Size-dependence of overall in-plane plasticity for fiber composites

For composite materials, a size-dependent effective behavior may manifest when the particle size has the same order as the intrinsic length scale (grain size for a polycrystalline material for example) of the matrix material. This size-dependent effective nonlinear property of a fiber composite is investigated by an analytical micromechanical method. The non-local effect of the matrix with a coarse-grain microstructure is considered by idealizing it as a micropolar material. Mori-Tanaka's method and generalized self-consistent method are extended to a micropolar fiber composite, the effective shear and in-plane bulk moduli are obtained analytically. The results show that the effective in-plane shear modulus is large for the composites with small diameter fibers, and the effective in-plane bulk modulus will not depend on the fiber size. We further extend the secant moduli method based on second-order stress moment to micropolar composites. Size-dependent yield functions and effective stress and strain relations of a micropolar fiber composite are derived in an analytical way. The size dependence is more pronounced for the composite reinforced by hard fibers and for shear loading. The proposed method shares the same structure as in the classical micromechanics, and when the fiber size is very large compared to the intrinsic length of the matrix, the classical micromechanics method can be recovered, as expected.