Elastic modulus and stress–strain response of human enamel by nano-indentation

Abstract

Nano-indentation with a sharp (Berkovich) and two spherical indenters with nominal tip radii of 5 and 20 μm was used to determine the elastic modulus and stress–strain response of human enamel. Indentation tests were made over a wide range of peak loads from 1 to 450 mN in two orthogonal directions, i.e., parallel and perpendicular to enamel prisms. The elastic modulus and hardness (mean contact pressure) versus depth of penetration were determined for the three indenters. From the spherical indentation data, stress–strain curves (H−tan θ curve) of enamel were determined in the two orthogonal directions and were found to be different. The elastic modulus showed load dependence for both orientations of the enamel rod structure that depended on the indenter. However, these differences could be normalized upon considering the contact diameter. The indented sample was imaged with an SEM to investigate the near surface damage. In conclusion, prism-sheath structure played an important role in determining the mechanical properties as well as the localized fracture of enamel.

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.