Influence of Up-down-up Constitutive Equation Parameters on ‎Yield Plateau Stage of Mild Steel Samples Subjected to Stretching

Document Type : Research Paper


1 National Research Tomsk State University, 36 Lenin Pr., Tomsk, 634050, Russian Federation

2 Institute of Strength Physics and Materials Science of the Siberian Branch of the Russian Academy of Sciences,‎ ‎2/4 Akademicheskii Pr., Tomsk, 634055, Russian Federation‎


In this work, the computational study of Lüders phenomenon is addressed. The material for investigation is low-carbon steel demonstrating the yield point phenomenon when pulled in tension. Modeling of samples loading is carried out in the framework of three-dimensional finite-difference method. Judging by the literature review, there is a lack of papers thoroughly addressing the curves of dependences of Lüders elongation and front propagation velocity on parameters of up-down-up constitutive equation. This work fills this gap. It is shown that the difference between the true upper and lower yield stresses, and strain hardening factor have a strong impact on the duration of the yield plateau stage and ratio of front propagation velocity vf to loading velocity vl. The results of computational study complement the experimental data presented in available literature.


Main Subjects

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[1] Schwab, R., Ruff, V., On the nature of the yield point phenomenon, Acta Materialia, 61(5), 2013, 1798-1808.
[2] Hallai, J., Kyriakides, S., On the effect of Luders bands on the bending of steel tubes. part II: Analysis, International Journal of Solids and Structures, 48(24), 2011, 3285-3298.
[3] Romanova, V., Balokhonov, R., Schmauder, S., Three-dimensional analysis of mesoscale deformation phenomena in welded low-carbon steel, Materials Science and Engineering: A, 528(15), 2011, 5271-5277.
[4] Danilov, V., Gorbatenko, V., Zuev, L., Orlova, D., Kinetics and morphology of Luders deformation in specimens with homogeneous structure and with a weld joint, Materials Science and Engineering: A, 714, 2018, 160-166.
[5] Johnson, D., Edwards, M., Chard-Tuckey, P., Microstructural effects on the magnitude of Luders strains in a low alloy steel, Materials Science and Engineering: A, 625, 2015, 36 – 45.
[6] Makarov, P., Eremin, M., Jerky flow model as a basis for research in deformation instabilities, Physical Mesomechanics, 17(1), 2014, 62-80.
[7] Wenman, M., Chard-Tuckey, P., Modelling and experimental characterisation of the Luders strain in complex loaded ferritic steel compact tension specimens, International Journal of Plasticity, 26(7), 2010, 1013-1028.
[8] Coer, J., Manach, P., Laurent, H., Oliveira, M., Menezes, L., Piobert-Luders plateau and Portevin-le Chatelier effect in an Al-Mg alloy in simple shear, Mechanics Research Communications, 48, 2013, 1-7.
[9] Mao, B., Liao, Y., Modeling of Luders elongation and work hardening behaviors of ferrite-pearlite dual phase steels under tension, Mechanics of Materials, 129, 2019, 222-229.
[10] Maziere, M., Luis, C., Marais, A., Forest, S., Gasperini, M., Experimental and numerical analysis of the Luders phenomenon in simple shear, International Journal of Solids and Structures, 106-107, 2017, 305-314.
[11] Hajidehi, M., Stupkiewicz, S., Gradient-enhanced model and its micromorphic regularization for simulation of Lüders-like bands in shape memory alloys, International Journal of Solid and Structures, 135, 2018, 208-218.
[12] Shaw, J.A., Kyriakides, S., Initiation and propagation of localized deformation in elasto-plastic strips under uniaxial tension, International Journal of Plasticity, 13(10), 1997, 837-871.
[13] Hall, E.O., Yield Point Phenomena in Metals and Alloys, Springer Science & Business Media, 1970.
[14] Wilkins, M., Computer Simulation of Dynamic Phenomena, Springer-Verlag., 1999
[15] Makarov, P.V., Smolin, I.Yu., Khon, Yu.A., Eremin, M.O., Bakeev, R.A., Peryshkin, A.Yu., Zimina, V.A., Chirkov, A., Kazakbaeva, A.A., and Akhmetov, A.Zh., Autosoliton View of the Seismic Process. Part 2. Possibility of Generation and Propagation of Slow Deformation Autosoliton Disturbances in Geomedia, Physical Mesomechanics, 24(4), 2021, 375–390.
[16] Balokhonov, R., Zinoviev, A., Romanova, V., Zinovieva, O., The computational micromechanics of materials with porous ceramic coatings, Meccanica, 51(2), 2016, 415-428.
[17] Smolin, I., Makarov, P., Eremin, M., Matyko, K., Numerical simulation of mesomechanical behavior of porous brittle materials, Procedia Structural Integrity, 2, 2016, 3353-3360.
[18] Eremin, M.O., Chirkov, A.O., Nadezhkin, M.V., Zuev, L.B., Microstructure-based finite-difference analysis of the plastic flow in low-carbon steel, European Journal of Mechanics - A/Solids, 93, 2022, 104531.
[19] Makarov, P.V., Smolin, I.Yu., Zimina, V.A., The structure of deformation autosoliton fronts in rocks and geomedia, Geodynamics & Tectonophysics, 12(1), 2021, 100-111.
[20] Lim, H., Battaile, C.C., Bishop, J.E., Foulk, J.W., Investigating mesh sensitivity and polycrystalline RVEs in crystal plasticity finite element simulations, International Journal of Plasticity, 121, 2019, 101-115.
[21] Barannikova, S., Ponomareva, A.V., Zuev, L.B., Vekilov, Yu.Kh., Abrikosov, I.A., Significant correlation between macroscopic and microscopic parameters for the description of localized plastic flow auto-waves in deforming alloys, Solid State Communications, 152(9), 2012, 784-787.
[22] Butler, J.F., Lüders front propagation in low carbon steels, Journal of the Mechanics and Physics of Solids, 10(4), 1962, 313–318.
[23] Danilov, V., Gorbatenko, V., Zuev, L., Orlova, D., Danilova, L., Luders deformation of low-carbon steel, Steel in Translation, 47(10), 2017, 662-668.
[24] Zuev, L., Barannikova, S., Experimental study of plastic flow macro-scale localization process: Pattern, propagation rate, dispersion, International Journal of Mechanical Sciences, 88, 2014, 1-7.