Penetration Fracture of Ice Plate: 2D Analysis and Size Effect

Abstract

The problem of static penetration of an object through a sea ice plate is studied as a two‐dimensional fracture problem using linear elastic fracture mechanics. The ice sheet floating on water is modeled as a thin elastic plate resting on Winkler's elastic foundation. The equilibrium equations are established by minimizing the potential energy approximated by finite differences in terms of nodal deflections. The growth of radial cracks is analyzed using the plate bending theory. The fracture process zone is assumed to be a point in the plane of plate. The maximum load is found to occur when circumferential cracks begin to form, which is governed by a strength criterion. As a refinement and extension of a previous idea, a theory of initial crack spacing is proposed to estimate the number of radial cracks formed during penetration. This theory can also explain the change of the failure mechanism, from failure by formation of circumferential cracks to failure by a conic crack. Particular attention is paid to the size effect. In addition to the size effect described by a simplified one‐dimensional solution in a previous paper, the influence of the difference in the number of radial cracks on the size effect is discovered and analyzed.