Threshold damage mechanisms in brittle solids and their impact on advanced technologies.

Threshold damage mechanisms in brittle covalent-ionic solids are outlined. Fracture and deformation modes are analyzed in terms of classical contact mechanics. Distinctions are made between brittle, ductile and quasiplastic mechanisms in both axial and translational contact. Special attention is devoted to the relatively unexplored subthreshold region where macrofracture is largely suppressed, a region of increasing relevance in the relentless move toward ever smaller devices and precision shaping technologies in the manufacturing sector. Cross-section micrographic images illustrate the fundamental nature of shear events within the hardness deformation zone responsible for crack initiation and propagation. Basic analytical relations for the strengths of surfaces with contact-induced damage in the postthreshold and subthreshold regions are presented, with emphasis on concept rather than fine detail. Strength data for a prototypical brittle material after sharp-indenter damage are presented to highlight the vital role of microstructure in determining transitions between brittle and quasiplastic responses. Pristine defect-free solids are shown to be highly vulnerable to contact damage, even in the subthreshold region. Heterogeneous solids with granular microstructures have lower initial strengths, but are more flaw tolerant. Brittle solids are also highly susceptible to degradation by surface removal processes in wear and machining settings, to a large extent depending again on microstructure. Implications of these findings concerning advanced technological applications of covalent-ionic solids are discussed.

Fundamental mechanics of tooth fracture and wear: implications for humans and other primates.

Until recently, there had been little attempt in the literature to identify and quantify the underlying mechanics of tooth durability in terms of materials engineering concepts. In humans and most mammals, teeth must endure a lifetime of sustained occlusal mastication-they have to resist fracture and wear. It is well documented that teeth are resilient, but what are the unique features that make this possible? The present article surveys recent materials engineering research aimed at addressing this fundamental question. Elements that determine the mechanics and micromechanics of tooth fracture and wear are analysed: at the macrostructural level, the geometry of the enamel shell and cuspal configuration; and at the microstructural level, interfacial weakness and property gradients. Inferences concerning dietary history in relation to evolutionary pressures are discussed.

Micromechanics of Machining and Wear in Hard and Brittle Materials.

Hard and brittle solids with covalent/ionic bonding are used in a wide range of modern-day manufacturing technologies. Optimization of a shaping process can shorten manufacturing time and cost of component production, and at the same time extend component longevity. The same process may contribute to wear and fatigue degradation in service. Educated development of advanced finishing protocols for this class of solids requires a comprehensive understanding of damage mechanisms at small-scale contacts from a materials science perspective. In this article the fundamentals of brittle-ductile transitions in indentation stress fields are surveyed, with distinctions between axial and sliding loading and blunt and sharp contacts. Attendant deformation and removal mechanisms in microcontact processes are analyzed and discussed in the context of brittle and ductile machining and severe and mild wear. The central role of material microstructure in material removal modes is demonstrated.

Phytoliths can cause tooth wear.

Comparative laboratory sliding wear tests on extracted human molar teeth in artificial saliva with third-body particulates demonstrate that phytoliths can be as effective as silica grit in the abrasion of enamel. A pin-on-disc wear testing configuration is employed, with an extracted molar cusp as a pin on a hard disc antagonist, under loading conditions representative of normal chewing forces. Concentrations and sizes of phytoliths in the wear test media match those of silica particles. Cusp geometries and ensuing abrasion volumes are measured by digital profilometry. The wear data are considered in relation to a debate by evolutionary biologists concerning the relative capacities of intrinsic mineral bodies within plant tissue and exogenous grit in the atmosphere to act as agents of tooth wear in various animal species.

On the vital role of enamel prism interfaces and graded properties in human tooth survival.

Teeth of omnivores face a formidable evolutionary challenge: how to protect against fracture and abrasive wear caused by the wide variety of foods they process. It is hypothesized that this challenge is met in part by adaptations in enamel microstructure. The low-crowned teeth of humans and some other omnivorous mammals exhibit multiple fissures running longitudinally along the outer enamel walls, yet remain intact. It is proposed that inter-prism weakness and enamel property gradation act together to avert entry of these fissures into vulnerable inner tooth regions and, at the same time, confer wear resistance at the occlusal surface. A simple indentation experiment is employed to quantify crack paths and energetics in human enamel, and an extended-finite-element model to evaluate longitudinal crack growth histories. Consideration is given as to how tooth microstructure may have played a vital role in human evolution, and by extension to other omnivorous mammals.

Inverse correlations between wear and mechanical properties in biphasic dental materials with ceramic constituents.

The objective of this study is to elucidate the interdependence of competing mechanical degradation processes in biphasic dental materials with ceramic constituents in the region of high-pressure occlusal loading. It is hypothesized that wear resistance in this region correlates inversely with basic material parameters (modulus, hardness, toughness, strength) evaluated from 'standardized' test specimens. Ball-on-flat wear tests in simulation of oral function are used to quantify susceptibility to protracted sliding contact damage. Wear rates for this class of dental material tend to increase with quasistatic parameter values, so the latter do not provide a reliable guide to longevity. The generation of severe-wear facets involves cumulative quasiplastic deformation and microcrack coalescence at the grain level. It is implied that interplay between wear and fracture mechanisms should be an important consideration in future microstructural design of dental ceramics, especially in the quest to balance durability against esthetics.

Wear of ceramic-based dental materials.

An investigation is made of wear mechanisms in a suite of dental materials with a ceramic component and tooth enamel using a laboratory test that simulates clinically observable wear facets. A ball-on-3-specimen wear tester in a tetrahedral configuration with a rotating hard antagonist zirconia sphere is used to produce circular wear scars on polished surfaces of dental materials in artificial saliva. Images of the wear scars enable interpretation of wear mechanisms, and measurements of scar dimensions quantify wear rates. Rates are lowest for zirconia ceramics, highest for lithium disilicate, with feldspathic ceramic and ceramic-polymer composite intermediate. Examination of wear scars reveals surface debris, indicative of a mechanism of material removal at the microstructural level. Microplasticity and microcracking models account for mild and severe wear regions. Wear models are used to evaluate potential longevity for each dental material. It is demonstrated that controlled laboratory testing can identify and quantify wear susceptibility under conditions that reflect the essence of basic occlusal contact. In addition to causing severe material loss, wear damage can lead to premature tooth or prosthetic failure.

Evaluating dental zirconia.

OBJECTIVES: To survey simple contact testing protocols for evaluating the mechanical integrity of zirconia dental ceramics. Specifically, to map vital material property variations and to quantify competing damage modes. METHODS: Exploratory contact tests are conducted on layer structures representative of zirconia crowns on dentin. RESULTS: Sharp-tip micro- and nano-indentations were used to investigate the roles of weak interfaces and residual stresses in veneered zirconia, and to map property variations in graded structures. Tests with blunt sphere indenters on flat specimens were used to identify and quantify various critical damage modes in simulated occlusal loading in veneered and monolithic zirconia. SIGNIFICANCE: Contact testing is a powerful tool for elucidating the fracture and deformation modes that control the lifetimes of zirconia dental ceramics. The advocated tests are simple, and provide a sound physical basis for analyzing damage resistance of anatomically-correct crowns and other complex dental prostheses.

Role of particulate concentration in tooth wear.

Results are presented for wear tests on human molar enamel in silica particle mediums. Data for different particle concentrations show severe wear indicative of material removal by plasticity-induced microcrack formation, in accordance with earlier studies. The wear rates are independent of low vol% particles, consistent with theoretical models in which occlusal loads are distributed evenly over all interfacial microcontacts. However, perhaps counter-intuitively, the wear rate diminishes substantially at higher vol%. This is attributed to a greater proportion of lower-load microcontacts transitioning into a region of mild wear, where microcracking is suppressed. Implications of these results in relation to evolutionary biology and dentistry are explored.

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 evolutionary advantage of multi-cusped teeth.

A hallmark of mammalian evolution is a progressive complexity in postcanine tooth morphology. However, the driving force for this complexity remains unclear: whether to expand the versatility in diet source, or to bolster tooth structural integrity. In this study, we take a quantitative approach to this question by examining the roles of number, position and height of multiple cusps in determining sustainable bite forces. Our approach is to use an extended finite-element methodology with due provision for step-by-step growth of an embedded crack to determine how fracture progresses with increasing occlusal load. We argue that multi-cusp postcanine teeth are well configured to withstand high bite forces provided that multiple cusps are contacted simultaneously to share the load. However, contact on a single near-wall cusp diminishes the strength. Location of the load points and cusp height, rather than cusp number or radius, are principal governing factors. Given these findings, we conclude that while complex tooth structures can enhance durability, increases in cusp number are more likely to be driven by the demands of food manipulation. Structural integrity of complex teeth is maintained when individual cusps remain sufficiently distant from the side walls and do not become excessively tall relative to tooth width.

Simulation of enamel wear for reconstruction of diet and feeding behavior in fossil animals: A micromechanics approach.

The deformation and wear events that underlie microwear and macrowear signals commonly used for dietary reconstruction in fossil animals can be replicated and quantified by controlled laboratory tests on extracted tooth specimens in conjunction with fundamental micromechanics analysis. Key variables governing wear relations include angularity, stiffness (modulus), and size of the contacting particle, along with material properties of enamel. Both axial and sliding contacts can result in the removal of tooth enamel. The degree of removal, characterized by a "wear coefficient," varies strongly with particle content at the occlusal interface. Conditions leading to a transition from mild to severe wear are discussed. Measurements of wear traces can provide information about contact force and particle shape. The potential utility of the micromechanics methodology as an adjunct for investigating tooth durability and reconstructing diet is explored.

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.

Mechanics of microwear traces in tooth enamel.

It is hypothesized that microwear traces in natural tooth enamel can be simulated and quantified using microindentation mechanics. Microcontacts associated with particulates in the oral wear medium are modeled as sharp indenters with fixed semi-apical angle. Distinction is made between markings from static contacts (pits) and translational contacts (scratches). Relations for the forces required to produce contacts of given dimensions are derived, with particle angularity and compliance specifically taken into account so as to distinguish between different abrasives in food sources. Images of patterns made on human enamel with sharp indenters in axial and sliding loading are correlated with theoretical predictions. Special attention is given to threshold conditions for transition from a microplasticity to a microcracking mode, corresponding to mild and severe wear domains. It is demonstrated that the typical microwear trace is generated at loads on the order of 1N - i.e. much less than the forces exerted in normal biting - attesting to the susceptibility of teeth to wear in everyday mastication, especially in diets with sharp, hard and large inclusive intrinsic or extraneous particulates.

A model for predicting wear rates in tooth enamel.

It is hypothesized that wear of enamel is sensitive to the presence of sharp particulates in oral fluids and masticated foods. To this end, a generic model for predicting wear rates in brittle materials is developed, with specific application to tooth enamel. Wear is assumed to result from an accumulation of elastic-plastic micro-asperity events. Integration over all such events leads to a wear rate relation analogous to Archard׳s law, but with allowance for variation in asperity angle and compliance. The coefficient K in this relation quantifies the wear severity, with an arbitrary distinction between 'mild' wear (low K) and 'severe' wear (high K). Data from the literature and in-house wear-test experiments on enamel specimens in lubricant media (water, oil) with and without sharp third-body particulates (silica, diamond) are used to validate the model. Measured wear rates can vary over several orders of magnitude, depending on contact asperity conditions, accounting for the occurrence of severe enamel removal in some human patients (bruxing). Expressions for the depth removal rate and number of cycles to wear down occlusal enamel in the low-crowned tooth forms of some mammals are derived, with tooth size and enamel thickness as key variables. The role of 'hard' versus 'soft' food diets in determining evolutionary paths in different hominin species is briefly considered. A feature of the model is that it does not require recourse to specific material removal mechanisms, although processes involving microplastic extrusion and microcrack coalescence are indicated.

Role of multiple cusps in tooth fracture.

The role of multiple cusps in the biomechanics of human molar tooth fracture is analysed. A model with four cusps at the bite surface replaces the single dome structure used in previous simulations. Extended finite element modelling, with provision to embed longitudinal cracks into the enamel walls, enables full analysis of crack propagation from initial extension to final failure. The cracks propagate longitudinally around the enamel side walls from starter cracks placed either at the top surface (radial cracks) or from the tooth base (margin cracks). A feature of the crack evolution is its stability, meaning that extension occurs steadily with increasing applied force. Predictions from the model are validated by comparison with experimental data from earlier publications, in which crack development was followed in situ during occlusal loading of extracted human molars. The results show substantial increase in critical forces to produce longitudinal fractures with number of cuspal contacts, indicating a capacity for an individual tooth to spread the load during mastication. It is argued that explicit critical force equations derived in previous studies remain valid, at the least as a means for comparing the capacity for teeth of different dimensions to sustain high bite forces.

Edge chipping and flexural resistance of monolithic ceramics.

OBJECTIVE: Test the hypothesis that monolithic ceramics can be developed with combined esthetics and superior fracture resistance to circumvent processing and performance drawbacks of traditional all-ceramic crowns and fixed-dental-prostheses consisting of a hard and strong core with an esthetic porcelain veneer. Specifically, to demonstrate that monolithic prostheses can be produced with a much reduced susceptibility to fracture. METHODS: Protocols were applied for quantifying resistance to chipping as well as resistance to flexural failure in two classes of dental ceramic, microstructurally-modified zirconias and lithium disilicate glass-ceramics. A sharp indenter was used to induce chips near the edges of flat-layer specimens, and the results compared with predictions from a critical load equation. The critical loads required to produce cementation surface failure in monolithic specimens bonded to dentin were computed from established flexural strength relations and the predictions validated with experimental data. RESULTS: Monolithic zirconias have superior chipping and flexural fracture resistance relative to their veneered counterparts. While they have superior esthetics, glass-ceramics exhibit lower strength but higher chip fracture resistance relative to porcelain-veneered zirconias. SIGNIFICANCE: The study suggests a promising future for new and improved monolithic ceramic restorations, with combined durability and acceptable esthetics.

Fatigue of dental ceramics.

OBJECTIVES: Clinical data on survival rates reveal that all-ceramic dental prostheses are susceptible to fracture from repetitive occlusal loading. The objective of this review is to examine the underlying mechanisms of fatigue in current and future dental ceramics. DATA/SOURCES: The nature of various fatigue modes is elucidated using fracture test data on ceramic layer specimens from the dental and biomechanics literature. CONCLUSIONS: Failure modes can change over a lifetime, depending on restoration geometry, loading conditions and material properties. Modes that operate in single-cycle loading may be dominated by alternative modes in multi-cycle loading. While post-mortem examination of failed prostheses can determine the sources of certain fractures, the evolution of these fractures en route to failure remains poorly understood. Whereas it is commonly held that loss of load-bearing capacity of dental ceramics in repetitive loading is attributable to chemically assisted 'slow crack growth' in the presence of water, we demonstrate the existence of more deleterious fatigue mechanisms, mechanical rather than chemical in nature. Neglecting to account for mechanical fatigue can lead to gross overestimates in predicted survival rates. CLINICAL SIGNIFICANCE: Strategies for prolonging the clinical lifetimes of ceramic restorations are proposed based on a crack-containment philosophy.

Inferring biological evolution from fracture patterns in teeth.

It is hypothesised that specific tooth forms are adapted to resist fracture, in order to accommodate the high bite forces needed to secure, break down and consume food. Three distinct modes of tooth fracture are identified: longitudinal fracture, where cracks run vertically between the occlusal contact and the crown margin (or vice versa) within the enamel side wall; chipping fracture, where cracks run from near the edge of the occlusal surface to form a spall in the enamel at the side wall; and transverse fracture, where a crack runs horizontally through the entire section of the tooth to break off a fragment and expose the inner pulp. Explicit equations are presented expressing critical bite force for each fracture mode in terms of characteristic tooth dimensions. Distinctive transitions between modes occur depending on tooth form and size, and loading location and direction. Attention is focussed on the relatively flat, low-crowned molars of omnivorous mammals, including humans and other hominins and the elongate canines of living carnivores. At the same time, allusion to other tooth forms - the canines of the extinct sabre-tooth (Smilodon fatalis), the conical dentition of reptiles, and the columnar teeth of herbivores - is made to highlight the generality of the methodology. How these considerations impact on dietary behaviour in fossil and living taxa is discussed.

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.