SIZE EFFECT IN PENETRATION OF SEA-ICE PLATE WITH PART-THROUGH CRACKS - I - THEORY

The paper analyzes the vertical penetration of a small object through a floating sea ice plate. The analysis takes into account the fact tha t the bending cracks reach only through part of the ice plate thicknes s and have a variable depth profile. The cracks are modeled according to the Rice-Levy nonlinear softening line spring model. The plate-crac k interaction is characterized in terms of the compliance functions fo r the bending moments and normal forces in the crack plane, which are computed by an energy-based variational finite-difference method. The radial crack is divided into vertical strips, and a numerical algorith m with step-by-step loading is developed to calculate the vertical gro wth of the crack in each strip for a prescribed radial crack length in crement. The initiation of crack strips from the surface of the plate is decided on the basis of a yield strength criterion with a fracture based flow rule. Systems of up to 300 nonlinear equations are solved b y the Levenberg-Marquardt optimization algorithm. The maximum load is reached when the circumferential cracks begin to form. Numerical calcu lations, comparison of the results with test data, and a study of scal ing laws are relegated to the companion paper, which follows in this i ssue. Numerical calculations show a typical quasi brittle size effect such that the plot of log sigma(N) versus log h (where sigma(N) = nomi nal stress at maximum load and h = plate thickness) is a descending cu rve whose slope is negligible only for h < 0.2 m and then gets gradual ly steeper, asymptotically approaching -1/2. The calculated size effec t agrees with the existing test data, and contradicts previous plastic ity solutions.