Endochronic Analysis for Viscoplastic Collapse of a Thin-Walled Tube under Combined Bending and External Pressure

Abstract

In this study, we employ the ordinary differential constitutive equations of endochronic theory to investigate the collapse of a thin-walled tube subjected to bending. A virtual work approach is used to formulate the problem, which results in a set of nonlinear algebraic equations that are numerically solved. Experimental data on a 6061-T6 aluminum alloy under cyclic bending and 304 stainless steel under combined bending and external pressure found in previous literature are compared with the theoretical simulation. The experimental and theoretical results are in good agreement. Finally, by using the rate-sensitivity function of the intrinsic time measure in the theory, the theoretical analysis is extended to investigate the viscoplastic collapse of a thin-walled tube subjected to bending. Owing to the hardening of the metal tube for a faster curvature rate, the magnitude of the limit moment, the ovalization of the tube cross section and the value of curvature at collapse are theoretically demonstrated to have increased.