Analytical solutions for local stress concentrations in long fiber reinforced unidirectional composites with a fiber breakage

In this study, two analytical solutions are obtained for the stress profiles in the fibers neighboring to a broken fiber in unidirectional composites. To this end, a hexagonal fiber array model containing a broken fiber is considered to derive differential equations based on a shear lag concept, in which matrix plasticity is simply taken into account by means of plastic secant modulus. It is thus shown that all affecting material parameters are consolidated into a characteristic value if a bilinear stress profile prevails in the broken fiber due to significant interfacial sliding. The governing equations are then analytically solved by assuming negligible stress concentrations in the second and third nearest-neighbor fibers, respectively. The resulting two analysical solutions are verified by solving more generally the governing equations using a finite difference method. The solutions are, moreover, compared with 3D finite element analysis published in recent literatures, leading to the soundness of the present solutions and the effectiveness of the characteristic value.