Radial cracking with closure

Progressive radial cracking of a clamped plate subjected to crack-face closure is studied. The material behavior is assumed to be elastic-brittle. The cracks are assumed to be relatively long in the sense that the three-dimensional contact problem can be described via a statically equivalent two-dimensional idealization. The number of cracks is supposed large enough to permit a quasi-continuum approach rather than one involving the discussion of discrete sectors. The formulation incorporates the action of both bending and stretching as well as closure effects of the radial crack face contact. Fracture mechanics is used to explore the load-carrying capacity and the importance of the role of the crack-surface-interaction. For a given crack radius, the closure contact width is assumed to be constant. Under this condition, a closed-form solution is obtained for the case of a finite clamped plate subjected to a concentrated force. Crack growth stability considerations predict that the system of radial cracks will initiate and grow unstably over a significant portion of the plate radius. The closure stress distribution is determined exactly in the case of narrow contact widths and approximately otherwise.