抄録
The dispersion of fibers in the transverse direction of a unidirectional fiber-reinforced composite material has very strong influence on the local stress field occurred in the material and hence may be affect the transverse strength of the material. The distribution of areas of Dirichlet polygons obtained by the Dirichlet tessellations constructed upon such dispersion of fibers may be closely related with that of the nearest neighbour distances between fibers in the material. In the present research, therefore, the probability density function of the nearest neighbour distances is derived in order to characterize the inhomogeneous dispersion of fibers. By assuming that the area of the Dirichlet polygon is equal to that of a circle whose radius is half of the nearest neighbour distance and the outward region to the polygon is a homogeneous one whose elastic modulus is equal to the overall modulus of the composite material, the material can be modeled as a double inclusion. By analyzing the mean stresses occurred in the double inclusion model, the transverse strength of the material can be examined. Its value increases with increase in the degree of inhomogeneity of the dispersion of fibers. This is consistent with experimental results obtained by Pyrz.
