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Visco-Plastic Ratcheting Evaluation of Steel Alloys undergoing various Step-Loading Conditions by means of Isotropic-Kinematic Hardening Rules

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posted on 30.05.2022, 18:49 by Poorya Karvan

The present thesis develops visco-plastic constitutive equations to assess ratcheting response of several steel alloys of 304, austenitic Z2CND18.12N, U71Mn, and 316 examined  under various step-loading conditions through use of the Ohno-Wang (O-W) and Ahmadzadeh- Varvani (A-V) kinematic hardening rules. The framework of hardening rules was incorporated  isotropic hardening rules of Lee and Zavrel (Iso-LZ), Chaboche (Iso-C), and Kang (Iso-K) to emulate expansion of yield surfaces. The unified visco-plastic flow rule was adapted to account for the effects of stress rate and time-dependency in ratcheting assessment of steel samples. Kang's function on dynamic strain aging was employed to further evaluate time-dependent ratcheting response at operating room and elevated temperatures. This function was integrated to the dynamic recovery terms leading to drop in ratcheting magnitude and rate resulting in plastic shakedown shortly after a few stress cycles over Low-High loading sequence. The effect of the presence of peak/valley holding time resulting in static recovery was introduced into the kinematic hardening rules through inclusion of a backstress-dependent function proposed earlier by Ding. This integration enabled hardening rules to predict the excess of ratcheting strain values generated by static loading at maximum and minimum stresses over each loading cycle. Visco-plastic ratcheting evaluation of various stainless steel samples were evaluated at various stress rate, stress levels, loading steps and sequences, operating temperatures and holding times through use of the O-W and A-V hardening rules. The predicted ratcheting curves and hysteresis loops by the O-W and A-V frameworks were compared with those obtained experimentally. The predicted ratcheting curves of steel samples tested at Low-High-Low and High-Low-High loading sequences and at room and elevated temperatures revealed that both frameworks elevated ratcheting strains over Low-High loading sequence and dropped them over High-Low loading sequence. Choices of material constants and number of segments taken from stress-strain curve based on the O-W model noticeably influenced ratcheting response of steel samples. The O-W model held more backstress components, and consequently more coefficients, requiring longer Central Processing Unit (CPU) time for ratcheting evaluation than the A-V model which possessed a less complex framework with a fewer number of coefficients.





Doctor of Philosophy


Mechanical and Industrial Engineering

Granting Institution

Ryerson University

LAC Thesis Type


Thesis Advisor

A. Varvani-Farahani