Penetration Fracture of Sea Ice Plate: Simplified Analysis and Size Effect

Vertical penetration of an object through a floating elastic‐brittle plate from the bottom up or the top down is studied. Based on field observations, it is assumed that many symmetric cracks grow radially from a small loaded area, and the maximum load is achieved at the initiation of circumferential cracks. Nevel's approximation, in which the plate wedges between the radial cracks are analyzed as narrow floating beams of linearly varying width, is adopted. This makes an analytical solution possible. The rate of energy release due to the radial crack growth is calculated according to linear elastic fracture mechanics and the theory of thin plates. This yields the dependence of the radial crack length on the load, which is considered to be uniformly distributed along a small circle. It is confirmed that there is a size effect such that the nominal stress (load divided by ice thickness squared) that causes similar cracks to grow is proportional to $(\mathrm{ice}\mathrm{thickness}{)}^{-3/8}$ or, equivalently, to $(\mathrm{flexural}\mathrm{wavelengths}{)}^{-1/2}$. However, the maximum load does not follow this size effect, because it is attained at the initiation of circumferential cracks, which is governed by a strength type of criterion and causes no size effect. When the size of the loaded area is fixed, there is a size effect due to an increase of load concentration, that is, a decrease of the ratio of the loaded circle diameter to the thickness. This size effect is intensified by the size dependence of the rupture modulus for bending, but in the normal size range, such a size effect is not significant. The relation between the length of the radial cracks and the applied load calculated by fracture mechanics is also useful for other methods of predicting the penetration load.