CLOSED-FORM SOLUTION FOR WEDGE CUTTING FORCE THROUGH THIN METAL SHEETS

A simple kinematic model is developed which describes the main feature s of the process of the cutting of a plate by a rigid wedge. It is ass umed in this model that the plate material curls up into two inclined cylinders as the wedge advances into the plate, This results in membra ne stretching up to fracture of the material near the wedge tip, while the ''flaps'' in the wake of the cut undergo cylindrical bending. Sel f-consistent, single-term formulas for the indentation force and the e nergy absorption are arrived at by relating the ''far-field'' and ''ne ar-tip'' deformation events through a single geometric parameter, the instantaneous rolling radius. Further analysis of this solution reveal s a weak dependence on the wedge angle and a strong dependence on fric tion coefficient. The final equation for the approximate cutting force over a range of wedge semiangles 10-degrees less-than-or-equal-to the ta less-than-or-equal-to 30-degrees and friction coefficients 0.1 less -than-or-equal-to mu less-than-or-equal-to 0.4 is: F = 3.28sigma0(delt a(t)BAR)0.2l0.4t1.6mu0.4, which is identical in form and characteristi cs to the empirical results recently reported by Lu and Calladine [Int . J. Mech. Sci. 32, 295-313 (1990)]. This analysis is believed to reso lve a controversy recently developed in the literature over the interp retation of plate cutting experiments.