Impact on an Ice Floe With a Surface Crack

A floating two-dimensional ice plate with a crack on its lower surface is considered. Deflection of the plate is caused by an external impulsive load. The ice floe dynamics is described by thin compound elastic plate equation. Two parts of the plate are of constant thickness and are connected by a torsional spring which models the crack effect on the elastic deflection of the plate. The stiffness of the equivalent torsional spring is given as a function of the plate parameters and the crack length. Both the motions of the ice plate and the stresses near the crack tip are determined without account for gravity and surface tension effects. In the symmetric problem, the crack is always perpendicular to the plate surface. The growth of the crack is governed by the condition of the crack equilibrium at each time instant. The conditions of the impact, the magnitude of the impact force and its duration, which lead to the crack growth are studied within the water impact theory.