Analysis of Plasticity, Fracture and Friction in Steady State Plate Cutting

A closed form solution to the problem of steady state wedge cutting through a ductile metal plate is presented. The considered problem is an idealization of a ship bottom raking process, i.e. a continuous cutting damage of a ship bottom by a hard knife-like rock in a grounding event. A new kinematic model is proposed for the strain and displacement fields and it is demonstrated that the analysis is greatly simplified if the strain field is assumed to be dominated by plastic shear strains and moving hinge lines. Also, it is shown that the present shear model offers the basis for a convenient extension of the presented plate model to include more structural members as for example the stiffeners attached to a ship bottom plating. The fracture process is discussed and the model is formulated partly on the basis of the material fracture toughness. The effect of friction and the reaction force perpendicular to the direction of motion is derived theoretically in a new consistent manner. The perpendicular reaction force is of paramount importance for predicting the structural damage of a ship hull because it governs the vertical ship motion and rock penetration which is strongly coupled with the horizontal resistance and thus with the damaged length. The derived expressions are discussed and compared to previously published experimental results and formulas.