Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 01 Dec 2010

Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

Page Range: 286 – 307
DOI: 10.2346/1.3519536
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Abstract

Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

Keywords: Fiber/matrix bond; elastic properties; mathematical model
Copyright: The Tire Society
FIG. 1
FIG. 1

Fiber reinforced composite with three layers.

FIG. 2
FIG. 2

Linearly graded transition zone. A typical profile of one of the engineering constants graphed in relation to the radius of the fiber, transition zone and matrix.

FIG. 3
FIG. 3

Radial displacement under radial loading.

FIG. 4
FIG. 4

Radial strain under radial loading.

FIG. 5
FIG. 5

Angular strain under radial loading.

FIG. 6
FIG. 6

Radial stress under radial loading.

FIG. 7
FIG. 7

Radial stress under axial loading.

FIG. 8
FIG. 8

Radial strain under axial loading.

FIG. 9
FIG. 9

Angular strain under axial loading.

FIG. 10
FIG. 10

Radial displacement under axial loading.

FIG. 11
FIG. 11

Radial displacement under r-θ shear loading.

FIG. 12
FIG. 12

Radial strain under r-θ shear loading.

FIG. 13
FIG. 13

Axial displacement under r-z shear loading.

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