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%.

Crack arrest within teeth at the dentinoenamel junction caused by elastic modulus mismatch.

Enamel and dentin compose the crowns of human teeth. They are joined at the dentinoenamel junction (DEJ) which is a very strong and well-bonded interface unlikely to fail within healthy teeth despite the formation of multiple cracks within enamel during a lifetime of exposure to masticatory forces. These cracks commonly are arrested when reaching the DEJ. The phenomenon of crack arrest at the DEJ is described in many publications but there is little consensus on the underlying cause and mechanism. Explanations range from the DEJ having a larger toughness than both enamel and dentin up to the assumption that not the DEJ itself causes crack arrest but the so-called mantle dentin, a thin material layer close to the DEJ that is somewhat softer than the bulk dentin. In this study we conducted 3-point bending experiments with bending bars consisting of the DEJ and surrounding enamel and dentin to investigate crack propagation and arrest within the DEJ region. Calculated stress intensities around crack tips were found to be highly influenced by the elastic modulus mismatch between enamel and dentin and hence, the phenomenon of crack arrest at the DEJ could be explained accordingly via this elastic modulus mismatch.

The fracture behaviour of dental enamel.

Enamel is the hardest tissue in the human body covering the crowns of teeth. Whereas the underlying dental material dentin is very well characterized in terms of mechanical and fracture properties, available data for enamel are quite limited and are apart from the most recent investigation mainly based on indentation studies. Within the current study, stable crack-growth experiments in bovine enamel have been performed, to measure fracture resistance curves for enamel. Single edge notched bending specimens (SENB) prepared out of bovine incisors were tested in 3-point bending and subsequently analysed using optical and environmental scanning electron microscopy. Cracks propagated primarily within the protein-rich rod sheaths and crack propagation occurred under an inclined angle to initial notch direction not only due to enamel rod and hydroxyapatite crystallite orientation but potentially also due to protein shearing. Determined mode I fracture resistance curves ranged from 0.8-1.5 MPa*m(1/2) at the beginning of crack propagation up to 4.4 MPa*m(1/2) at 500 microm crack extension; corresponding mode II values ranged from 0.3 to 1.5 MPa*m(1/2).