13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- here will be helpful to understand the internal architecture and hierarchical properties of human dental tissues. Quite a few models of composites have been proposed to describe the interaction of different phases, including bounding principles of Voigt and Reuss, as well as Jones and BW models [15,16]. One widely accepted model, also used in this study, is the Eshelby inclusion model, often used to describe the structure-property relationship of materials like composites [17,18]. Recently, it has been applied in the research of dentine [19,20], and has been proven to be useful to predict the elastic response of dentine. However, this Eshelby approach has not been used to describe human enamel. In this paper, the elastic lattice strain, orientation and degree of alignment of HAp crystals within a human enamel sample under compressive loading were measured by the combined in situ synchrotron X-ray techniques (WAXS and SAXS). The multi-scale Eshelby model was developed to reflect the hierarchical structure of enamel, and to predict the elastic response to mechanical loading. The model was validated by comparison with experimental data. 2. Method and Materials 2.1. Sample preparation A freshly extracted sound human third molar (ethical approval obtained from the National Research Ethics Committee; NHS-REC reference 09.H0405.33/Consortium R&D No.1465) was washed and mechanically cleaned in distilled water to eliminate residues and kept in a -20°C freezer for a maximum of 14 days before the experiment. The tooth was rehydrated using distilled water and 2mm thick enamel disks were cut just below the enamel-cement line using a low speed diamond saw (Isomet Buehler Ltd., Lake Bluff, Illinois, USA). The disks were further cut into smaller bars and polished using a series of polishing papers to produce a 2×2×2mm cube of enamel. The sample was kept for 5 days in distilled water in a commercial fridge at 4°C until the experiment was undertaken. 2.2. In-situ scattering measurements Figure 1. In situ loading of enamel under simultaneous WAXS/SAXS experimental set-up The experiment was performed on the B16 beamline at Diamond Light Source (DLS, Oxford, UK). A schematic diagram of the experimental set-up is shown in Fig. 1. The cubic sample of human enamel was slowly deformed along x-direction in the laboratory coordinate system (Fig. 1) under compressive loading at a displacement rate of 0.2 mm/min until failure, using a remotely operated and monitored compression rig (Deben, Suffolk, UK) with a 5KN calibrated load cell.
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