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A computational procedure for the local stress field of multiple fibers in a unidirectional composite is formulated based on the eigenfunction expansion of the displacement field and a collocation technique. This paper deals with the longitudinal shear deformation of a unidirectional composite consisting of clustered multiple fibers embedded in the matrix. Based on the proposed procedure, the influence of the fiber arrangement and the fiber volume fraction on the local stress field is analyzed. In particular, the correlation between the maximum interface shear stress for each fiber and the distance to the neighboring fiber is examined in detail for both regular and irregular fiber arrangements. For regular arrangements, high interface shear stresses are found for fibers located at the periphery of the cluster, especially for the square arrangement of fibers aligned with the shearing direction. For random fiber distributions, the interface stresses are found to be high in the interior of the cluster when the neighboring fibers are closely aligned parallel to the shearing direction. The correlation between the neighboring-fiber distance and the magnitude of the maximum interface shear stress for random fiber distributions is discussed in comparison with the results for regular fiber arrangements.

Micromechanical Stress Field for Clustered Multiple Fibers in Unidirectional Composite under Longitudinal Shear