Acta Mechanica 61, 1--14 (1986) ACTA MECHANICA | by Springer-Verlag 1986 The Elastic-Plastic Shrink Fit with Supcrcritical Interference ~ By U. Gamer, Wien, Austria With 8 Figures (Received October 3, 1985) Summary An interference, for which Tresca's yield criterion predicts vanishing of the circum- ferential stress at the bore of the hub of an elastic-plastic shrink fit, is called critical. It is shown that Tresca's criterion does not admit a solution of the supercritieal shrink fit problem for perfectly plastic materials. For hardening materials, stress, displacement and plastic strain in the supercritical shrink fit are derived. The occurrence of a supercritical interference as well as the range of validity of the results presented are discussed. 1. Introduction The distribution of stress and displacement in an elastic-perfectly plastic shrink fit based on Tresca's yield criterion is well known [1]. However, the elastic-plastic solution derived there is not universally applicable. There exists, depending on the ratio of the radii of the hub, Q : = a/b, a well defined inter- ference, for which the validity of the above solution ceases. (Neglecting thermal stresses, the assemblage process may be simulated simply by increasing inter- ference.) For Q > 1/e and 12 ~ 1/Q ~, where I : ~ Ei/(aoa) with the interference i and the yield limit a0, the elastic zone of the hub vanishes. Yet increasing inter- ference does not lead to unrestricted plastic flow in the hub but has no influence on the interface pressure. More interesting is the case Q < 1/e. For the critical interference Ic given by Q2/~ _ log Ir A- 1 = 0, (1.1) the circumferential stress at the inner edge r ~ a of the hub vanishes. The corre- sponding image point in the stress plane reaches the corner (--(r0, 0) of the Tresca * Dedicated r Professor Dr.-Eng. Theodor Lehmann on the occasion of the 65th anni- versary of his birthday. 1 Acta Mech. 61/1--4