A numerical study on the thermal expansion coefficients of fiber

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• The composite is macroscopically homogeneous and orthotropic, linearly
elastic, initially stress free, and free of voids. There is complete bonding at
the interface of the constituents and there is no transitional region between
them. The displacements are continuous across the fiber matrix interphase
(there is no interfacial slip).
• The fibers are homogeneous, linearly elastic, isotropic or orthotropic,
regularly spaced, perfectly aligned, circular in cross section, and infinitely
long in the longitudinal direction.
• The matrix is homogeneous, linearly elastic, and isotropic.
• The temperature is uniform and remains uniform during the temperature
increase. Constituent material properties do not vary with temperature.
3.4.1 Some of the Existing Theories
Consider a random two-phase composite. Assuming that one of the phases,
subscript f, is dispersed in a polymer phase, subscript m, and α m > α f , where α is the
thermal expansion coefficient of the phases. When such a composite is heated, even
under conditions of no external loading, the matrix will wish to expand more than the
fillers and if the interface is capable of transmitting the stresses which are set up as a
result of differences between the thermal expansion coefficients and elastic constants
of the constituents so that the expansion of the matrix will be reduced. These thermal
stresses cause stress concentrations which may initiate yielding or debonding.
Therefore, in design analysis, it is important to understand how these stresses arise
and how to control the thermal expansion coefficients of the composite. In the
theoretical treatments to be described, except for the equations of Sideridis (1994), it
is assumed that the adhesion at the interface is adequate to withstand this task.
3.4.1.1 Law of Mixtures
If each phase is assumed homogeneous and isotropic and linearly elastic over a
small range of volumetric strains, in the absence of the phase interaction, one may