Closed form solutions for inelastic cyclic bending of steel tubulars using continuous stress-strain model

The current paper deals with the cyclic softening/hardening and strain ratcheting behavior of circular steel tubes under repeated inelastic pure bending. A relatively simple closed-form solution is proposed to tackle the problem. Key physical features involved are the elastic after-effect, accumulated cyclic (creep type) ovalisation of the cross-section, cyclic plasticity including the Bauschinger effect, cyclic softening/hardening of the material and ratcheting effect. The moment-curvature formulation of the tube is derived in an ovalised configuration. Tvergaard stress-strain relation is used to describe the elasto-plastic stress–strain relationship of the material. This continuous nonlinear constitutive model considerably abridges the solution. A combined nonlinear kinematic/nonlinear isotropic hardening rule is used to describe the cyclic uniaxial stress-strain. The analysis of the low cycle pure inelastic bending of the tube is performed under a curvature-control regime. The cycle by cycle growth (creep type) in the ovalization of the cross-section is modeled using a modified version of the Bailey–Norton creep law. 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.