applied fracture mechanics

Fracture of Dental Materials 119Crack growth in the inner enamel was accompanied by a host of mechanisms operatingfrom the micro- to the nano-scale. Decussation in the inner enamel promoted crackdeflection and twist, resulting in a reduction of the local stress intensity at the crack tip(Figures 6 and 7). In addition, extrinsic mechanisms such as bridging by unbroken ligamentsof the tissue and the organic matrix promoted crack closure. Micro-cracking due toloosening of prisms was also identified as an active source of energy dissipation. The uniquemicrostructure of enamel in the decussated region promotes crack growth toughness that isapproximately three times that of dentin and over ten times that of bone.In addition to the micro- and nano-structure of enamel, the tooth anatomy by itself is suchthat it has adapted to force conditions present in the oral cavity. Anderson et al. [12]modeled what they believed drove the initial evolution of the cingulum. Recent work onphysical modeling of fracture mechanics has shown that structures which approximatemammalian dentition (hard enamel shell surrounding a softer/tougher dentine interior)undergo specific fracture patterns dependent on the material properties of the food items [9,13]. Soft materials result in fractures occurring at the base of the stiff shell away from thecontact point due to heightened tensile strains. These tensile strains occur around themargin in the region where cingula develop. In Anderson et al.’s [12] study, they testedwhether the presence of a cingulum structure would reduce the tensile strains seen inenamel using basic finite element models of bilayered cones. Finite element models ofgeneric cone shaped ‘‘teeth’’ were created both with and without cingula of various shapesand sizes. Various forces were applied to the models to examine the relative magnitudesand directions of average maximum principal strain in the enamel. The addition of acingulum greatly reduces tensile strains in the enamel caused by ‘‘soft-food’’ forces. Therelative shape and size of the cingulum has a strong effect on strain magnitudes as well.Scaling issues between shapes are explored and show that the effectiveness of a givencingulum to reducing tensile strains is dependent on how the cingulum is created. Partialcingula, which only surround a portion of the tooth, are shown to be especially effective atreducing strain caused by asymmetrical loads, and shed new light on the potential earlyfunction and evolution of mammalian dentitions.2.2. Fracture mechanical aspects of dentinDentin is not as brittle as enamel. However, considering that enamel rests on dentin, andthat cracks may propagate through the enamel, it is important to understand the fracturemechanics of dentin.Human dentin is known to be susceptible to failure under repetitive cyclic fatigue loading.Nalla et al. [14] addressed the paucity of fatigue data through a systematic investigation ofthe effects of prolonged cyclical loading on human dentin. They performed the evaluationsin an environment of ambient temperature and where the dentin was kept in a Hank’sbalanced salt solution. The results they got were discussed in the context of possiblemechanisms of fatigue damage and failure. The stiffness loss data collected were used todeduce crack velocities and the thresholds for such cracking. They concluded that the