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Research Papers

Development of Strong Surfaces Using Functionally Graded Composites Inspired by Natural Teeth—A Theoretical Approach

[+] Author and Article Information
A. E. Giannakopoulos, A. Kordolemis

Department of Civil Engineering, Laboratory for Strength of Materials and Micromechanics, University of Thessaly, Volos 38336, Greece

Th. Zisis1

Department of Civil Engineering, Laboratory for Strength of Materials and Micromechanics, University of Thessaly, Volos 38336, Greecezisis@metal.ntua.gr

1

Corresponding author.

J. Eng. Mater. Technol 132(1), 011009 (Nov 05, 2009) (7 pages) doi:10.1115/1.3184037 History: Received January 14, 2009; Revised May 12, 2009; Published November 05, 2009; Online November 05, 2009

In recent years functionally-graded composites have been proposed to develop strong surfaces that can withstand high contact and frictional forces. The present work presents a new graded composite that can be used for the development of surfaces with excellent strength properties. The composite is inspired by the human teeth, which nature builds as a hard and tough functionally-graded composite. The outer surface of teeth is of enamel, composed of prismatic hydroxyapatite crystallites, whereas the inner part of teeth is of dentine, composed collagen fibrils and hydroxyapatite. Enamel is hard, brittle, and wear resistant, while dentine is softer and flexible. The dentine-enamel junction is formed as a region at which enamel mixes with dentine in a continuous way. The nanomechanical properties of the transition zone have been recently revealed. Of particular interest in this investigation is the variation in the elastic modulus from the pure enamel to the pure dentine material, which leads to biomimetic graded composites that exhibit high surface strength. This work presents analytical solutions for the stress and displacement fields on an actual composite substrate, which is loaded by a line load. The elastic modulus of the substrate follows approximately the theoretical distribution.

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Figures

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Figure 1

(a) The applied vertical P and horizontal Q line loads acting at the surface of a semi-infinite substrate and (b) the polar coordinate system

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Figure 2

The displacement field due to the vertical line load P

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Figure 3

Elastic modulus varying continuously with depth. A multilayer substrate (say, of six layers) that follows the “continuous” variation: E1>E2>E3>E4>E5>E6 is assumed. The continuous modulus is implemented by a distribution of the type E=E0y0/y by layers of equal thickness and constant elastic modulus within each layer.

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Figure 6

Displacement distribution along a path on the x-axis at depth equal to y/y0=−0.65 from the surface of the substrate. Results are shown for (a) vertical displacements ux and (b) normal displacements uy for homogeneous and FGM substrate. (y=−1.95 m, E0=1000 Pa, y0=3 m, and y∗=243 m).

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Figure 5

Isobar: σrr=−2P/(π×1), —— and E: constant ---- E=A/y, for (a) vertical load and (b) horizontal load

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Figure 4

Stress distribution along a path on the x-axis at depth equal to y/y0=−0.65 from the surface of the substrate for normal line load. Results are shown for homogeneous and FGM substrate. (P=1 N/m, y0=3 m, and E0=1000 Pa).

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