Micromechanical analysis of fiber-reinforced composites on account of influence of fiber coatings

The new asymptotic method for the analysis of inhomogeneous composite materials on account of the micromechanical influence of fiber coatings is proposed in the present paper. The problem of longitudinal shear of the fiber-reinforced composites with the square and hexagonal lattices of periodically distributed parallel cylindrical fibers is examined. The asymptotic homogenization method is applied and the relevant unit cell problem is solved with the aid of the method of perturbation of boundary shape. The asymptotic analytical solutions are found for the effective longitudinal shear moduli and for the local stresses occurring in the composites on the microlevel. Local shear stresses along the fiber-coating and the matrix-coating interfaces are calculated. The influence of properties of coatings on the maximum local shear stresses on the interfaces of constituents is analysed. The obtained results are suitable for any values of stiffness and volume fractions of constituents, including the limiting case of absolutely rigid fibers converging to contact.