ELASTO-PLASTIC ANALYSIS OF PIPES WITH STRAIN HARDENING

Abstract

A small-strain elasto-plastic analysis of strain-hardening circular thin-walled pipes in the non-buckled configuration subjected to simultaneous bending moment, internal pressure and axial loads is carried out. Based on the Hill yield criterion and the deformation theory of plasticity, an associated rule for a stable plastic material in the Drucker sense is derived. The pipes are of either an isotropic or a specially-orthotropic homogeneous material. A bi-linear form of material behavior is assumed taking into account various values of strain-hardening. The analysis considers the circumferential effects of pressure either singly (as in an open tube) or simultaneously with the longitudinal effects (as in a closed tube). The computations proceed with a numerical process utilizing the Newton-Raphson method for the plastic axial stresses and Simpson's rule for the moment and force integrals. Results given for an incompressible material cover moment-pressure interaction in the presence of an axial force; spread of plastic deformation through the pipe cross section; moment-curvature relations in combination with an axial force; degree of shift of the neutral axis from the geometric centerline position during loading; and axial stress variation across the pipe section. The results for a compressible material are also presented and compared ~ith those for an incompressible one. Finally, the results for the compressible material are verified by comparing with the work of past investigators and with the results obtained using a finite element software PAFEC Level 6.1.