Uniaxial time-dependent ratchetting: Visco-plastic model and finite element application

Based on a visco-plastic model, a time-dependent formulation was introduced. The model can describe as time-dependent ratchetting in term of revising the Abdel-Karim–Ohno nonlinear kinematic hardening rule [M. Abdel-Karim, N. Ohno, Kinematic hardening model suitable for ratchetting with steady-state, Int. J. Plast. 16 (2000) 225–240] by a static recovery term. It is shown that the simulated results are in good agreement with the corresponding experiment results of SS304 stainless steel [G.Z. Kang, Q.H. Kan, J. Zhang, Time-dependent ratchetting experiments of SS304 stainless steel, Int. J. Plast. 22 (2006) 858–894]. Then, the proposed model with static recovery term was implemented into the finite element package. Based on the radial return method and backward Euler’s integration, a new implicit stress integration algorithm was proposed, and a new expression of consistent tangent modulus was derived. Finally, the reasonability of such implementation was verified by some numerical samples.