Plastic depth and load-bearing capacity of autofrettaged cylinders

Autofrettage technology is usually adopted to even out and reduce stresses as well as improve the load-bearing capacity of a variety of cylindrical ultra-high mechanical apparatuses. The autofrettage of cylinders is theoretically investigated based on maximum shear stress theory or the Tresca criterion to establish the general law for autofrettage theory. The equation for the optimum plastic depth for a certain load and radius ratio is derived to ensure that the equivalent stress of the total stress does not exceed the yield limit and the absolute value of the equivalent stress of the residual stress at the internal surface likewise does not exceed the yield limit. Through this equation, a set of concise equations for total stress and residual stresses are obtained. The safe and optimum load-bearing conditions for cylinders are presented. Results show that, provided the pressure contained in a cylinder is equal to the autofrettage pressure, irrespective of k _j, the equivalent total stress, σ_e, equals the yield limit everywhere in the entire plastic zone, that is, σ_e is a constant. In the elastic zone, σ_e is always lower than the yield limit, but if k _j is outside the quasi-infinite area enclosed by the curves of the sense and possible plastic depth, then either compressive yield occurs or k _j is meaningless. The results based on the Mises criterion and Tresca criteria are compared.