On the mechanics of stress analysis of fiber-reinforced composites
A general mathematical formulation is developed for the three-dimensional inclusion and inhomogeneity problems, which are practically important in many engineering applications such as fiber pullout of reinforced composites, load transfer behavior in the stiffened structural components, and material defects and impurities existing in engineering materials. First, the displacement field (Green's function) for an elastic solid subjected to various distributions of ring loading is derived in closed form using the Papkovich-Neuber displacement potentials and the Hankel transforms. The Green's functions are used to derive the displacement and stress fields due to a finite cylindrical inclusion of prescribed dilatational eigenstrain such as thermal expansion caused by an internal heat source. Unlike an elliptical inclusion, the interior stress field in the cylindrical inclusion is not uniform. Next, the three-dimensional inhomogeneity problem of a cylindrical fiber embedded in an infinite matrix of different material properties is considered to study load transfer of a finite fiber to an elastic medium. By using the equivalent inclusion method, the fiber is modeled as an inclusion with distributed eigenstrains of unknown strength, and the inhomogeneity problem can be treated as an equivalent inclusion problem. The eigenstrains are determined to simulate the disturbance due to the existing fiber. The equivalency of elastic field between inhomogeneity and inclusion problems leads to a set of integral equations. To solve the integral equations, the inclusion domain is discretized into a finite number of sub-inclusions with uniform eigenstrains, and the integral equations are reduced to a set of algebraic equations. The distributions of eigenstrains, interior stress field and axial force along the fiber are presented for various fiber lengths and the ratio of material properties of the fiber relative to the matrix.
- Research Organization:
- Northwestern Univ., Chicago, IL (United States)
- OSTI ID:
- 7020289
- Resource Relation:
- Other Information: Ph.D. Thesis
- Country of Publication:
- United States
- Language:
- English
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