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Ratcheting Assessment of Rail Steel at Elevated Temperatures in the Presence of Dynamic Strain Aging

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Abstract

The present study intends to evaluate the ratcheting of U75VG rail steel samples tested at different stress levels and various temperatures through a combined isotropic–kinematic hardening rule. Through the Lee–Zavrel (L–Z) isotropic description, the actual yield surface was determined by the superposition of the initial yield surface and the isotropic hardening variable. The saturated yield surface was then translated through the Ahmadzadeh–Varvani (A–V) kinematic hardening rule as the loading excursion exceeded the elastic limit. Ratcheting data in the rail steel samples demonstrated a negative strain-rate sensitivity when the operating temperature ranged between 573 and 873 K, at which dislocations and solute atoms are believed to interact with each other improving the strength of materials. Within this temperature range, referred to as the dynamic strain aging (DSA) temperature domain, materials showed no noticeable increase in ratcheting magnitude over the asymmetric loading cycles. The influence of operating temperature on the ratcheting of steel samples was introduced through an exponential function into the dynamic recovery of the hardening framework. Within the DSA temperature domain, the exponential function formed a plateau with a value as low as \(\psi\) = 0.3. A drop in function \(\psi\) at the DSA temperature domain directly influenced the magnitude of backstress increments and the translation of the yield surfaces. At the operating temperatures beyond the DSA domain, the yield strength noticeably declined resulting in materials softening. The predicted ratcheting curves and those measured data at the DSA temperature domain were found in close agreement.

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Abbreviations

\(\psi \left( {p,T} \right)\) :

A function to address an active domain for dynamic strain aging phenomenon

\(C\), \(\gamma_1\), \(\gamma_2\), \(\delta\) :

Coefficients of the A–V model

\(\overline{a}\) :

Backstress tensor

\(\overline{b}\) :

Internal variable of the A–V model

\({\text{S}}\) :

State of stress in deviatoric space

\(\sigma_y\) :

Actual yield stress

\(\sigma_y^0\) :

Initial yield stress

\(R\) :

Internal variable of isotropic hardening

R:

Stress ratio

\(\sigma\) :

Applied stress

\({\text{I}}\) :

Unit tensor

\(\overline{n}\) :

Unit normal vector on the yield surface

\(E\) :

Elastic modulus

\(G\) :

Shear modulus

\(H_p\) :

Plastic modulus function

\(Q\) :

Saturated value of internal variable R

\(b\) :

Exponent defining evolution rate of R

\(p\) :

Accumulated plastic strain

\(\psi_\infty \left( T \right), \lambda\) :

Temperature-dependent material constants

\(\sigma_v\), \(K\), \(\eta\) :

Viscous stress, drag stress, and viscous exponent, respectively

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Acknowledgments

Authors wish to acknowledge the financial support through Natural Sciences and Engineering Research Council of Canada (NSERC) through Dr. Varvani (RGPIN-2021-03047).

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  1. Department of Mechanical, Industrial, and Mechatronics Engineering, Toronto Metropolitan University, 350 Victoria Street, Toronto, ON, M5B 2K3, Canada

    M. Karimi & A. Varvani-Farahani

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Correspondence to A. Varvani-Farahani.

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Karimi, M., Varvani-Farahani, A. Ratcheting Assessment of Rail Steel at Elevated Temperatures in the Presence of Dynamic Strain Aging. J. of Materi Eng and Perform (2024). https://doi.org/10.1007/s11665-024-09663-5

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