ON THE CUTTING OF A PLATE BY A WEDGE

The paper describes a study of the cutting of a metal plate by a rigid wedge which is pushed into it in a direction almost parallel to the plate. In the main series of tests, wedges were pushed slowly into mild-steel plates having thickness in the range 0.7-2 mm; and various angular parameters-e.g. the included angle of the wedge-were varied. On the hypothesis that the yield stress is the only relevant property of the material, the theory of dimensional analysis gives only two dimensionless groups for a given set of angular parameters; and when these are plotted against each other the curves corresponding to plates of different thickness come together. From this emerges a simple empirical formula for the energy absorbed (W) in terms of the yield stress (σy), the length of cut (l) and thickness (t): W = C1.3σyl1.3t1.7, 5 < l t < 150. Here, C1.3 is a purely numerical constant whose value depends somewhat on the angular parameters. We argue that the exponent of t in this formula is not related to the mechanics of cutting in the vicinity of the wedge tip, but to the mechanics of rolling and folding of "the flaps" which are formed in the wake of the cut, and which affects the exponent of t via the exponent of l. We show that the results of other workers obtained by use of drop-hammer tests may be correlated in the same way, though with somewhat different values of C1.3; and we discuss qualitatively the effects of inertia, variation of friction with sliding velocity and material strain-rate effects in order to resolve these differences. By means of a subsidiary study of the cutting process in plates made of four other materials, we show that friction has a significant effect upon the value of C1.3. © 1990.