き裂問題へのMori-Tanakaの定理の拡張 : 第3報,2方向に配向したスリットき裂を含む材料の巨視的弾性係数

概要

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A partial differential equation is derived for the macroscopic total strain of a material containing mutual perpendicular slit-like cracks with respect to the crack densities of the cracks by using the incremental form of the Mori-Tanaka theorem. By solving the partial differential equation, the macroscopic total strain, the average interaction stress and hence the macroscopic elastic moduli are formulated as a function of the crack densities of the cracks. On the contrary to the results obtained by the ordinary Mori-Tanaka theorem, the resulting macroscopic elastic moduli asymptotically tend to zero as the crack densities of the cracks increse. The present results are in good agreement with the analytical results by means of the differential scheme and the numerical results given by Huang et al. [Int. J. Solids Struct., 33 (1996), 1575-1586] especially at relatively low crack density when the magnitudes of the crack densities of the mutual perpendicular slit-like cracks are equal to each other.
社団法人日本機械学会の論文
2005-01-25