Sub-10-micrometer toughening and crack tip toughness of dental enamel.

In previous studies, enamel showed indications to occlude small cracks in-vivo and exhibited R-curve behaviors for bigger cracks ex-vivo. This study quantifies the crack tip's toughness (K(I0),K(III0)), the crack's closure stress and the cohesive zone size at the crack tip of enamel and investigates the toughening mechanisms near the crack tip down to the length scale of a single enamel crystallite. The crack-opening-displacement (COD) profile of cracks induced by Vickers indents on mature bovine enamel was studied using atomic force microscopy (AFM). The mode I crack tip toughness K(I0) of cracks along enamel rod boundaries and across enamel rods exhibit a similar range of values: K(I0,Ir)=0.5-1.6MPa m(0.5) (based on Irwin's 'near-field' solution) and K(I0,cz)=0.8-1.5MPa m(0.5) (based on the cohesive zone solution of the Dugdale-Muskhelishvili (DM) crack model). The mode III crack tip toughness K(III0,Ir) was computed as 0.02-0.15MPa m(0.5). The crack-closure stress at the crack tip was computed as 163-770 MPa with a cohesive zone length and width 1.6-10.1µm and 24-44 nm utilizing the cohesive zone solution. Toughening elements were observed under AFM and SEM: crack bridging due to protein ligament and hydroxyapatite fibres (micro- and nanometer scale) as well as microcracks were identified.

On the mechanical properties of hierarchically structured biological materials.

Many biological materials are hierarchically structured which means that they are designed from the nano- to the macro-scale in a sometimes self-similar way. There are lots of papers published including very detailed descriptions of these structures at all length scales--however, investigations of mechanical properties are most often focused on either nano-indentation or bulk mechanical testing characterizing properties at the smallest or largest size scale. Interestingly, there are hardly any investigations that systematically interconnect mechanical properties of different length scales. Nevertheless there are often conclusions drawn like the one that "biological materials exhibit their excellent mechanical properties due to their hierarchical structuring". Thus, we think there is a gap and discrepancy between the detection and description of biological structures and the correlated determination and interpretation of their mechanical properties. Hence, in this paper we order hierarchically structured biological materials with high mineral content according to their hierarchical levels and attribute measured mechanical properties to them. This offers the possibility to gain insight into the mechanical properties on different hierarchical levels even though the entire biological materials were tested. On the other hand we use data of one material, namely enamel, where mechanical properties were measured on every length scale. This kind of data analysis allows to show how a theoretical model developed by Huajian Gao and co-workers can be used to get closer insights into experimental data of hierarchically structured materials.

Size-dependent elastic/inelastic behavior of enamel over millimeter and nanometer length scales.

The microstructure of enamel like most biological tissues has a hierarchical structure which determines their mechanical behavior. However, current studies of the mechanical behavior of enamel lack a systematic investigation of these hierarchical length scales. In this study, we performed macroscopic uni-axial compression tests and the spherical indentation with different indenter radii to probe enamel's elastic/inelastic transition over four hierarchical length scales, namely: 'bulk enamel' (mm), 'multiple-rod' (10's microm), 'intra-rod' (100's nm with multiple crystallites) and finally 'single-crystallite' (10's nm with an area of approximately one hydroxyapatite crystallite). The enamel's elastic/inelastic transitions were observed at 0.4-17 GPa depending on the length scale and were compared with the values of synthetic hydroxyapatite crystallites. The elastic limit of a material is important as it provides insights into the deformability of the material before fracture. At the smallest investigated length scale (contact radius approximately 20 nm), elastic limit is followed by plastic deformation. At the largest investigated length scale (contact size approximately 2 mm), only elastic then micro-crack induced response was observed. A map of elastic/inelastic regions of enamel from millimeter to nanometer length scale is presented. Possible underlying mechanisms are also discussed.

Determination of the elastic/plastic transition of human enamel by nanoindentation.

OBJECTIVES/METHODS: From a materials scientist's perspective, dental materials used for tooth repair should exhibit compatible mechanical properties. Fulfillment of this criterion is complicated by the fact that teeth have a hierarchical structure with changing mechanical behavior at different length scales. In this study, nanoindentation with an 8 microm spherical indenter was used to determine the elastic/plastic transition under contact loading for enamel. RESULTS: The indentation elastic/plastic transition of enamel at the length scale of several hundreds of hydroxyapatite crystallites, which are within one enamel rod, is revealed for the first time. The corresponding penetration depth at the determined indentation yield point of 1.6GPa and 0.6% strain is only 7 nm. As a consequence of the small depth it is decisive for the experiment to calibrate the indenter tip radius in this loading regime. The elastic modulus of 123GPa was evaluated directly by the Hertzian penetration and not by the unloading part of the indentation curve. SIGNIFICANCE: We believe these data are also a valuable contribution to understand the mechanical behavior of enamel and to develop nanoscale biomimetic materials.