Ratcheting assessment of steel samples under various non-proportional loading paths by means of kinematic hardening rules

• Multiaxial ratcheting response of 1045 and 1Cr18Ni9Ti steel samples was studied.
• A hardening rule was further developed and compared with other well-known rules.
• The modified model introduced the non-proportionality effect in its dynamic recovery.
• The modified model is capable of assessing ratcheting under non-proportional loading.

The present study predicts ratcheting response of 1045 and 1Cr18Ni9Ti tubular steel samples using nonlinear kinematic hardening rules of Ohno-Wang (O–W), Jiang–Sehitoglu (J–S), McDowell, Chen–Jiao–Kim (C–J–K) and newly modified model based on the hardening rule of Ahmadzadeh–Varvani (A–V) under various multiaxial loading histories. The modified hardening rule with less complexity holds components of backstress unity vector a¯/a¯ and the normal vector to the yield surface n¯ in its dynamic recovery to encounter non-proportionality. The components in the Macaulay brackets dε¯p⋅a¯/a¯ possessing different directions enable the hardening rule to track different directions under multiaxial stress cycles. Coefficient γ2 controls the ratcheting rate 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.The O–W, J–S and McDowell models persistently overestimated ratcheting curves in 1045 and 1Cr18Ni9Ti steel alloys for various multiaxial loading paths. Chen–Jiao–Kim modified the O–W model and possessed lower ratcheting results as compared with those predicted by other hardening rules. The predicted ratcheting curves through the modified model closely agreed with experimental data obtained under various multiaxial loading paths.

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