3
Mechanics
The mechanics of materials deal with stresses, strains, and deformations in
engineering structures subjected to mechanical and thermal loads. A common
assumption in the mechanics of conventional materials, such as steel and
aluminum, is that they are homogeneous and isotropic continua. For a homo
geneous material, properties do not depend on the location, and for an iso
tropic material, properties do not depend on the orientation. Unless severely
coldworked, grains in metallic materials are randomly oriented so that, on a
statistical basis, the assumption of isotropy can be justified. Fiberreinforced
composites, on the other hand, are microscopically inhomogeneous and non
isotropic (orthotropic). As a result, the mechanics of fiberreinforced composites
are far more complex than that of conventional materials.
The mechanics of fiberreinforced composite materials are studied at
two levels:
1. The micromechanics level, in which the interaction of the constituent
materials is examined on a microscopic scale. Equations describing the
elastic and thermal characteristics of a lamina are, in general, based on
micromechanics formulations. An understanding of the interaction
between various constituents is also useful in delineating the failure
modes in a fiberreinforced composite material.
2. The macromechanics level, in which the response of a fiberreinforced
composite material to mechanical and thermal loads is examined on a
macroscopic scale. The material is assumed to be homogeneous. Equa
tions of orthotropic elasticity are used to calculate stresses, strains, and
deflections.
In this chapter, we look into a few basic concepts as well as a number of simple
working equations used in the micro and macromechanics of fiberreinforced
composite materials. Detailed derivations of these equations are given in the
references cited in the text.
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2007 by Taylor & Francis Group, LLC.
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3.1
FIBER–MATRIX INTERACTIONS IN A UNIDIRECTIONAL
LAMINA
We consider the mechanics of materials approach [1] in describing fiber–matrix
interactions in a unidirectional lamina owing to tensile and compressive load
ings. The basic assumptions in this vastly simplified approach are as follows:
1. Fibers are uniformly distributed throughout the matrix.
2. Perfect bonding exists between the fibers and the matrix.
3. The matrix is free of voids.
4. The applied force is either parallel to or normal to the fiber direction.
5. The lamina is initially in a stressfree state (i.e., no residual stresses are
present in the fibers and the matrix).
6. Both fibers and matrix behave as linearly elastic materials.
A review of other approaches to the micromechanical behavior of a composite
lamina is given in Ref. [2].
3.1.1
L
ONGITUDINAL
T
ENSILE
L
OADING
In this case, the load on the composite lamina is a tensile force applied parallel
to the longitudinal direction of the fibers.
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 Fall '11
 RW
 Deformation, Strain, Stress, Tensile strength, Taylor & Francis Group

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