| Materials used in various engineering applications are often anisotropic. Cracks may develop in them, and they, generally, reduce stiffness. Degradation of stiffness is obvious importance in continuum mechanics. The key problem is contribution of one crack to the overall stiffness reduction. Analysis of effective properties can be conveniently done in terms of the crack compliance tensor (or COD tensor of a crack) B, which depends on crack size and shape, on the elastic properties of the matrix and, in case of anisotropic matrix, on the orientation of the crack with respect to the matrix anisotropy axes. In case of a body of finite size, it also depends on the body's geometry. B tensor for a two-dimensional (2-D) orthotropic solid, expressed in coordinate system x 1, x2 of the matrix, is constant , independent of crack orientation. The center point of this study is to verify the hypothesis that B tensor is approximately constant in three-dimensional (3-D) transversely isotropic solid.; A finite element models are established to simulate the two and three dimensional "penny-shaped" crack analyses. Method development is first performed on the 2-D model, and data are compared to the analytically known solutions. Three dimensional analysis of the B tensor components is performed in several, with respect to the extent of anisotropy, transversely isotropic solids for 0°-90° crack orientations. |
