failure stress of the cross-sectional multi-layer beams was, however, ∼30% lower than that of their Enamel or Dentin layer counterparts, regardless of material tested. SIGNIFICANCE: The weakness of interfaces is a drawback in these materials. Additionally, when measuring strength using short beam flexure, friction between the specimen and supporting pins and accuracy in determining loading span distances may lead to major errors.

Miniature specimens for fracture toughness evaluation of dental resin composites.

OBJECTIVE: Millimeter-scale ("miniature") specimens enable in-situ evaluation of mechanical properties of engineering materials at reduced cost. Here three such specimens for measuring fracture toughness (KC) are developed and implemented to new dental materials. The latter include concurrent methacrylate-based and new ether-based resin composites designed to reduce polymerization stress and enhance service life in restored teeth. METHODS: Fracture toughness of four experimental and one commercial dental resin composites are evaluated using three-point bending (3PB), wedge double-cantilever-beam (WDCD) and edge chipping miniature test specimens. The values of KC were compared with those obtained following ISO standard method ISO6872: 2014. The stress intensity factor (K) for the 3PB and WDCB specimens was determined using linear fracture mechanics analyses made in conjunction with the Finite Element technique, with due consideration given to the finite width of pre-crack. RESULTS: Analytic expressions for predicting KC were developed for all three miniature specimens. The width of pre-crack, generally neglected for conventional specimens, significantly affect K. Measured KC conclusively agree with those of commercial or well-studied materials as obtained using conventional specimens, with error bounded by 5-10 percent. SIGNIFICANCE: The edge chipping test was successfully applied for the first time to non-brittle materials like dental resin composites. The miniature specimens developed will expedite the evaluation of fracture toughness of dental resin composites by saving materials and provide needed in-situ assessment capability. The chipping test which requires no introduction of initial crack and involves no use of elastic constants is especially suitable to functionally graded materials and in-situ study of restored teeth. The WDCB specimen enables stable crack growth, a useful trait in fatigue studies.

Dentin horn angle and enamel thickness interactively control tooth resilience and bite force.

Fossil teeth are a primary source for inferring species development via evolutionary adaptation due to their linkage to feeding ecology and well perseverance. The main working tools in such studies are bite force analysis derived from jaw musculature and lever arms and morphogenetic based on enamel thickness and occlusal surface area. Despite progress made, quantitative correlation between predictions and behavior is still lacking. We studied histological sections in varieties of extracted premolar and molar human teeth. Sections corresponding to planes intersecting tips of primary cusps as well as more random planes were considered. The results revealed a unique, conclusive link between cuspal enamel thickness dc and dentin horn angle φ, a developmental parameter which contribution to tooth functioning has been overlooked. Naturally led by design principles of corbel arches, we examined the bending stress at the horn apex due to axial cuspal loading. The results show that this dc vs. φ relationship produces a constant force causing cusp fracture PF, making the latter a viable measure of tooth resilience. A preliminary study on published sections of extinct hominin teeth showed that their dc vs. φ behavior is consistent with modern humans albeit with varying PF. Scaling BF with PF enables direct estimate of bite force from measures of dc and φ in fossil teeth, achievable nondestructively from micro-computed tomography scans. STATEMENT OF SIGNIFICANCE: The correspondence between cuspal enamel thickness and dentin horn angle in the postcanine row is a natural design here revealed for the first time. This correspondence yields constant force causing fracture at the horn apex, PF, making the latter a viable measure of tooth resilience. Scaling bite force (BF) with PF enables direct estimate of BF. The proposed mechanistic link between bite force and anatomical parameters dc and φ, expressed in a simple analytic form, offers direct, development-based expectation for examining evolutionary processes in hominins.

Vertical Root Fracture in Buccal Roots of Bifurcated Maxillary Premolars from Condensation of Gutta-percha.

INTRODUCTION: Maxillary premolars are among the teeth most susceptible to vertical root fracture (VRF) from lateral condensation of gutta-percha. These teeth are distinguished by a complex anatomy of the buccal root including a large depression in the dentin wall facing the bifurcation. It is hypothesized that tooth sectioning coupled with 2-dimensional fracture analysis is instrumental in understanding VRF in such teeth. VRF was examined by tooth sectioning following the development of a fracture mechanics analysis to predict VRF in such roots. METHODS: The fracture morphology in teeth extracted from patients because of VRFs was examined from a series of horizontal cross sections. 2-dimensional fracture mechanics analysis in conjunction with the finite element technique was developed to evaluate VRF caused by canal pressure (q). As in our previous single-rooted tooth model, the apical obturation force (F) was related to q using a simple formula. RESULTS: Fracture was mostly limited to the buccal root, exhibiting some competing modes including fracture from the depression peak to the canal surface and the canal surface to the root surface, which may occur either along straight lines or curved trajectories resembling the depression outline. The analysis predicted clinical fractures well, yielding VRF force values in the upper range used by clinicians during lateral condensation of gutta-percha. CONCLUSIONS: The main etiology for VRF is stress concentration resulting from the combined effect of wedgelike canal depression and the flexibility of periodontal ligament tissue joining the root and bone. This drawback can be alleviated by minimizing canal enlargement and apical condensation force during root canal therapy.

Using glass-graded zirconia to increase delamination growth resistance in porcelain/zirconia dental structures.

OBJECTIVE: Porcelain fused to zirconia (PFZ) restorations are widely used in prosthetic dentistry. However, their tendency to delaminate along the P/Z interface remains a practical problem so that assessing and improving the interfacial strength are important design aspects. This work examines the effect of modifying the zirconia veneering surface with an in-house felspathic glass on the interfacial fracture resistance of fused P/Z. METHODS: Three material systems are studied: porcelain fused to zirconia (control) and porcelain fused to glass-graded zirconia with and without the presence of a glass interlayer. The specimens were loaded in a four-point-bend fixture with the porcelain veneer in tension. The evolution of damage is followed with the aid of a video camera. The interfacial fracture energy GC was determined with the aid of a FEA, taking into account the stress shielding effects due to the presence of adjacent channel cracks. RESULTS: Similarly to a previous study on PFZ specimens, the fracture sequence consisted of unstable growth of channel cracks in the veneer followed by stable cracking along the P/Z interface. However, the value of GC for the graded zirconia was approximately 3 times that of the control zirconia, which is due to the good adhesion between porcelain and the glass network structure on the zirconia surface. SIGNIFICANCE: Combined with its improved bonding to resin-based cements, increased resistance to surface damage and good esthetic quality, graded zirconia emerges as a viable material concept for dental restorations.

Fracture resistance of molar teeth with mesial-occlusal-distal (MOD) restorations.

OBJECTIVE: Filled MOD restorations show near-complete recovery of tooth strength relative to the newly prepared, unfilled state. The present study examines the underlying mechanics of this recovery by more closely quantifying the mode of splitting fracture from the cavity base. By understanding the role of specific cavity dimensions on fracture resistance, useful clinical guidelines concerning MOD morphologies are formulated. METHODS: A systematic in vitro study is made of the load-bearing capacity of filled and unfilled MOD cavities by axially loading extracted molar teeth with a hard metal ball. Filled and unfilled cavities are considered as bounding cases. Focus is placed on drillings with rectangular or rounded tips, covering a range of cavity widths and depths. The failure process is monitored during loading by a video camera, enabling the entire damage evolution from first contact to ultimate failure to be recorded. SIGNIFICANCE: While respecting the widely accepted clinical practice of drilling cavities with internal widths less than one third that of the entire tooth, a stronger correlation is obtained between critical splitting load PC and ratio of cavity wall thickness h (distance between cavity wall and outer tooth surface) to cavity depth D. Imposing a conservative upper limit on PC for tooth survival, the study recommends that MOD cavities be prepared such that the ratio remains in the region h>D, regardless of the tooth size.

On the interfacial fracture resistance of resin-bonded zirconia and glass-infiltrated graded zirconia.

OBJECTIVE: A major limiting factor for the widespread use of zirconia in prosthetic dentistry is its poor resin-cement bonding capabilities. We show that this deficiency can be overcome by infiltrating the zirconia cementation surface with glass. Current methods for assessing the fracture resistance of resin-ceramic bonds are marred by uneven stress distribution at the interface, which may result in erroneous interfacial fracture resistance values. We have applied a wedge-loaded double-cantilever-beam testing approach to accurately measure the interfacial fracture resistance of adhesively bonded zirconia-based restorative materials. METHODS: The interfacial fracture energy GC was determined for adhesively bonded zirconia, graded zirconia and feldspathic ceramic bars. The bonding surfaces were subjected to sandblasting or acid etching treatments. Baseline GC was measured for bonded specimens subjected to 7 days hydration at 37°C. Long-term GC was determined for specimens exposed to 20,000 thermal cycles between 5 and 55°C followed by 2-month aging at 37°C in water. The test data were interpreted with the aid of a 2D finite element fracture analysis. RESULTS: The baseline and long-term GC for graded zirconia was 2-3 and 8 times greater than that for zirconia, respectively. More significantly, both the baseline and long-term GC of graded zirconia were similar to those for feldspathic ceramic. SIGNIFICANCE: The interfacial fracture energy of feldspathic ceramic and graded zirconia was controlled by the fracture energy of the resin cement while that of zirconia by the interface. GC for the graded zirconia was as large as for feldspathic ceramic, making it an attractive material for use in dentistry.

The Effect of Isthmus on Vertical Root Fracture in Endodontically Treated Teeth.

INTRODUCTION: Vertical root fracture (VRF) from apical condensation of gutta-percha is a common failure mode in endodontically treated teeth. Virtually all previous studies of VRF are limited to 1-canal roots. In this study, we consider experimentally and analytically VRF in roots with 2 canals. METHODS: The interior root morphology in mandibular molar teeth extracted from patients due to VRF or other reason was examined from a series of polished horizontal cross sections. A 2-dimensional fracture mechanics analysis was used to determine crack growth from the canal surface to the outer root surface and evaluate the apical load needed to cause VRF, Fmax. RESULTS: From a mechanistic viewpoint, the isthmus connecting root canals can be regarded as a natural weak plane or crack. The results expose the prime role of isthmus in reducing Fmax, from ≈ 50 N with no isthmus present to ≈ 10 N. CONCLUSIONS: Two-canal mesial roots are much more prone to VRF than 1-canal distal roots. We suggest that VRF may occur during clinical condensation of gutta-percha in mesial roots of mandibular molars as well as other roots with canals connected by isthmus.

On crack growth in molar teeth from contact on the inclined occlusal surface.

Extracted human molar teeth are indented by hard balls laid at the central fossa, sectioned, and their interior examined for damage. Contact on the fissured enamel coat generally occurs on three distinct spots. The main forms of damage are radial cracks growing from the DEJ to the occlusal surface and median radial and cylindrical cracks growing from a contact spot to the DEJ. For large balls failure by edge chipping near a cusp apex may occur. The median cracks tend to run unstably to the DEJ upon reaching the middle part of the enamel coat. The corresponding load, PFM, and the load needed to initiate radial cracks at the DEJ, PFR, are taken to signal crown failure. The mean values of PFM and PFR are on the order of 1000N. A conical bilayer model defined by thickness d, inclination angle θ, failure stress σF and toughness KC of the enamel coat is developed to assess crown failure. The analytical predictions for PFR and PFM agree well with the tests. The results indicate that enamel thickness is so designed as to ensure that PFR and PFM just exceed the maximum bite force under normal conditions while the choice of θ seems to reflect a compromise between needs to resist crown failure and break hard food particles. Both PFR and PFM are greatly reduced with reducing d, which points to the danger posed by tooth wear. The analytical expressions for PFR and PFM may also apply to other multi-cusp mammalian or prosthetic molar crowns. Cone cracking, suppressed in the anisotropic tooth enamel, may be an important failure mode in prosthetic crowns.

Mechanics analysis of molar tooth splitting.

A model for the splitting of teeth from wedge loading of molar cusps from a round indenting object is presented. The model is developed in two parts: first, a simple 2D fracture mechanics configuration with the wedged tooth simulated by a compact tension specimen; second, a full 3D numerical analysis using extended finite element modeling (XFEM) with an embedded crack. The result is an explicit equation for splitting load in terms of indenter radius and key tooth dimensions. Fracture experiments on extracted human molars loaded axially with metal spheres are used to quantify the splitting forces and thence to validate the model. The XFEM calculations enable the complex crack propagation, initially in the enamel coat and subsequently in the interior dentin, to be followed incrementally with increasing load. The fracture evolution is shown to be stable prior to failure, so that dentin toughness, not strength, is the controlling material parameter. Critical conditions under which tooth splitting in biological and dental settings are likely to be met, however rare, are considered.

On the mechanical properties of tooth enamel under spherical indentation.

The mechanical properties of tooth enamel generally exhibit large variations, which reflect its structural and material complexity. Some key properties were evaluated under localized contact, simulating actual functioning conditions. Prominent cusps of extracted human molar teeth were polished down ~0.7 mm below the cusp tip and indented by tungsten carbide balls. The internal damage was assessed after unloading from longitudinal or transverse sections. The ultimate tensile stress (UTS) was determined using a novel bilayer specimen. The damage is characterized by penny-like radial cracks driven by hoop stresses and cylindrical cracks driven along protein-rich interrod materials by shear stresses. Shallow cone cracks typical of homogeneous materials which may cause rapid tooth wear under repeat contact are thus avoided. The mean stress vs. indentation strain curve is highly nonlinear, attributable to plastic shearing of protein between and within enamel rods. This curve is also affected by damage, especially radial cracks, the onset of which depends on ball radius. Several material properties were extracted from the tests, including shear strain at the onset of ring cracks γ(F) (=0.14), UTS (=119 MPa), toughness K(C) (=0.94 MPa m(1/2)), a crack propagation law and a constitutive response determined by trial and error with the aid of a finite-element analysis. These quantities, which are only slightly sensitive to anatomical location within the enamel region tested, facilitate a quantitative assessment of crown failure. Causes for variations in published UTS and K(C) values are discussed.

On the interfacial fracture of porcelain/zirconia and graded zirconia dental structures.

Porcelain fused to zirconia (PFZ) restorations are widely used in prosthetic dentistry. However, their susceptibility to fracture remains a practical problem. The failure of PFZ prostheses often involves crack initiation and growth in the porcelain, which may be followed by fracture along the porcelain/zirconia (P/Z) interface. In this work, we characterized the process of fracture in two PFZ systems, as well as a newly developed graded glass-zirconia structure with emphases placed on resistance to interfacial cracking. Thin porcelain layers were fused onto Y-TZP plates with or without the presence of a glass binder. The specimens were loaded in a four-point-bending fixture with the thin porcelain veneer in tension, simulating the lower portion of the connectors and marginal areas of a fixed dental prosthesis (FDP) during occlusal loading. The evolution of damage was observed by a video camera. The fracture was characterized by unstable growth of cracks perpendicular to the P/Z interface (channel cracks) in the porcelain layer, which was followed by stable cracking along the P/Z interface. The interfacial fracture energy GC was determined by a finite-element analysis taking into account stress-shielding effects due to the presence of adjacent channel cracks. The resulting GC was considerably less than commonly reported values for similar systems. Fracture in the graded Y-TZP samples occurred via a single channel crack at a much greater stress than for PFZ. No delamination between the residual glass layer and graded zirconia occurred in any of the tests. Combined with its enhanced resistance to edge chipping and good esthetic quality, graded Y-TZP emerges as a viable material concept for dental restorations.

Transverse fracture of canine teeth.

The critical conditions to effect transverse fracture in canine teeth of carnivores in lateral loading are analyzed. The teeth are modeled as tapered coaxial beams with uniformly thin enamel coats. A stress analysis is first carried out using beam theory, and stress intensity factors for inward propagating cracks at the location of maximum tensile stress along the lingual face are then determined. The fracture begins as arrested channel cracks within the enamel, followed by stable penetration around the tooth and into the dentin to the point of failure. Two- and three-dimensional finite element models are used to evaluate the full fracture evolution. The analysis yields an explicit scaling relation for the critical fracture load in terms of characteristic tooth dimensions, notably tooth height and base radius. The role of enamel, ignored in previous 'strength of materials' analyses, is shown to be important in determining the precursor crack equilibrium prior to full fracture. Implications concerning allometry are briefly discussed.

Fracture mechanics analysis of vertical root fracture from condensation of gutta-percha.

A two-dimensional fracture mechanics analysis of vertical root fracture (VRF) in single-canal roots from apical condensation of gutta-percha (gp) is developed. The resulting analytic relation for apical load causing VRF agrees with major trends reported in in-vitro tests on roots subjected to either continuous or, the more clinically relevant, repeating vertical condensation of gp. The model explicitly exposes the role of root canal morphology and dentin fracture toughness on VRF. Ovoid and irregular canals are prone to fracture while the effect of mean root canal radius is modest. Canal taper and instrumentation details may affect VRF only marginally and indirectly. The model predicts dentinal cracks to occur following root canal instrumentation and obturation, which may pose long-term threats to tooth integrity.