Effective in plane moduli of composites with a micropolar matrix and coated fibers

Stress and couple stress distributions are determined analytically for a coated fiber in an infinite micropolar matrix, loaded remotely by classical symmetric stresses. The determined stresses are then compared with those predicted by Cauchy theory, a size dependence is predicted in the framework of micropolar theory, and when the fiber's diameter is much larger than the characteristic length of the matrix, the classical prediction can be recovered. The exact average stress in a fiber for a fiber-matrix system (without interphase) is also compared with that approximately derived by the average equivalent inclusion method (AEIM), based on the micropolar Eshelby tensor given by Cheng and He [Int. J. Eng. Sci. 35 (7) (1997) 659], the results show that the approximate AEIM method can give an accurate prediction for the size dependence of the average stress in a fiber. A micro-macro transition method is also proposed to determine effective in plane moduli of a heterogeneous micropolar material, the effective shear and in plane bulk moduli of a micropolar composite with coated fibers are derived analytically by extending Mori-Tanaka's method to a micropolar composite, and the effective shear and in plane bulk moduli for a two-phase fiber composite (without interphase) are also obtained as a special case. The results show that the effective in plane bulk modulus is identical to that obtained by Cauchy theory, however the effective shear modulus depends on fiber's diameter, it increases with decreasing fiber's diameter at the same fiber volume fraction, and the classical prediction is recovered when the fiber's diameter becomes large compared to the matrix characteristic length.