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Part-through bending cracks in sea ice plates: Mathematical modeling

AMD-Vol. 207, Ice Mechanics ASME 1995 PART-THROUGH BENDING CRACKS IN SEA ICE PLATES: MATHEMATICAL MODELING Zdenek P. BaZant, J.J.H. Kim and Yuan N. U Department of Civil Engineering Northwestern University Evanston, Illinois 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. INTRODUCTION Sea ice plates under vertical loading from above or from below often fail by propagation of radial cracks from the loaded area (Fig. 1). The maximum or failure load is reached when circumferential cracks start to form from the radial cracks. This type of failure is important for many commercial as well as defense applications. such as a submarine sail penetrating through the ice or an airplane landing on the ice. Due to these practical needs, this problem has been studied extensively for a long time. However, due to the relatively recent initiation of fracture mechanics of ice, the problem has been solved using a strength criterion or plastic limit analysis. Obviously, since ice is a quasibrittle material, the plastic limit analysis is unrealistic and more importantly, it does not capture the size effect on the nominal strength. In early studies of the penetration problem. the load capacity of a floating ice plate was determined by the tensile strength criterion (e.g. Bernstein. 1929). Nevel (1958) analyzed the strength of the ice plate assuming that the number of radial bending cracks is very large and that the ice plate is thus split into wedges of very small angle, which can be treated as beams of variable cross section. An excellent review of the early studies of the load capacity of the floating ice plate was given by Kerr (1975).