Ratcheting of 304 stainless steel under multiaxial step-loading conditions

• Ratcheting response of 304 steel was studied under multiaxial step-loading histories.
• A modified hardening rule was proposed and compared with earlier well-known models.
• The modified model introduced the non-proportionality effect in its dynamic recovery.
• The modified model was capable of assessing ratcheting under multi-step loading.

The present study predicts ratcheting response of 304 tubular stainless steel samples undergoing multiaxial step-loading histories by means of nonlinear kinematic hardening rules of Ohno–Wang (O–W), Chen–Jiao–Kim (C–J–K) and the modified rule on the basis of Ahmadzadeh–Varvani (A–V) model. The plastic strain increment, dε¯p, and the backstress unity vector a¯/|a¯| as components in the MaCaulay brackets enabled the modified rule to track different ratcheting directions over multiaxial loading. Term (2−n¯⋅a¯/|a¯|) further regulated coefficient γ2 to account the effect of non-proportionality. The modified rule held term to prevent the model experiencing plastic shakedown.Predicted ratcheting results by means of O–W model showed deviation from experimental data. Chen–Jiao–Kim modified the O–W model and possessed lower ratcheting results as compared with those of predicted by the O–W. The hardening rules enabled to assess ratcheting in different directions as loading steps possessed high–low sequence in the second and third steps. The choice of hardening rule to assess ratcheting of steel samples was found very much dependent on complexities involved with ratcheting algorithms, their constitutive equations and framework, coefficients, and Central Processing Unit (CPU) time required to run ratcheting programs over loading steps.