A kinematic hardening rule to investigate the impact of loading path and direction on ratcheting response of steel alloys. (October 2016) - Ahmadzadeh, G.R.; Varvani-Farahani, A.
Highlights: 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. Abstract: 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 〈 d ɛ ¯ p · a ¯ / | a ¯ | 〉 enable the hardening rule to track different directions under multiaxial stress cycles. Coefficient γ 2 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 γ 2 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.