Abstract
The paper proposes an incremental relaxation plasticity (IRP) model for predicting possible instabilities and overall behavior of flow curves under dynamic loads. Compared to its original non-incremental version, the IRP model allows one to predict the behavior of stress-strain curves over a longer time after the start of yielding and to more accurately describe their instabilities such as sharp yield points (yield drops) and further nonmonotonic or oscillatory effects. The efficiency of the IRP model is demonstrated by comparing its predictions with those of the original non-incremental version and of the widely known Johnson–Cook model on the example of experimental flow curves for dual-phase high-strength steel DP800 and aluminum alloy 2519A. The major feature of the proposed IRP model is that its parameters are invariant with the loading history and strain rate of a material and are related only to the evolution of its defect structure on the micro- and mesoscales. With such a set of IRP model parameters, one can obtain a variety of flow curves of the same material at widely varied strain rates.
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REFERENCES
Johnson, G.R. and Cook, W.H., A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates, and High Temperatures, in Proc. 7th Int. Symp. Ballistics, The Hague, 1983, pp. 541–547.
Khan, A.S. and Huang, S., Experimental and Theoretical Study of Mechanical Behavior of 1100 Aluminum in the Strain Rate Range 10–5–104 s–1, Int. J. Plasticity, 1992, vol. 8, pp. 397–424. https://doi.org/10.1016/0749-6419(92)90057-J
Lin, Y., Chen, X., and Liu, G., A Modified Johnson–Cook Model for Tensile Behaviors of Typical High-Strength Alloy Steel, Mater. Sci. Eng. A, 2010, vol. 527, no. 26, pp. 6980–6986. https://doi.org/10.1016/j.msea.2010.07.061
Gambirasio, L. and Rizzi, E., An Enhanced Johnson–Cook Strength Model for Splitting Strain Rate and Temperature Effects on Lower Yield Stress and Plastic Flow, Comput. Mater. Sci., 2016, vol. 113, pp. 231–265. https://doi.org/10.1016/j.commatsci.2015.11.034
Meyers, M.A. and Chawla, K.K., Mechanical Behavior of Materials, Cambridge: Cambridge University Press, 2009.
Krasnikov, V.S., Mayer, A.E., and Yalovets, A.P., Dislocation Based High-Rate Plasticity Model and Its Application to Plate-Impact and Ultra Short Electron Irradiation Simulations, Int. J. Plasticity, 2011, vol. 27, no. 8, pp. 1294–1308. https://doi.org/10.1016/j.ijplas.2011.02.008
Uenishi, A. and Teodosiu, C., Constitutive Modelling of the High Strain Rate Behaviour of Interstitial-Free Steel, Int. J. Plasticity, 2004, vol. 20, no. 4–5, pp. 915–936. https://doi.org/10.1016/j.ijplas.2003.06.004
Petrov, Y.V. and Borodin, E.N., Relaxation Mechanism of Plastic Deformation and Its Justification Using the Example of the Sharp Yield Point Phenomenon in Whiskers, Phys. Solid State, 2015, vol. 57, no. 2, pp. 353–359. https://doi.org/10.1134/S1063783415020286
Selyutina, N.S. and Petrov, Y.V., Comparative Analysis of Dynamic Plasticity Models, Rev. Adv. Mater. Sci., 2018, vol. 57, no. 2, pp. 199–211. https://doi.org/10.1515/rams-2018-0065
Selyutina, N., Borodin, E.N., Petrov, Y.V., and Mayer, A.E., The Definition of Characteristic Times of Plastic Relaxation by Dislocation Slip and Grain Boundary Sliding in Copper and Nickel, Int. J. Plasticity, 2016, vol. 82, pp. 97–111. https://doi.org/10.1016/j.ijplas.2016.02.004
Petrov, Y.V., On the Incubation Stage of Fracture and Structural Transformations in Continuous Media under Pulse Energy Injection, Mech. Solids, 2007, vol. 42, no. 5, pp. 692–699. https://doi.org/10.3103/S0025654407050044
Petrov, Y.V. and Sitnikova, Y.V., Temperature Dependence of Spall Strength and the Effect of Anomalous Melting Temperatures in Shock-Wave Loading, Tech. Phys., 2005, vol. 50, no. 8, pp. 1034–1037.
Petrov, Y.V. and Selyutina, N.S., Effect of Plastic Strain Stabilization under Low-Cycle Deformation, Phys. Mesomech., 2020, vol. 23, no. 5, pp. 384–389. https://doi.org/10.1134/S1029959920050033
Cowper, G.R. and Symonds, P.S., Strain-Hardening and Strain-Rate Effects in the Impact Loading of Cantilever Beams, Tech. Rep., Division of Applied Mathematics, Brown University, 1957, no. 28.
Vulikh, B.Z., A Brief Course in the Theory of Functions of a Real Variable, Moscow: Mir, 1976.
Cadoni, E., Aiuto, F.D., and Albertini, C., Dynamic Behaviour of Advanced High Strength Steels Used in the Automobile Structures, DYMAT, 2009, pp. 135–142. https://doi.org/10.1051/dymat/2009018
Liu, W., He, Z., Chen, Y., and Tang, S., Dynamic Mechanical Properties and Constitutive Equations of 2519A Aluminum Alloy, Trans. Nonfer. Met. Soc. China, 2014, vol. 24, pp. 2179−2186. https://doi.org/10.1016/S1003-6326(14)63330-6
Funding
The work was supported by RFBR (grant No. 20-01-00291). G.A. Volkov is thankful to RFBR-BRICS (grant No. 18-51-80008) for support of the studies reported in Sects. 2, 5.
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Translated from Fizicheskaya Mezomekhanika, 2022, Vol. 25, No. 1, pp. 35–42.
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Zhao, S., Petrov, Y.V. & Volkov, G.A. Modeling the Nonmonotonic Behavior Flow Curves under Dynamic Loads. Phys Mesomech 25, 221–226 (2022). https://doi.org/10.1134/S1029959922030031
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DOI: https://doi.org/10.1134/S1029959922030031