Elastic modulus and stress–strain response of human enamel by nano-indentation
Introduction
Enamel, the outer cover of a tooth, is the hardest and stiffest structure of the body. The functional requirements of teeth are that they be able to bear the range of imposed loads and consequent contact-induced stresses without failure and retain their shapes while doing so [1]. Besides the normal loads, enamel will bear shear forces because of the direct contact with opposite teeth and external objects during mastication. Moreover, unlike other calcified skeletal structures, fracture of dental tissue is not repairable. The ability of enamel to meet such critical requirements has resulted in the structure and mechanical properties of this natural material attracting numerous researchers’ interests.
Enamel is composed of inorganic mineral crystals and a small volume of water and protein that holds the inorganic crystals together. The inorganic part of enamel is a form of carbonate hydroxyapatite and the organic part is mainly protein. Though free water and protein comprise only a minor part of mature enamel, they are crucial to its development and are important in understanding its structural organization and physical properties [2]. After maturation, some acidic proteins called enamelins and tuftelins remain inside enamel [3] and act as a “glue” between crystallites [4] and as the cover sheath of the prisms or rods that extend from the dentine enamel junction to the enamel surface. Most free water within enamel is bound within the sheath structure and has an influence on enamel's compressibility, permeability and ionic conductivity [5]. The resulting composite material is much tougher than apatite mineral alone [6]. The mineral and non-mineral components are organized into a complex textured nano-crystallite material that very effectively dissipates forces applied to teeth and protects them from fracture.
Although the high mineral content accounts for enamel's hardness, it is the arrangement and organization of its inorganic and organic constituents (enamel micro-structure) that modulates the way enamel responds to stress [2]. Enamel structure may be visualized as a number of hierarchical levels of increasing complexity and scale from crystal level to pattern level [2], [7]. Among them, the most useful and practical model from a mechanical perspective are the prism rods. Human enamel at this level is composed of a rod and inter-rod sheath structure [8]. The diameter of keyhole-like rods is about 5 μm. They align parallel from enamel–dentin junction to the surface of the tooth and are covered by a thin organic sheath. Recently, an FEA model at this level has been developed to predict the orientation and mineral dependence of the elastic properties of enamel [9].
The well arranged prism micro-structure results in anisotropy of enamel's mechanical properties. During the past half-century, several methods, including both macroscopic and microscopic approaches, were used to determine the mechanical properties such as elastic modulus, strength and toughness of dental tissues [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]. Despite such studies, there are virtually no direct measurements of the stress–strain response of enamel that have been reported.
Since the introduction of the spherical indentation method to nano-indentation by Field and Swain [21] and its subsequent verification using the Oliver and Pharr [22] approach, spherical indenters have been used for measuring elastic–plastic and stress–strain properties of some engineering materials [23], [24], [25], [26], [27], [28]. In this paper, we extend this approach and develop a new method for measuring the stress–strain relationship of enamel in different directions and compare the results with those obtained using a pointed Berkovich indenter.
Section snippets
Theory
In the field of nano-indentation, the Berkovich tip has been widely used to measure the mechanical properties of bulk materials and thin films. This indenter has a triangular shaped tip with the total included angle of 142.3° and half-angle of 65.35°; this tip can only produce a constant equivalent strain value during a test procedure. To measure the stress–strain response of the material, changing strain values are necessary during the course of the test. A spherical tipped indenter becomes a
Materials and methods
A Berkovich indenter and two spherical tipped indenters (Synton, Switzerland) with nominal indenter radii of 5 and 20 μm were chosen for this study. Fused silica acted as the standard calibration material.
A healthy premolar tooth extracted for orthodontic reasons was embedded with a cold-curing epoxy resin (Epofix, Struers, Copenhagen, Denmark). The top surface and cross-sectional surface of the tooth were chosen for testing. The cutting directions were selected so that the enamel prism
Indenter tip calibration
The Berkovich indenter tip was calibrated with fused silica using the approach outlined by Oliver and Pharr [30]. The two spherical indenters were calibrated with fused silica using the methods described above to acquire the a−hp curve and its functional form. The results from more than 200 individual indentation tests on fused silica for each indenter were fitted to power-law functions as shown in Figs. 2a and b. The curve generated for the nominally 5 μm radius spherical tip (Fig. 2a) was
Spherical indentation techniques
The stresses and deflections arising from the contact between two elastic solids are of particular interest to those undertaking indentation testing. From Fig. 1, it is not difficult to see that a−hp curve describes the actual shape of the contact surface of the tip. Figs. 2a and b show the effective tip shape of the spherical indenters used in this study. It is not surprising that the indenter has a parabolic shape rather than perfect spherical form at this scale, because it is impossible to
Conclusions
Nano-indentation is an attractive method for measuring the mechanical behavior of small specimen volumes. Using this technique, the mechanical properties of enamel were investigated in directions parallel and perpendicular to the prisms. From the present study using both pointed and spherical-tipped indenters the following conclusions are proposed.
- 1.
Elastic modulus of enamel is influenced by prism-sheath structure and in the case of nano-indentation it is a function of contact area. This
Acknowledgements
The first author gratefully acknowledges the Australian Department of Education, Science and Training (DEST) and University of Sydney for financial support in the form of IPRS scholarship. Partial support from an ARC Discovery grant (DP0666446) and ARC Linkage grant (LP0561184) are also acknowledged. The authors also acknowledge the facilities as well as scientific and technical assistance from staff in the NANO Major National Research Facility at the Electron Microscope Unit, The University of
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