Calibration of thermo-viscoplastic constitutive model under biaxial loadings: A Feasibility Study
WANG Zhihao, GUINES Dominique, LEOTOING Lionel
download PDFAbstract. In this study, an inverse identification strategy based on the finite element model updating (FEMU) method is proposed to calibrate the parameters of a temperature and strain rate dependent constitutive model. The mechanical responses of a dedicated cruciform specimen with heterogeneous temperature field under biaxial loading are employed to supply information to the inverse scheme. A combination of Particle Swarm Optimization (PSO) and SIMPLEX optimization algorithm is employed to find the optimal values of the material parameters. In order to validate the proposed identification strategy, a virtual experiment is designed and performed with a reference material constitutive model. The proposed strategy is proved to be feasible as all seven parameters of the constitutive model are accurately identified. In addition, the influences of measurement noise of force, temperature, and strain data are analyzed by means of a sensitivity study. The experimental data after the localized necking should be avoided for parameter identification. The proposed inverse identification strategy shows good robustness to strain noise.
Keywords
Thermo-Viscoplastic Model, Thermal Biaxial Tensile Test, Calibration
Published online 4/19/2023, 10 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: WANG Zhihao, GUINES Dominique, LEOTOING Lionel, Calibration of thermo-viscoplastic constitutive model under biaxial loadings: A Feasibility Study, Materials Research Proceedings, Vol. 28, pp 1397-1406, 2023
DOI: https://doi.org/10.21741/9781644902479-151
The article was published as article 151 of the book Material Forming
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] R. Zarea, J. Fernández-Sáez, An implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations in adiabatic conditions and finite deformations, Int. J. Solid. Struct. 43 (2006) 1594-1612. https://doi.org/10.1016/j.ijsolstr.2005.03.070
[2] G.R. Johnson, W.H. Cook, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, In Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands, 19–21 April 1983, pp. 541-547.
[3] A.S. Khan, Y.S. Suh, R. Kazmi, Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys, Int. J. Plast. 20 (2004) 2233-2248. https://doi.org/10.1016/j.ijplas.2003.06.005
[4] F.J. Zerilli, R.W. Armstrong, Dislocation-mechanics based constitutive relations for material dynamics calculations, J. Appl. Phys. 61 (1987) 1816-1825.
[5] G.Z. Voyiadjis, F.H. Abed, Microstructural based models for bcc and fcc metals with temperature and strain rate dependency, Mech. Mater. 37 (2005) 355-378. http://doi.org/10.1016/j.mechmat.2004.02.003
[6] X. Li, C.C. Roth, C. Bonatti, D. Mohr, Counterexample-trained neural network model of rate and temperature dependent hardening with dynamic strain aging, Int. J. Plast. 151 (2022) 103218. https://doi.org/10.1016/j.ijplas.2022.103218
[7] H. Shang, P. Wu, Y. Lou, J. Wang, Q. Chen, Machine learning-based modeling of the coupling effect of strain rate and temperature on strain hardening for 5182-O aluminum alloy, J. Mater. Process. Tech. 302 (2022) 117501. https://doi.org/10.1016/j.jmatprotec.2022.117501
[8] J.M.P. Martins, A. Andrade-Campos, S. Thuillier, Comparison of inverse identification strategies for constitutive mechanical models using full-field measurements, Int. J. Mech. Sci. 145 (2018) 330-345. https://doi.org/10.1016/j.ijmecsci.2018.07.013
[9] Z. Wang, S. Zang, X. Chu, S. Zhang, L. Leotoing, Identification of 7B04 aluminum alloy anisotropy yield criteria with conventional test and Pottier test at elevated temperature, Results. Phys. 15 (2019) 102655. https://doi.org/10.1016/j.rinp.2019.102655
[10] P. Prates, A. Pereira, N. Sakharova, M. Oliveira, J Fernandes, Inverse strategies for identifying the parameters of constitutive laws of metal sheets, Adv. Mater. Sci. Eng. 2016 (2016) 1-18. https://doi.org/10.1155/2016/4152963
[11] S. Avril, F. Pierron, Y. Pannier, R. Rotinat, Stress reconstruction and constitutive parameter identification in plane-stress elasto-plastic problems using surface measurements of deformation fields, Exp. Mech. 48 (2008) 403-419. https://doi.org/10.1007/s11340-007-9084-2
[12] J.H. Holland, Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, Ann. Arbor., MI, University of Michigan Press.
[13] J. Kennedy, R.C. Eberhart, Particle Swarm Optimization, in: Proceedings of the IEEE International Conference on Neural Networks, Piscataway, vol. IV, 1995, pp. 1942-1948.
[14] P.A. Prates, M.C. Oliveira, J.V. Fernandes, A new strategy for the simultaneous identification of constitutive laws parameters of metal sheets using a single test, Comp. Mater. Sci. 84 (2014) 102-120. http://doi.org/10.13140/RG.2.2.25692.80004
[15] S. Zhang, L. Leotoing, D. Guines, S. Thuillier, S. Zang, Calibration of anisotropic yield criterion with conventional tests or biaxial test, Int. J. Mech. Sci. 85 (2014) 142-151. https://doi.org/10.1016/j.ijmecsci.2014.05.020
[16] Z. Wang, D. Guines, X. Chu, L. Leotoing, Characterization of forming limits at fracture from shear to plane strain with a dedicated cruciform specimen, Int. J. Mater. Form. 7 (2022) 15. http://doi.org/10.1007/s12289-022-01658-8
[17] W. Liu, D. Guines, L. Leotoing, E. Ragneau, Identification of sheet metal hardening for large strains with an in-plane biaxial tensile test and a dedicated cross specimen, Int. J. Mech. Sci. 101-102 (2015) 387-398. https://doi.org/10.1016/j.ijmecsci.2015.08.022
[18] J. Liang, D. Guines, L. Leotoing, Effect of temperature and strain rate on the plastic anisotropic behavior characterized by a single biaxial tensile test, Procedia Manuf. 47 (2020) 1532-1539. https://doi.org/10.1016/j.promfg.2020.04.346
[19] J. Gao, Y. Cao, L. Lu, Z. Hu, K. Wang, F. Guo, Y. Yan, Study on the interaction between nanosecond laser and 6061 aluminum alloy considering temperature dependence, J. Alloy. Compd. 892 (2022) 162044. https://doi.org/10.1016/j.jallcom.2021.162044
[20] A.G. Gad, Particle Swarm Optimization Algorithm and Its Applications: A Systematic Review, Arch. Computat. Meth. Eng. 29 (2022) 2531-2561. http://doi.org/10.1007/s11831-021-09694-4
