PART-THROUGH BENDING CRACKS IN SEA ICE PLATES: MATHEMATICAL MODELING

The paper presents a new mathematical model for propagation of part-through bending cracks in floating sea ice plate, which is a problem of considerable practical importance, for example, the load carrying capacity or penetration through the ice plate. After reviewing the previous work on propagation of through-cracks due to transverse loads, the three-dimensional problem of part-through cracks is simplified as two-dimensional using the well known approximation by line springs. These nonlinear springs describe the relation of rotation and additional in-plane expansion due to part-through crack to the bending moment and normal force transmitted through the crack. The problem of several radial cracks emanating from a small loaded area is analyzed. The bending and in-plane elastic responses of the floating plate are described by compliance functions. It is shown that the rotations across the crack cause the compression resultant in the plates and the neutral axis of the stress to shift above the mid-thickness of plates. This represents a dome effect which carries a significant part of the load. The profile of the crack depth propagating upward and the shape of the dome are calculated. A study of the failure loads and the size effect is left for a subsequent paper