An exact elasto-plastic solution for an open-ended thick-walled cylinder of a strain-hardening material

Abstract

In this paper, a closed-form analytical solution for the elasto-plastic stress, strain, and displacement components of an internally pressurized open-ended thick-walled cylinder made of a strain-hardening material is obtained by using the deformation theory of Hencky and the yield criterion of Von Mises and choosing stress components as basic unknowns. On the basis of the elastic power-law plastic material model and a modified Nadai's auxiliary-variable method, this solution provides a new analytical pattern for the elasto-plastic analysis and the strength design of a strain-hardening-material open-ended thick-walled cylinder. It is shown that the solution is a general one with on the one hand Nadai's known solution for stress components and on the other P.C.T. Chen's solution for strain components of an open-ended thick-walled cylinder made of elastic-perfectly-plastic material as its two specific cases. The calculation formula for the plastic-limit pressure of the cylinder given in the paper, which is able to account for the strain-hardening effect of material, furnishes a new and more reasonable theoretical basis for the strength design by plastic-limit analysis and the autofrettage design of an open-ended thick-walled cylinder made of strain-hardening material.