A closed-form analytical solution for the ratcheting response of steel tubes with wall-thinning under inelastic symmetric constant amplitude cyclic bending

Abstract

Metallic tubes experiences a progressive accumulation of ovalisation, or ratchet, under cyclic inelastic bending. During their life time, the tubes may also suffer from different types of mechanically and/or chemically originated defects. The current paper discusses a closed-form solution for the response analysis of defective circular steel tubes under monotonic and cyclic inelastic bending. The defect in the tube is idealised as a uniform patch type wall thinning.The material model considers the cyclic hardening/softening features based on a combined non-linear hardening law. To account for the non-fading memory characteristics of the steel material, the hardening modulus in each half-cycle is introduced as a state variable. A modified version of the Bailey–Norton law is used for the cyclic growth (cyclic creep) in the ovalisation of the cross-section. In overall, the solution considers the geometrical non-linearity due to the ovalisation as well as the hysteresis effects.The study also includes monotonic and cyclic inelastic bending experiments on small-scale, thick-walled, high strength, low alloy carbon steel defective tubes. The analytical solutions for the inelastic monotonic and cyclic bending of the tubes are validated against these experimental data and reasonable agreements are noticed and reported.