き裂問題へのMori-Tanakaの定理の拡張

第4報, 母材き裂を含む1方向繊維強化複合材料の巨視的弾性定数

抄録

For a unidirectional fiber-reinforced composite material containing matrix cracks, the differential equation for the macroscopic total strain of the material is derived with respect to the crack density by adding only a small amount of cracks into the matrix and by adopting the incremental form of the Mori-Tanaka theorem to the resultant model of the material. By solving the differential equation, the macroscopic elastic moduli are formulated as a function of crack density. By comparing the resulting macroscopic elastic moduli with those obtained by Taya's method, the range of crack density in which Taya's method is applicable is clarified. This range becomes wider when the volume fraction and the aspect ratio of fibers increase.