A kinematic hardening rule to investigate the impact of loading path and direction on ratcheting response of steel alloys

• Ratcheting strain of steel samples under uniaxial and multiaxial paths was assessed.
• Ratcheting was assessed based on the A-V hardening rule at various loading paths.
• Ratcheting of forward and reverse butterflies at different load sequences was examined.
• The A-V model due to its dynamic recovery terms accounted for loading pathology.

The present study investigates ratcheting response of 304, 1045, 1026 and 1018 steel samples undergoing butterfly loading paths with different loading sequences/ directions through the newly developed kinematic hardening rule of Ahmadzadeh–Varvani (A-V). Components of backstress unity vector and the normal vector to the yield surface in the dynamic recovery of the model account for loading non-proportionality. The MaCaulay brackets 〈dɛ¯p·a¯/|a¯|〉 enable the hardening rule to track different directions under multiaxial stress cycles. Coefficient γ2 controls the rate of ratcheting and is regulated by term (2−n¯.a¯/|a¯|) to further lower the ratcheting strain curve. Term 〈n¯.a¯/|a¯|〉1/2 in the dynamic recovery prevents ratcheting plastic shakedown as stress cycles progress. Constant γ2 introduces a gradual decrease in the magnitude of (a¯−b¯) as the stress cycles advances. The movement of tensor b¯ with the initial value of zero follows backstress (a¯)exponentially over stress cycles. The difference in the magnitudes of b¯ and a¯ curves in butterfly down BFD (forward) and butterfly up BFU (reverse) histories verifies the loading path accountability through the dynamic recovery in the A-V model. This difference is initially large and as the number of cycles increases, term (a¯−b¯) decays and then stays constant and unchanged. History BFD with higher magnitude of term (a¯−b¯) possessed higher ratcheting as compared with BFU history. The predicted ratcheting curves through the A-V model consistently agreed with experimental data obtained under different loading paths and directions.