ENLARGEMENT OF A HOLE IN A RIGID-WORKHARDENING DISK OF NON-UNIFORM INITIAL THICKNESS

A complete solution is obtained for the enlargement of a circular hole in a disk whose initial contour is given by h0 = αr0n, 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. © 1969.