Abstract
It is almost commonplace to say that physics-based constitutive models developed to characterize the mechanical behavior of materials are to be preferred over phenomenological models. However, the constitutive relations offered by physics-based approaches are oftentimes too involved to be handled in finite element (FE) simulations for practical applications. There is a demand for physics-based, yet robust and user-friendly models, and one such model will be highlighted in this article. A simple constitutive model developed recently by Bouaziz to extend the classical physics-based Kocks-Mecking model provides a viable tool for modelling a broad range of materials – beyond the single-phase coarse-grained materials it was initially devised for. The efficacy of the model was put to the test by investigating its applicability for different materials. A broad interval of the true stress vs. true strain curve was studied by the measurement-in-neck-section method in the uniaxial tensile mode for six types of metallic materials, and simulations using the finite element method emulating the experimental conditions were developed. In this way, the engineering stress-strain curves were obtained corresponding to the true stress-strain curves for these materials. A comparison of the numerical simulations of the tensile behaviour of all six materials with the experimental results for a broad range of strains showed that among the models trialled, the Bouaziz model was the best-performing one. The proposed model can be recommended for use in FE simulations of the mechanical behaviour of engineering structures as a viable alternative to complex physics-based or simplistic phenomenological constitutive models.
Similar content being viewed by others
References
Zhang ZL, Hauge M, Ødegård J, Thaulow C (1999) Determining material true stress-strain curve from tensile specimens with rectangular cross-section. Int J Solids Struct 36:3497–3516. https://doi.org/10.1016/S0020-7683(98)00153-X
Byun TS, Hashimoto N (2006) Strain hardening and long-range internal stress in the localized deformation of irradiated polycrystalline metals. J Nucl Mater 354:123–130. https://doi.org/10.1016/j.jnucmat.2006.02.099
Örnek C, Şeşen BM, Ürgen MK (2022) Understanding hydrogen-induced strain localization in super duplex stainless steel using digital image correlation technique. Met Mater Int 28:475–486. https://doi.org/10.1007/s12540-021-01123-2
Zhu F, Bai P, Zhang J et al (2015) Measurement of true stress-strain curves and evolution of plastic zone of low carbon steel under uniaxial tension using digital image correlation. Opt Lasers Eng 65:81–88. https://doi.org/10.1016/j.optlaseng.2014.06.013
Gu GH, Moon J, Park HK et al (2021) Obtaining a wide-strain-range true stress–strain curve ysing the measurement-in-neck-section method. Exp Mech 61:1343–1348. https://doi.org/10.1007/s11340-021-00747-0
Gu GH, Ahn SY, Kim Y et al (2022) Determining reliable wide-strain-range equivalent stress–strain curves using 3D digital image correlation. J Mater Res Technol 19:2822–2830. https://doi.org/10.1016/j.jmrt.2022.06.054
Gu GH, Kim Y, Kim RE et al (2022) A new digital image correlation method for measuring wide strain range true stress–strain curve of clad materials. Met Mater Int 2–7. https://doi.org/10.1007/s12540-022-01219-3
Kim K, Il, Oh Y, Kim DU et al (2022) Strain analysis of multi-phase steel using in-situ EBSD tensile testing and digital image correlation. Met Mater Int 28:1094–1104. https://doi.org/10.1007/s12540-021-01044-0
Estrin Y (1996) Dislocation-density-related constitutive modelling. In: Krausz AS, Krausz K (eds) Unified Constitutive Laws of Plastic Deformation. Academic, pp 69–106. https://doi.org/10.1016/B978-012425970-6/50003-5
Pham QT, Lee BH, Park KC, Kim YS (2018) Influence of the post-necking prediction of hardening law on the theoretical forming limit curve of aluminium sheets. Int J Mech Sci 140:521–536. https://doi.org/10.1016/j.ijmecsci.2018.02.040
Kim Y, Gu GH, Asghari-Rad P et al (2022) Novel deep learning approach for practical applications of indentation. Mater Today Adv 13:100207. https://doi.org/10.1016/j.mtadv.2022.100207
Yang H, Li H, Ma J et al (2019) Constitutive modeling related uncertainties: effects on deformation prediction accuracy of sheet metallic materials. Int J Mech Sci 157–158:574–598. https://doi.org/10.1016/j.ijmecsci.2019.05.004
Sung JH, Kim JH, Wagoner RH (2010) A plastic constitutive equation incorporating strain, strain-rate, and temperature. Int J Plast 26:1746–1771. https://doi.org/10.1016/j.ijplas.2010.02.005
Gavrus A (2012) Constitutive equation for description of metallic materials behavior during static and dynamic loadings taking into account important gradients of plastic deformation. Key Eng Mater 504–506:697–702. https://doi.org/10.4028/www.scientific.net/KEM.504-506.697
Kim Y, Asghari-Rad P, Lee J et al (2022) Solid solution induced back-stress in multi-principal element alloys: experiment and modeling. Mater Sci Eng A 835:142621. https://doi.org/10.1016/j.msea.2022.142621
Kim Y, Jung J, Park HK, Kim HS (2022) Importance of microstructural features in bimodal structure–property linkage. Met Mater Int 4:1–6. https://doi.org/10.1007/s12540-022-01200-0
Bouaziz O, Barbier D, Embury JD, Badinier G (2013) An extension of the Kocks-Mecking model of work hardening to include kinematic hardening and its application to solutes in ferrite. Philos Mag 93:247–255. https://doi.org/10.1080/14786435.2012.704419
Kocks UF, Mecking H (2003) Physics and phenomenology of strain hardening: the FCC case. Prog Mater Sci 48:171–273. https://doi.org/10.1016/S0079-6425(02)00003-8
Bouaziz O, Lloyd D (2022) Assessment of a physical based modelling suitable to capture the mechanical behaviour at large plastic strain of aluminium alloys. Metall Res Technol 419:4–7. https://doi.org/10.1051/metal/2022064
Bouaziz O (2012) Revisited storage and dynamic recovery of dislocation density evolution law: toward a generalized kocks-mecking model of strain-hardening. Adv Eng Mater 14:759–761. https://doi.org/10.1002/adem.201200083
Gu GH, Kim RE, Ahn SE et al (2022) Multi-scale investigation on local strain and damage evolution of Al1050 / steel / Al1050 clad sheet. J Mater Res Technol 20:128–138. https://doi.org/10.1016/j.jmrt.2022.07.056
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (NRF-2021R1A2C3006662) and (NRF-2022R1A5A1030054).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
None.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kim, Y., Gu, G.H., Bouaziz, O. et al. A simple physics-based constitutive model to describe strain hardening in a wide strain range. Int J Mater Form 16, 19 (2023). https://doi.org/10.1007/s12289-023-01741-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12289-023-01741-8