On the R-curve behavior of human tooth enamel

In this study the crack growth resistance behavior and fracture toughness of human tooth enamel were quantified using incremental crack growth measures and conventional fracture mechanics. Results showed that enamel undergoes an increase in crack growth resistance (i.e. rising R-curve) with crack extension from the outer to the inner enamel, and that the rise in toughness is a function of distance from the dentin enamel junction (DEJ). The outer enamel exhibited the lowest apparent toughness (0.67 ± 0.12 MPa m^0.5), and the inner enamel exhibited a rise in the growth toughness from 1.13 MPa m^0.5/mm to 3.93 MPa m^0.5/mm. The maximum crack growth resistance at fracture (i.e. fracture toughness (K_c)) ranged from 1.79 to 2.37 MPa m^0.5. Crack growth in the inner enamel was accompanied by a host of mechanisms operating from the micro- to the nano-scale. Decussation in the inner enamel promoted crack deflection and twist, resulting in a reduction of the local stress intensity at the crack tip. In addition, extrinsic mechanisms such as bridging by unbroken ligaments of the tissue and the organic matrix promoted crack closure. Microcracking due to loosening of prisms was also identified as an active source of energy dissipation. In summary, the unique microstructure of enamel in the decussated region promotes crack growth toughness that is approximately three times that of dentin and over ten times that of bone.     

Mixed-mode stress intensity factors for kink cracks with finite kink length loaded in tension and bending: Application to dentin and enamel

Fracture toughness resistance curves describe a material’s resistance against crack propagation. These curves are often used to characterize biomaterials like bone, nacre or dentin as these materials commonly exhibit a pronounced increase in fracture toughness with crack extension due to co-acting mechanisms such as crack bridging, crack deflection and microcracking. The knowledge of appropriate stress intensity factors which depend on the sample and crack geometry is essential for determining these curves. For the dental biomaterials enamel and dentin it was observed that, under bending and tensile loading, crack propagation occurs under certain constant angles to the initial notch direction during testing procedures used for fracture resistance curve determination. For this special crack geometry (a kink crack of finite length in a finite body) appropriate geometric function solutions are missing. Hence, we present in this study new mixed-mode stress intensity factors for kink cracks with finite kink length within samples of finite dimensions for two loading cases (tension and bending) which were derived from a combination of mixed-mode stress intensity factors of kink cracks with infinitely small kinks and of slant cracks. These results were further applied to determine the fracture resistance curves of enamel and dentin by testing single edge notched bending (SENB) specimens. It was found that kink cracks with finite kink length exhibit identical stress fields to slant cracks as soon as the kink length exceeds 0.15 times the initial straight crack or notch length. The use of stress intensity factor solutions for infinitely small kink cracks for the determination of dentin fracture resistance curves (as was done by other researchers) leads to an overestimation of dentin’s fracture resistance of up to 30%.     

Mechanical properties of the dentinoenamel junction: AFM studies of nanohardness, elastic modulus, and fracture

The dentinoenamel junction (DEJ) is a complex and poorly defined structure that unites the brittle overlying enamel with the dentin that forms the bulk of the tooth. In addition, this structure appears to confer excellent toughness and crack deflecting properties to the tooth, and has drawn considerable interest as a biomimetic model of a structure uniting dissimilar materials. This work sought to characterize the nanomechanical properties in the region of the DEJ using modified AFM based nanoindentation to determine nanohardness and elastic modulus. Lines of indentations traversing the DEJ were made at 1-2 microm intervals from the dentin to enamel along three directions on polished sagittal sections from three third molars. Nanohardness and elastic modulus rose steadily across the DEJ from bulk dentin to enamel. DEJ width was estimated by local polynomial regression fits for each sample and location of the mechanical property curves for the data gradient from enamel to dentin, and gave a mean value of 11.8 microm, which did not vary significantly with intratooth location or among teeth. Nanoindentation was also used to initiate cracks in the DEJ region. In agreement with prior work, it was difficult to initiate cracks that traversed the DEJ, or to produce cracks in the dentin. The fracture toughness values for enamel of 0.6-0.9 MPa . m(1/2) were in good agreement with recent microindentation fracture results. Our results suggest that the DEJ displays a gradient in structure and that nanoindenation methods show promise for further understanding its structure and function.     

A simple model for enamel fracture from margin cracks

We present results of in situ fracture tests on extracted human molar teeth showing failure by margin cracking. The teeth are mounted into an epoxy base and loaded with a rod indenter capped with a Teflon insert, as representative of food modulus. In situ observations of cracks extending longitudinally upward from the cervical margins are recorded in real time with a video camera. The cracks appear above some threshold and grow steadily within the enamel coat toward the occlusal surface in a configuration reminiscent of channel-like cracks in brittle films. Substantially higher loading is required to delaminate the enamel from the dentin, attesting to the resilience of the tooth structure. A simplistic fracture mechanics analysis is applied to determine the critical load relation for traversal of the margin crack along the full length of the side wall. The capacity of any given tooth to resist failure by margin cracking is predicted to increase with greater enamel thickness and cuspal radius. Implications in relation to dentistry and evolutionary biology are briefly considered.     

Mechanics of longitudinal cracks in tooth enamel

A study is made of longitudinal "channel" cracking in tooth enamel from axial compressive loading. The cracks simulate those generated in the molar and premolar teeth of humans and animals by natural tooth function. Contact loading tests are made on extracted human molars with hard and soft indenting plates to determine the evolution of such cracks with increasing load. Fracture is largely stable, with initial slow growth followed by acceleration as the cracks approach completion around an enamel side wall. A simple power law relation expresses the critical load for full fracture in terms of characteristic tooth dimensions-base radius and enamel thickness-as well as enamel toughness. Extended three-dimensional finite element modeling with provision for growth of embedded cracks is used to validate this relation. The cracks leave "fingerprints" that offer valuable clues to dietary habits, and provide a basis for a priori prediction of bite forces for different animals from measured tooth dimensions.     

Fatigue crack propagation path across the dentinoenamel junction complex in human teeth

The human tooth structures should be understood clearly to improve clinically used restorative materials. The dentinoenamel junction (DEJ) plays a key role in resisting crack propagation in teeth. The aim of this study was to determine the fracture toughness of the enamel-DEJ-dentin complex and to investigate the influence of the DEJ on the fatigue crack propagation path across it by characterizing fatigue-fractured enamel-DEJ-dentin complexes using optical and scanning electron microscopy. The results of this study showed that the fracture toughness of the enamel-DEJ-dentin complex was 1.50 +/- 0.28 Mpa x m(1/2). Based on the results of this investigation, it was concluded that the DEJ complex played a critical role in resisting crack propagation from enamel into dentin. The DEJ complex is, approximately, a 100 to 150 microm broad region at the interface between enamel and dentin. The toughening mechanism of the DEJ complex may be explained by the fact that crack paths were deflected as cracks propagated across it. Understanding the mechanism of crack deflection could help in improving dentin-composite as well as ceramic-cement interfacial qualities with the aim to decrease the risk of clinical failure of restorations. Both can be viewed as being composed from a layer of material of high strength and hardness bonded to a softer but tougher substratum (dentin). The bonding agent or the luting cement layer may play the critical role of the DEJ in improving the strength of these restorations in clinical situations.     

Role of prism decussation on fatigue crack growth and fracture of human enamel

The role of prism decussation on the crack growth resistance of human enamel is evaluated. Miniature inset compact tension (CT) specimens embodying a section of cuspal enamel were subjected to Mode I cyclic or monotonic loads. Cracks were grown in either the forward (from outer enamel inwards) or reverse (from inner enamel outwards) direction and the responses were compared quantitatively. Results showed that the outer enamel exhibits lower resistance to the inception and growth of cracks. Regardless of the growth direction, the near-threshold region of cyclic extension was typical of “short crack” behavior (i.e. deceleration of growth with an increase in crack length). Cyclic crack growth was more stable in the forward direction and occurred over twice the spatial distance achieved in the reverse direction. In response to the monotonic loads, a rising R-curve response was exhibited by growth in the forward direction only. The total energy absorbed in fracture for the forward direction was more than three times that in the reverse. The rise in crack growth resistance was largely attributed to a combination of mechanisms that included crack bridging, crack bifurcation and crack curving, which were induced by decussation in the inner enamel. An analysis of the responses distinguished that the microstructure of enamel appears optimized for resisting crack growth initiating from damage at the tooth’s surface.     

Fracture of tooth enamel from incipient microstructural defects

We present definitive evidence for crack growth from internal defects called ‘tufts’ in human enamel. Transverse slices (normal to the tooth axis) sawn from extracted human teeth are embedded in a polycarbonate sandwich configuration and tested in simple flexural loading. The evolution of ensuing cracks across the enamel sections is viewed in situ by a video camera. The observations unequivocally identify tufts as sources of internal tooth fracture. In sufficiently thin slices the enamel becomes translucent, allowing for through-thickness observations of the crack topography. Crack segments that appear to be disjointed on a section surface link up into a contiguous primary crack below the surface, suggesting some crack resistance by ‘bridging’ behind the advancing crack tip. The role of these and other microstructural factors in determining the resilience of tooth structures is considered.     

A comparison of fatigue crack growth in human enamel and hydroxyapatite

Cracks and craze lines are often observed in the enamel of human teeth, but they rarely cause tooth fracture. The present study evaluates fatigue crack growth in human enamel, and compares that to the fatigue response of sintered hydroxyapatite (HAp) with similar crystallinity, chemistry and density. Miniature inset compact tension (CT) specimens were prepared that embodied a small piece of enamel (N=8) or HAp (N=6). The specimens were subjected to mode I cyclic loads and the steady state crack growth responses were modeled using the Paris Law. Results showed that the fatigue crack growth exponent (m) for enamel (m=7.7+/-1.0) was similar to that for HAp (m=7.9+/-1.4), whereas the crack growth coefficient (C) for enamel (C=8.7 E-04 (mm/cycle)x(MPa m(0.5))(-m)) was significantly lower (p<0.0001) than that for HAp (C=2.0 E+00 (mm/cycle)x(MPa m(0.5))(-m)). Micrographs of the fracture surfaces showed that crack growth in the enamel occurred primarily along the prism boundaries. In regions of decussation, the microstructure promoted microcracking, crack bridging, crack deflection and crack bifurcation. Working in concert, these mechanisms increased the crack growth resistance and resulted in a sensitivity to crack growth (m) similar to bone and lower than that of human dentin. These mechanisms of toughening were not observed in the crack growth response of the sintered HAp. While enamel is the most highly mineralized tissue of the human body, the microstructural arrangement of the prisms promotes exceptional resistance to crack growth.     

Fracture toughening mechanism of cortical bone: an experimental and numerical approach

In this investigation, the crack propagation mechanisms contributing to the toughness of cortical bone were studied using a combination of experimental and numerical approaches. Compact tension (CT) specimens were prepared from bovine cortical bones to achieve crack propagation in the longitudinal and transverse directions. Stable crack extension experiments were conducted to distinguish the crack growth resistance curves, and virtual multidimensional internal bond (VMIB) modeling was adopted to simulate the fracture responses. Results from experiments indicated that cortical bone exhibited rising resistance curves (R-curves) for crack extension parallel and perpendicular to the bone axis; the transverse fracture toughness was significantly larger, indicating that the fracture properties of cortical bone are substantially anisotropic. Microscopic observations showed that the toughening mechanisms in the longitudinal and transverse directions were different. When the crack grew in the transverse direction, the crack deflected significantly, and crack bifurcations were found at the crack wake, while, in the longitudinal direction, the crack was straight and uncracked ligaments were observed. Numerical simulations also revealed that the fracture resistance in the transverse direction was greater than that in the longitudinal direction.     

Effect of aging on the transverse toughness of human cortical bone: evaluation by R-curves

The age-related deterioration in the quality (e.g., strength and fracture resistance) and quantity (e.g., bone-mineral density) of human bone, together with increased life expectancy, is responsible for increasing incidence of bone fracture in the elderly. The present study describes ex vivo fracture experiments to quantitatively assess the effect of aging on the fracture toughness properties of human cortical bone specifically in the transverse (breaking) orientation. Because bone exhibits rising crack-growth resistance with crack extension, the aging-related transverse toughness is evaluated in terms of resistance-curve (R-curve) behavior, measured for bone taken from a wide range of age groups (25–74 years). Using this approach, both the ex vivo crack-initiation and crack-growth toughness are determined and are found to deteriorate with age; however, the effect is far smaller than that reported for the longitudinal toughness of cortical bone. Whereas the longitudinal crack-growth toughness has been reported to be reduced by almost an order of magnitude for human cortical bone over this age range, the corresponding age-related decrease in transverse toughness is merely ∼14%. Similar to that reported for X-ray irradiated bone, with aging cracks in the transverse direction are subjected to an increasing incidence of crack deflection, principally along the cement lines, but the deflections are smaller and result in a generally less tortuous crack path.     

Microhardness and fracture toughness of dental materials by indentation method

The main objective of this study was to measure the fracture toughness of the human teeth enamel using the microindentation technique and to compare the results calculated from the equations developed for Palmqvist and radial-median cracks. Vickers microhardness measurements of dental ceramic (alumina) and human teeth were performed using indentation fracture method. The fracture toughness of enamel was calculated using different equations reported in the literature. Vickers microhardness of the sintered alumina specimen (98.8% theoretical density) was measured to be 14.92 GPa under 9.8 N indentation load. Three equations based on the radial-median cracks were found to be applicable for the fracture toughness determination of the enamel. Results show that indentation fracture method is adequate to measure microhardness and fracture toughness of dental materials. However the calculation of fracture toughness depended on the nature of the cracks and also on the location of the indentation. Therefore, it is necessary to identify the crack profile and to select the appropriate equation for accurate fracture toughness values.     

Quantitative analysis of the calcium and phosphorus content of developing and permanent human teeth.

It was the aim of this study to investigate the distribution of Ca, P and C in predentin, dentin and enamel in human tooth buds and permanent teeth by EDX element analysis. The mandible of a 16-week-old human fetus containing eight mineralizing tooth buds and three human permanent molars were fixed in formaldehyde and embedded in Technovit 9100. Serial sections of 80 microm thickness of the mandible were cut in the frontal-dorsal direction, and polarized light micrographs were taken of these sections. The permanent teeth were cut in mesio-distal direction. The sections were investigated with scanning electron microscopy and EDX element analysis with a Philips XL 30 FEG scanning microscope and an EDAX energy-dispersive X-ray system using spot measurements, EDX line-scans and element mapping. Quantitative measurements were made in predentin, mineralizing dentin adjacent to predentin, mature dentin, mineralizing enamel and young enamel of developing teeth and mature enamel of permanent teeth. In developing teeth the Ca and P content increased rapidly from outer predentin towards mineralizing dentin. In enamel prisms of developing teeth the Ca and P content increased linearly from the surface towards the enamel-dentin junction. In permanent teeth only a small layer of predentin was found. The Ca and P content in enamel and circumpulpal dentin of permanent teeth was higher than in developing teeth. The Ca/P ratio differed between predentin and dentin areas reflecting different calcium phosphate compositions, but it was the same in mineralizing and young enamel. The differences in the distribution of Ca and P reflect different mineralizing patterns of the enamel and dentin matrices.     

Contributions of aging to the fatigue crack growth resistance of human dentin

An evaluation of the fatigue crack resistance of human dentin was conducted to identify the degree of degradation that arises with aging and the dependency on tubule orientation. Fatigue crack growth was achieved in specimens of coronal dentin through application of Mode I cyclic loading and over clinically relevant lengths (0 ≤ a ≤ 2 mm). The study considered two directions of cyclic crack growth in which the crack was either in-plane (0°) or perpendicular (90°) to the dentin tubules. Results showed that regardless of tubule orientation, aging of dentin is accompanied by a significant reduction in the resistance to the initiation of fatigue crack growth, as well as a significant increase in the rate of incremental extension. Perpendicular to the tubules, the fatigue crack exponent increased significantly (from m=14.2 ± 1.5 to 24.1 ± 5.0), suggesting an increase in brittleness of the tissue with age. For cracks extending in-plane with the tubules, the fatigue crack growth exponent does not change significantly with patient age (from m=25.4 ± 3.03 to 22.9 ± 5.3), but there is a significant increase in the incremental crack growth rate. Regardless of age, coronal dentin exhibits the lowest resistance to fatigue crack growth perpendicular to the tubules. While there are changes in the cyclic crack growth rate and mechanisms of cyclic extension with aging, this tissue maintains its anisotropy.     

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.     

年龄变化对人牙本质裂纹扩展升阻能力的影响

目的通过有限元数值计算的方法研究年龄变化对牙本质断裂力学行为的影响。方法根据典型的紧凑拉伸试件形式建立有限元模型,采用内聚力模型分别模拟裂纹在年轻和老龄牙本质中稳态扩展的过程,并进行比较。结果老龄牙本质的扩展断裂韧度和断裂韧度趋于恒定时的值分别为0.51、1.19 MPa.m1/2,显著小于年轻牙本质的相应值(7.48、1.71 MPa.m1/2);然而,这两者之间的初始断裂韧度相差比较微小,年轻和老龄牙本质的初始断裂韧度分别为0.51和0.38 MPa.m1/2。结论随着年龄的增长,牙本质抵抗裂纹扩展的能力发生了明显的减弱。基于内聚力模型的数值方法能够很好地预测牙本质等力学性能与年龄相关的生物硬组织材料的裂纹扩展行为。     

Properties of tooth enamel in great apes

A comparative study has been made of human and great ape molar tooth enamel. Nanoindentation techniques are used to map profiles of elastic modulus and hardness across sections from the enamel–dentin junction to the outer tooth surface. The measured data profiles overlap between species, suggesting a degree of commonality in material properties. Using established deformation and fracture relations, critical loads to produce function-threatening damage in the enamel of each species are calculated for characteristic tooth sizes and enamel thicknesses. The results suggest that differences in load-bearing capacity of molar teeth in primates are less a function of underlying material properties than of morphology.     

The effects of tubule orientation on fatigue crack growth in dentin

The fracture of restored teeth is a significant obstacle to lifelong oral health. Recent studies suggest that fatigue cracks originate at flaws introduced during cavity preparation and that fatigue crack growth is a principle cause of restored tooth fractures. In this study, the rate of fatigue crack growth in bovine dentin was estimated under mode I cyclic loading. Double cantilever beam (DCB) specimens were obtained from bovine molars and subjected to high cycle fatigue loading (10(5) < N < 10(6)). The fatigue crack growth rates were measured and used to estimate the crack growth exponent and coefficient according to the Paris Law. The average fatigue crack growth exponent was 4.7 +/- 0.6 for crack growth parallel to the dentin tubules, which was significantly larger than 4.3 +/- 0.5 for crack growth perpendicular to the tubules (t-test, CI > 80%). Although the crack growth rates varied considerably, there was no significant dependence on tubule orientation or tubule density. However, specific features of the fracture surfaces and tendencies for crack curving away from the tubules suggested preferential fatigue crack growth perpendicular to the dentin tubules. Results from this study are being used to guide an experimental investigation of fatigue crack growth in human dentin.     

Fractography and fracture toughness of human dentin

Dentin, the mineralized tissue forming the bulk of the tooth, serves as an energy-absorbing cushion for the hard, wear-resistant enamel and protects the inner soft tissues. Several studies used fracture mechanics methods to study the fracture toughness of dentin. However, all of them utilized precracks and cannot be used to estimate the intrinsic critical flaw size of dentin. We applied quantitative fractography to study the fracture pattern and fracture toughness of human dentin. Sixteen specimens were prepared from the coronal dentin and fractured in three-point flexure. Fracture surfaces were examined using a scanning electron microscope and the fracture toughness was calculated using a fracture mechanics equation. It was found that human dentin has a fracture surface similar to those of brittle materials. Twist hackle markings were observed and were used to identify the fracture origins. Average fracture toughness of all specimens was found to be 2.3 MPa m^1/2 and the average critical flaw size was estimated to 120 μm. It is suggested that fractography is a promising technique in analyzing the fracture of dentin under catastrophic failure.     

Analysis of fracture and deformation modes in teeth subjected to occlusal loading

An analysis of fracture and deformation modes in tooth enamel subjected to occlusal loading is presented. Several competing modes are identified: deformation by yield beneath the indenter; median cracking from the ensuing plastic zone and analogous radial cracking from the dentin–enamel junction along the load axis; and margin cracking from the cervical enamel–cement junction. The analysis, based on a simple model of tooth geometry, presents relations for the critical loads to initiate these damage modes within the enamel, and to drive ensuing cracks longitudinally around the tooth walls to failure. The relations are explicit in their dependence on characteristic tooth dimensions – enamel thickness and cuspal radius – and on material properties – modulus, hardness, toughness and strength. Provision is made to incorporate properties of the occlusal contact, whether from opposing dentition or intervening food particles. All these features are demonstrated on critical-load master diagrams. A characteristic feature of the damage evolution is the gradual evolution of each mode with increasing load, so that failure is generally a prolonged rather than abrupt event. This accounts for the remarkable damage tolerance of natural teeth. The equations may enable basic predictions of tooth responses for humans and animals under a variety of specified dietary and functional conditions.