Dynamical Problems Of Ice Cover Fracture

ABSTRACT :

The problem of a crack in bending ice cover has been considered. The crack is assume to be straight and semi-infinite, propagating under the action of a moving load. The ice cover is supposed to be an elastic plate contacting a heavy perfect liquid. Steady-state and resonance cases have been examined.



INTRODUCTION

The problem of dynamical crack propagation in ice cover (which is assumed to be a homogeneous elastic plate) differs from the classical problems of fracture mechanics in certain features. First, it is non-locality, i.e., the action of forces bending the ice cover is transferred to its distant areas not only by the bending waves moving along the plate, but also by the waves in water. This fact considerably influences the mathematical formulation of the problem: Differential equations of dynamical bending of a plate contacting with water are transformed to a convolution-type equation (which makes its solution more difficult). That is why in this paper we shall first consider the fundamental problem of a normal moving force. Incidentally, solving this problem helps determine the feasibility of simplifications in the descriptions of plate-water interaction. Secondly, the problem under consideration is characterized by critical velocity (i.e., velocity of movement of normal force and crack propagation), which is very small as compared to the corresponding critical velocity of a crack in an elastic medium (usually it is Rayleigh''s waves velocity). The moving load induces waves carrying energy away "to infinity" if the velocity is greater than the critical one. In this case (in contrast to under-critical range) only a part of the energy is spent on fracture (flowing down a crack tip); another part is radiated by the waves mentioned above. This situation resembles the one of crack propagation in structured mediums (Slepian, 1985).