The enlargement of a hole in a rigid-workhardening disk of non-uniform initial thickness

Abstract

A complete solution is obtained for the enlargement of a circular hole in a disk whose initial contour is given by h 0 = α r 0 n , where α and n are constants, using an isotropic strain-hardening law with Mises' yield condition and its associated flow rule. The results are then compared with those obtained using: (i) Tresca's yield condition and its associated flow rule; (ii) Mises' yield condition for the neutral plastic region, and Tresca's yield condition and the flow rule associated with the Mises yield criterion for the active plastic region; and (iii) Tresca's yield condition for all plastic regions and the Saint Venant—Lévy—Mises flow rule. An interesting feature of the results is that, when material hardening exists and when the Saint Venant—Lévy—Mises flow rule is used, then, as the hole expands, there first occurs a thickening of the disk at the vicinity of the hole's edge, which thickening may then be followed by a thinning. It appears that this phenomenon has not been noticed before.