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Predicting Macro- and Microscopic Responses of Dual-Phase Steels under Low Cycle Fatigue Based on Multi-scale Finite Element Methods

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Abstract

In the current study, three different combinations of dual-phase (DP) steels,i.e., ferrite–pearlite, ferrite–bainite, and ferrite–martensite containing the nearly same amount of second phase/phase mixture, have been developed following suitable heat-treatment schedules using a low carbon steel. Tensile and strain-controlled low cycle fatigue (LCF) tests at different strain amplitudes have been performed to understand the role of microstructure on the static and cyclic plasticity characteristics of DP steels. The experimental results reveal wide variations in the nature of cyclic hardening–softening behavior depending on the nature of the second phase. For the isotropic hardening, a new formulation considering the variation of yield stress as a function of memory stress and accumulated plastic strain has been incorporated, and Ohno–Wang kinematic hardening model has been used to simulate the observed fatigue response of DP structures. The developed model is capable of predicting the fatigue characteristics such as the stress amplitude versus the number of cycles, maximum hardening stress, and the progressive hysteresis loops. Further, the LCF simulations have been performed for the developed DP steels based on the real microstructure-based models adopting a sub-modeling technique. The stress and strain levels at different phases in the DP steels and their influence on the fatigue properties are quantified and discussed.

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Abbreviations

DP steel:

Dual-phase steel

\(f\) :

Von Mises yield function

\(\underline{S}\) :

Deviatoric stress tensor

\(\underline{\alpha }\) :

Deviatoric backstress tensor

\(\underline{\varepsilon }^{p}\) :

Plastic strain tensor

\(d\underline{\alpha }\) :

Increment in total backstress

\(\dot{p}\) :

Increment in plastic strain

\(c^{\left( i \right)} ,{\kern 1pt} \gamma^{\left( i \right)} ,{\kern 1pt} {\kern 1pt} r^{\left( i \right)}\) :

Hardening coefficients

\(s\) :

Memory stress

\(p\) :

Accumulated plastic strain

\(\sigma\) :

Engineering stress

\(\varepsilon\) :

Engineering strain

\(\sigma_{cy}\) :

Cyclic yield stress

\(\sigma_{r}\) :

Stress range

\(\sigma_{a}\) :

Stress amplitude

\(\sigma_{{a{\kern 1pt} o}}\) :

Stress amplitude of first cycle subjected to fatigue load

\(p_{0}\) :

Range of plastic strain memory

\(\underline{\underline{D}}^{e}\) :

Elastic stiffness tensor

\(\underline{1}\) and \(\underline{\underline{I}}\) :

Second and fourth rank unit tensor

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Acknowledgments

The assistance received from the Center of Excellence, TEQIP-II, IIEST Shibpur to carry out a part of this work is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, West Bengal, India

    S. K. Basantia & N. Khutia

  2. Department of Metallurgy and Materials Engineering, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, West Bengal, India

    Md Abu Bakkar, A. Bhattacharya & D. Das

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Basantia, S.K., Bakkar, M.A., Bhattacharya, A. et al. Predicting Macro- and Microscopic Responses of Dual-Phase Steels under Low Cycle Fatigue Based on Multi-scale Finite Element Methods. J. of Materi Eng and Perform 32, 3298–3321 (2023). https://doi.org/10.1007/s11665-022-07298-y

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