Size effect on elastic stress concentrations in unidirectional fiber reinforced soft composites

Abstract

We revisit the classic problem of determining stress concentrations on neighboring fibers to multiple, transversely-aligned fiber breaks in a planar, unidirectional fiber–matrix composite. Fibers are assumed to be perfectly bonded to the elastic matrix. Finite size effects on stress concentration are studied by varying the overall length of the composite relative to the characteristic load transfer length between broken and intact fibers. As an alternative to the discrete fiber and matrix framework in the classic analysis of Hedgepeth, and its extension by Hikami and Chou, the fiber stress distribution in the composite is obtained through continuum modeling of the composite as a highly anisotropic elastic plate, whereby the stresses and stress concentration factors at fiber locations in the discrete model are extracted in a closed form. For composites of finite length, the stress concentration factors determined using the continuum model compare favorably with numerical solution of the discrete shear-lag model. In the limit of a plate with infinitely long fibers, our stress concentration factors also agree well with the exact results of Hikami and Chou. For composites having a length less than the characteristic elastic load transfer length, and loaded under displacement boundary conditions, we show that local stress concentrations vanish irrespective of the size of the crack or the number of fiber breaks. This behavior becomes important when modeling and interpreting laboratory experiments on the mechanical behavior of recent soft composite specimens consisting of stiff fibers in an extremely compliant elastic matrix.