On the ratcheting response of circular steel pipes subject to cyclic inelastic bending: A closed-form analytical solution

The current paper deals with the cyclic plastic response and strain ratcheting of circular steel tubes under repeated inelastic pure bending. A closed-form solution is proposed for the problem. The cyclic softening/hardening behaviour of the material is modelled using a combined bilinear kinematic/nonlinear isotropic hardening rule. The relative hardening modulus in each half-cycle is considered as an extra state variable to account for the non-fading memory characteristics of the material. The cycle by cycle growth (creep) in the ovalisation of the cross-section is modelled using a modified version of the Bailey-Norton creep law. The solution considers the material nonlinearity, the cyclic plasticity effects and the geometrical nonlinearity due to the ovalisation of the cross-section. The model predictions are examined against a number of available test data on the inelastic monotonic and cyclic bending of tubes and reasonable agreements are observed.