Periodic Crack Systems in a Transversally Isotropic Solid

Resumo

Three-dimensional problems are studied on periodic chains of elliptic cracks oriented along one of the coordinate axes lying in a plane that is perpendicular to the isotropy planes of a transversely isotropic elastic unbounded body. Using the integral Fourier transform, the problems are reduced to integro-differential equations, whose kernels are presented in the form of series and do not contain quadratures. To solve the problem, the regular asymptotic method by V. M. Alexandrov was used with the introduction of the main dimensionless parameter characterizing the relative distance of neighboring cracks from each other. The limits of applicability of the method depend on the anisotropy parameters and the location of the cracks; the method is effective for cracks relatively distant from each other. Asymptotics are obtained for the stress intensity factor related to the case of a single crack. Parameters of asymptotic solutions are calculated for different transversely isotropic materials.