SELF-CONSISTENT ANALYSTS OF WAVES IN A MATRIX-INCLUSION COMPOSITE .3.A MATRIX CONTAINING CRACKS

THE SELF-CONSISTENT analysis developed in Parts I and II is applied to the study of waves in a body containing cracks, by taking the limits of the formulae already derived as the aspect ratio of the spheroids t ends to zero. A direct formulation for cracks, which leads to the same equations, is briefly summarized. The numbers of equations that requi re solution for the various cases (empty or fluid-filled cavities, ali gned or randomly oriented) are reduced substantially for cracks in com parison with spheroids, because there is only one density (that of the matrix) and effective moduli are only altered from their matrix value s by components of stress that interact with the cracks. Sample result s are presented. These confirm calculations reported in Parts I and II , when the aspect ratio of the cavities was taken to be small, and dem onstrate that the ''crack'' limit is approached much more slowly as th e aspect ratio tends to zero when the cavities are fluid-filled than w hen they are empty.