Devendra Bajaj

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 MPam(0.5)), and the inner enamel exhibited a rise in the growth toughness from 1.13 MPam(0.5)/mm to 3.93 MPam(0.5)/mm. The maximum crack growth resistance at fracture (i.e. fracture toughness (K(c))) ranged from 1.79 to 2.37 MPam(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.

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.

Hidden contributions of the enamel rods on the fracture resistance of human teeth

The enamel of human teeth is generally regarded as a brittle material with low fracture toughness. Consequently, the contributions of this tissue in resisting tooth fracture and the importance of its complex microstructure have been largely overlooked. In this study an experimental evaluation of the crack growth resistance of human enamel was conducted to characterize the role of rod (i.e. prism) orientation and degree of decussation on the fracture behavior of this tissue. Incremental crack growth was achieved in-plane, with the rods in directions longitudinal or transverse to their axes. Results showed that the fracture resistance of enamel is both inhomogeneous and spatially anisotropic. Cracks extending transverse to the rods in the outer enamel undergo a lower rise in toughness with extension, and achieve significantly lower fracture resistance than in the longitudinal direction. Though cracks initiating at the surface of teeth may begin extension towards the dentin-enamel junction, they are deflected by the decussated rods and continue growth about the tooths periphery, transverse to the rods in the outer enamel. This process facilitates dissipation of fracture energy and averts cracks from extending towards the dentin and vital pulp.

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.

Comments on: “Hertzian contact response of dentin with loading rate and orientation” by N.R. da Silva, F. Lalani, P.G. Coelho, E.A. Clark, C.A. de Oliveira Fernandes, V.P. Thompson [Arch. Oral Biol. 53 (2008) 729–735]

A recently published article in the Archives of Oral Biology addresses the mechanical behaviour of dentin under Hertzian contact. The authors present an interesting study in which the contact modulus was deduced from spherical indentations introduced on polished dentin surfaces with tubules aligned either parallel or perpendicular to the prepared surface. Results of their evaluation reported contact modulus values that range from approximately 1.3 to over 2.1 GPa. There was no significant influence of tubule orientation but a significant increase in apparent contact modulus with loading rate. Though the rate dependent behaviour of dentin is an interesting topic and one that may provide a greater understanding of the microstructure – property relationships of this tissue, there are some critical shortcomings in the reported evaluation that should be considered in further research conducted by the dental materials community. The authors contend that after decades of research focused on mechanical properties of dentin there is little consistency in the testing methodology. That is certainly true, and has been largely reflected in the reported range of elastic modulus (2–28 GPa) as discussed in the detailed review by Kinney et al. The authors further contend that previous studies on properties of dentin have not examined the effect of loading rate on mechanical behaviour, and that differences in the measured responses (or inconsistencies) between reports could be attributed to this factor. They appear to have overlooked the work by Arola and Zheng, who studied the effect of loading rate on properties of dentin in some detail. The influence of loading rate on the flexure modulus, flexure strength and energy to fracture of dentin were determined in an evaluation of the dynamic fatigue behaviour. Specifically, beams of bovine dentin were prepared and subjected to fourpoint flexure under load control actuation to fracture over loading rates spanning five decades (i.e. from 0.001 to 10 N/s) in both hydrated and dehydrated conditions. Results of the evaluation showed that there was a significant increase in modulus ( p < 0.01), strength (p < 0.01) and energy to fracture (p < 0.01) with loading rate for the hydrated dentin (Fig. 1). Note that the modulus increased from approximately 14 GPa to more than 30 GPa over the span in loading rate, which directly agrees with perceived rate-dependence by Kinney et al. Although there was also an increase in the modulus of the dehydrated dentin with loading rate, there was a significant decrease in the flexure strength (p < 0.01) and energy to fracture (p < 0.01) as evident in Fig. 1. The results obtained by Arola and Zheng are difficult to compare with those of da Silva, which is due to the questionable modulii reported by the latter group. Indeed, their values are at least a factor of magnitude lower than the accepted elastic modulus of dentin (15–20 GPa). The cause for this discrepancy can be easily explained and is presented below. The authors of the paper in the Archives adopted a classical approach involving Hertzian contact mechanics to define the contact modulus for dentin that involves a measure of the contact load and corresponding contact patch radius. The contact modulus (Ec) was estimated according to Ec 1⁄4 pc ec ; pc 1⁄4 P p a2 ; ec 1⁄4 a r (1)