Slice-push, formation of grooves and the scale effect in cutting

Three separate aspects of cutting are investigated which complement other papers on the mechanics of separation processes presented at this interdisciplinary Theo Murphy meeting. They apply in all types of cutting whether blades are sharp or blunt, and whether the material being cut is 'hard, stiff and strong' or 'soft, compliant and weak'. The first topic discusses why it is easier to cut when there is motion along (parallel to) the blade as well motion across (perpendicular to) the cutting edge, and the analysis is applied to optimization of blade geometries to produce minimum cutting forces and hence minimum damage to cut surfaces. The second topic concerns cutting with more than one edge with particular application to the formation of grooves in surfaces by hard pointed tools. The mechanics are investigated and applied to the topic of abrasive wear by hard particles. Traditional analyses say that abrasive wear resistance increases monotonically with the hardness of the workpiece, but we show that the fracture toughness of the surface material is also important, and that behaviour is determined by the toughness-to-hardness ratio rather than hardness alone. Scaling forms the third subject. As cutting is a branch of elasto-plastic fracture mechanics, cube-square energy scaling applies in which the important length scale is (ER/k (2)), where E is Young's modulus, R is the fracture toughness and k is the shear yield strength. Whether, in cutting, material is removed as ductile ribbons, as semi-ductile discontinuous chips, or by brittle 'knocking lumps out' is shown to depend on the depth of cut relative to this characteristic length parameter. Scaling in biology is called allometry and its relationship with engineering scaling is discussed. Some speculative predictions are made in relation to the action of teeth on food.