Design of thick-walled cylindrical vessels under internal pressure based on elasto-plastic approach

By considering the Bauschinger effect and the yield criterion of Tresca, an exact elasto-plastic analytical solution for a thick-walled cylindrical vessel made of elastic linear-hardening material is derived. Having the working pressure and geometric dimensions of the vessel, the distribution of the hoop and equivalent stresses are optimized in the way that the distribution of stresses becomes smooth in the vessel wall. Based on two optimizing methods of the hoop and equivalent stresses, the best autofrettage pressure is determined. It is shown that this pressure is more than the working pressure and depends on the three following variables: Bauschinger effect, working pressure and geometric dimensions. In the next stage, the main task is to determine the wall thickness having the working pressure. To do this, two different design criteria namely; (i) optimizing the hoop stress distribution and (ii) assuming a suitable percent of yielding in the wall thickness are used. In the last step, for different types of structural materials under different working pressures, a number of different plots are given for the ratio of outer to inner radii and the best autofrettage pressure. It is shown that the design of vessels based on the elasto-plastic methods is much more economic than elastic methods. Also, it is seen that for a non-hardening material, the design of vessel is only done for the working pressure less than unit value.