Paper Number 6.2
Mathematical
Model of the Effective Properties
of a Fiber Reinforced Composite
with a Linearly Graded Transition Zone
Carey F. Childers,
175 Science and
Email: cchilders@clarion.edu
Voice: (330) 807-1514
Fax: (814) 393-2735
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 transversely
isotropic fiber and matrix separated by a thin 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.