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Research Papers

# Development of Strong Surfaces Using Functionally Graded Composites Inspired by Natural Teeth—Finite Element and Experimental Verification

[+] Author and Article Information
Th. Zisis1

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

A. Kordolemis, A. E. Giannakopoulos

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

1

Corresponding author.

J. Eng. Mater. Technol 132(1), 011010 (Nov 05, 2009) (9 pages) doi:10.1115/1.3184038 History: Received January 14, 2009; Revised May 13, 2009; Published November 05, 2009; Online November 05, 2009

## Abstract

Functionally graded materials (FGMs) are composite materials that exhibit a microstructure that varies locally in order to achieve a specific type of local material properties distribution. In recent years, FGMs appear to be more interesting in engineering application since they present an enhanced performance against deformation, fracture, and fatigue. The purpose of the present work is to present evidence of the excellent strength properties of a new graded composite that is inspired by the human teeth. The outer surface of the teeth exhibits high surface strength while it is brittle and wear resistant, whereas the inner part is softer and flexible. The specific variation in Young’s modulus along the thickness of the presented composite is of particular interest in our case. The present work presents a finite element analysis and an experimental verification of an actual composite with elastic modulus that follows approximately the theoretical distribution observed in the teeth.

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## Figures

Figure 1

The applied vertical P and horizontal Q line loads acting at the surface of a semi-infinite substrate

Figure 2

(a) Region of the mesh used for the finite element simulations with the appropriate boundary conditions. (b) Blown up view of the mesh around the center line. The mesh comprises 95517 nodes and 31600 8-node biquadratic plane strain quadrilateral elements (CPE8 in ABAQUS notation). Minimum element length: he=0.12 m.

Figure 3

Variation in the continuous Young’s modulus E, used in the FE model, as a function of the depth y for layer thickness (a) l=1 m, (b) l=0.5 m, and (c) l=0.25 m (E0=1 Pa, y0=1 m)

Figure 4

Stress distribution along a path on the x-axis at depth equal to y/y0=−1.95 from the surface of the substrate. Analytical and FE results for (a) normal line load and (b) tangential line load for homogeneous substrate (l=0.25 m, E0=1 Pa, y0=1 m).

Figure 5

Stress distribution along a path on the x-axis at depth equal to y/y0=−1.95 from the surface of the substrate. Analytical and FE results for (a) normal line load and (b) tangential line load for FGM substrate (l=0.25 m, E0=1 Pa, y0=1 m).

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. Analytical and FE results are shown for (a) vertical displacements ux and (b) normal displacements uy for homogeneous and FGM substrate (y=−1.95 m, l=3 m, E0=1000 Pa, y0=3 m, y∗=243 m).

Figure 7

(a) Equivalent stress field for (i) homogeneous (ii) graded with layer thickness l=1 m, (iii) graded with l=0.5 m, and (iv) graded with l=0.25 m substrate, with E0=1 Pa and y0=1 m, normally loaded with line force of 1 N/m; (b) in-plane σxx stress field for (i) homogeneous (ii) graded with layer thickness l=1 m, (iii) graded with l=0.5 m, and (iv) graded with l=0.25 m substrate, with E0=1 Pa and y0=1 m, normally loaded with line force of 1 N/m; (c) in-plane σxy stress field for (i) homogeneous (ii) graded with layer thickness l=1 m, (iii) graded with l=0.5 m, and (iv) graded with l=0.25 m substrate, with E0=1 P and y0=1 m, normally loaded with line force of 1 N/m; (d) in-plane σyy stress field for (i) homogeneous (ii) graded with layer thickness l=1 m, (iii) graded with l=0.5 m, and (iv) graded with l=0.25 m substrate, with E0=1 Pa and y0=1 m, normally loaded with line force of 1 N/m

Figure 8

(a) Equivalent stress field for (i) homogeneous (ii) graded with layer thickness l=1 m, (iii) graded with l=0.5 m, and (iv) graded with l=0.25 m substrate, with E0=1 Pa and y0=1 m, tangentially loaded with line force of 1 N/m; (b) in-plane σxx stress field for (i) homogeneous (ii) graded with layer thickness l=1 m, (iii) graded with l=0.5 m, and (iv) graded with l=0.25 m substrate, with E0=1 Pa and y0=1 m, tangentially loaded with line force of 1 N/m; (c) in-plane σxy stress field for (i) homogeneous (ii) graded with layer thickness l=1 m, (iii) graded with l=0.5 m, and (iv) graded with l=0.25 m substrate, with E0=1 Pa and y0=1 m, tangentially loaded with line force of 1 N/m; and (d) in-plane σyy stress field for (i) homogeneous (ii) graded with layer thickness l=1 m, (iii) graded with l=0.5 m, and (iv) graded with l=0.25 m substrate, with E0=1 Pa and y0=1 m, tangentially loaded with line force of 1 N/m

Figure 9

Side view of the specimens during loading. The self-tension mechanism with P=F/b, Q=7F/b, and b=30 cm.

Figure 10

Overall view of the specimens, loading and layers

Figure 11

Failure of the homogeneous specimen

Figure 12

Failure of the graded specimen

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