13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Multi-scale modeling and diffraction-based characterization of elastic behaviour of human enamel Tan Sui1,*, Michael A. Sandholzer2, Nikolaos Baimpas1, Igor Dolbnya3, Gabriel Landini2, Alexander M. Korsunsky1 1 Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom 2 School of Dentistry, College of Medical and Dental Sciences, University of Birmingham, St Chad’s Queensway, Birmingham B4 6NN, United Kingdom 3 Diamond Light Source, Harwell Oxford Campus, Didcot OX11 0DE, United Kingdom * Corresponding author: tan.sui@eng.ox.ac.uk Abstract The relationship between the ultrastructure of human enamel and its mechanical behaviour is studied in this paper. Two synchrotron X-ray diffraction techniques, wide and small angle X-ray scattering (WAXS/SAXS) were used in combination to obtain multi-scale quantitative information about the response of human enamel to in situ uniaxial compressive loading. The interpretation of WAXS data gives elastic lattice strains within the hydroxyapatite (HAp) crystals, the stiff reinforcing phase in human enamel. The apparent modulus was determined linking the external load and the internal HAp strain. SAXS interpretation, allows the quantification of the nano-scale HAp crystallite distribution within human enamel. A multi-scale Eshelby equivalent inclusion model of the enamel was proposed that represents the hierarchical mineralized tissue as a two-level composite: micro-level model with rod embedded in the homogenised enamel material, and nano-level model with HAp crystallites embedded in the rod. Satisfactory agreement was achieved between model and experiment, suggesting that the new multi-scale approach accurately reflects the structure and mechanics of human enamel, and may help guide new biomimetic designs. Keywords Enamel, WAXS/SAXS, Eshelby model, Mechanical properties 1. Introduction Enamel, a highly mineralized substance, is a hard and brittle material that covers the crown portion of teeth. It is predominately composed of inorganic hydroxyapatite (HAp) crystals and organic collagen [1]. While at the macro-scale the enamel can be thought of as a continuum, at the microstructural level some notable features are present, in particular, aligned long prisms (or rods) with a keyhole-shaped cross-section, and with the top oriented toward the crown of the tooth [2]. Further, at the nano-scale level, needle-like HAp crystals are found with several tens of nanometers in thickness [3]. Understanding the effects of microstructural features of enamel on the performance of human teeth requires the understanding of how the mechanical properties are related to the complex hierarchical structure. Over half a century, studies have been conducted on the macro-scale mechanical properties of enamel [4]. While an increasing number of publications describe microstructural effects [5], relatively few studies have focused on the influence of the nano-scale structure [6]. There appears to be a demand for further investigation across the scales using advanced techniques and models to establish a solid basis to understand the hierarchical structure-property relationship. One suitable method to study this is small angle X-ray scattering (SAXS), an advanced non-destructive technique used to reveal information about nano-scale structure and orientation in crystalline and amorphous materials [7]. Another X-ray technique, wide angle X-ray scattering (WAXS), is used to study crystal lattices and their deformation behaviour, e.g. the elastic properties of composites [8,9]. WAXS has been applied only recently to the study of mineralized biological composites, such as bones and bovine teeth [10-13], but few studies have been devoted to study human enamel [14]. Therefore, for the present study a combined SAXS/WAXS setup with in situ compressive loading of human enamel samples was selected. It is hoped that the results obtained
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