Most composites are fabricated at elevated temperatures and cooled to room temperature. The difference in coefficients of thermal expansion of the fiber and matrix may cause buckling of the slender-shaped microfibers. This would greatly reduce the initial strength of the composites. The primary objective of this paper is to explain qualitatively the basic phenomenon of buckled microfibers in a composite and to present some numerical results in certain ranges of elastic parameters. Our analysis is based on assumptions that (a) the volume percentage of fibers is small so that the mutual interference of fibers is negligible and the matrix surrounding a fiber may be considered as infinitely large; (b) the diameter of the fiber is very small in comparison to its length so that the fiber may be treated as a linear fiber with infinite length; (c) the constituents are homogeneous and isotropic and the classical linear theory of elasticity may be applied; and, (d) in the process of cooling, the fiber is subjected to compression but not twisting moment by the surrounding matrix. The analysis leads to a relation between the pertinent elastic and thermal characteristics of the matrix and microfiber and the compressive force along the axis of the microfiber at the critical moment of incipient buckling. With the knowledge of that relation, it is now possible to know in advance whether or not buckling is to be expected and to avoid such manufacturing methods in which a threat of having buckled microfibers is present.

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