Extension of Mori-Tanaka Theorem to Crack Problem: 4th Report, Macroscopic Elastic Moduli of the.Unidirectional Fiber-reinforced Composite Material Containing Matrix Cracking

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.