On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment

On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment


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Abstract. Modelling and simulation are critical stages of product development in modern industry. Simulation tools in solid mechanics use constitutive models and their parameters to describe the behaviour of materials. Nowadays, with the use of heterogeneous test configurations and full-field measurements, it is possible to measure a combination of multiple strain states, allowing for the identification of multiple parameters from a single test with reduced cost and time. This work aims to investigate the potential for obtaining heterogeneous states of strain\stress with the Arcan test configuration. A finite element model was developed using a specimen with a smooth arc section in which the loading and material directions varied, producing tensile, shear, or mixed mode responses. The most heterogeneous test configuration was selected using a heterogeneous criterion and the numerical results were used to generate synthetic speckle pattern images and further processed by digital image correlation (DIC). The DIC results were used as input for the identification procedure through the virtual fields method (VFM) for the simultaneous calibration of the Swift hardening law and the Hill’48 anisotropic yield criterion. The identified solution was compared with the ground truth material parameters. The results show the potential of combining the Arcan test with the VFM to simultaneously identify material parameters for anisotropic plasticity models of sheet metals.

Sheet Metal Forming, Anisotropic Plasticity, Arcan Test, Heterogeneous Test Evaluation, Inverse Identification, Digital Image Correlation, Synthetic Images

Published online 4/19/2023, 12 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: HENRIQUES Joao, ANDRADE-CAMPOS António, XAVIER José, On the inverse identification of sheet metal mechanical behaviour using a heterogeneous Arcan virtual experiment, Materials Research Proceedings, Vol. 28, pp 1131-1142, 2023

DOI: https://doi.org/10.21741/9781644902479-124

The article was published as article 124 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.

[1] A. Lattanzi, F. Barlat, F. Pierron, A. Marek, M. Rossi, Inverse identification strategies for the characterization of transformation-based anisotropic plasticity models with the non-linear VFM, Int. J. Mech. Sci. 173 (2020) 105422. https://doi.org/10.1016/j.ijmecsci.2020.105422
[2] P.D. Wu, S.R. MacEwen, D.J. Lloyd, M. Jain, P. Tugcu, K.W. Neale, On pre-straining and the evolution of material anisotropy in sheet metals, Int. J. Plast. 21 (2005) 723-739. https://doi.org/10.1016/j.ijplas.2004.05.007
[3] J.M.P. Martins, A. Andrade-Campos, S. Thuillier, Calibration of anisotropic plasticity models using a biaxial test and the virtual fields method, Int. J. Solids Struct. 172 (2019) 21-37. https://doi.org/10.1016/j.ijsolstr.2019.05.019
[4] N. Souto, S. Thuillier, A. Andrade-Campos, Design of an indicator to characterize and classify mechanical tests for sheet metals, Int. J. Mech. Sci. 101-102 (2015) 252-271. https://doi.org/10.1016/j.ijmecsci.2015.07.026
[5] M. Sutton, J. Orteu, H. Schreier, Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications, first ed., Springer, New York, 2009. https://doi.org/10.1007/978-0-387-78747-3
[6] F. Pierron, M. Grédiac, Towards Material Testing 2.0. A review of test design for identification of constitutive parameters from full-field measurements, Strain 57 (2021) 12370. https://doi.org/10.1111/str.12370
[7] F. Pierron, M. Grédiac, The virtual fields method. Extracting constitutive mechanical parameters from full-field deformation measurements, first ed., Springer, New York, 2012. https://doi.org/10.1007/978-1-4614-1824-5
[8] J. Henriques, J. Xavier, A. Andrade-Campos, Identification of Orthotropic Elastic Properties of Wood by a Synthetic Image Approach Based on Digital Image Correlation, Materials 15 (2022) 625. https://doi.org/10.3390/ma15020625
[9] J. Aquino, A. Andrade-Campos, J.M.P. Martins, S. Thuillier, Design of heterogeneous mechanical tests: Numerical methodology and experimental validation, Strain 55 (2019) 12313. https://doi.org/ 10.1111/str.12313
[10] J. Fu, W. Xie, L. Qi, An Identification Method for Anisotropic Plastic Constitutive Parameters of Sheet Metals, Procedia Manuf. 47 (2020) 812-815. https://doi.org/10.1016/j.promfg.2020.04.251
[11] T. Pottier, P. Vacher, F. Toussaint, H. Louche, T. Coudert, Out-of-plane Testing Procedure for Inverse Identification Purpose: Application in Sheet Metal Plasticity, Exp. Mech. 52 (2012) 951-963. https://doi.org/10.1007/s11340-011-9555-3
[12] M. Conde, Y. Zhang, J. Henriques, S. Coppieters, A. Andrade-Campos, Design and validation of a heterogeneous interior notched specimen for inverse material parameter identification, Finite. Elem. Anal. Des. 214 (2023) 103866. https://doi.org/10.1016/j.finel.2022.103866
[13] M. Gonçalves, A. Andrade-Campos, B. Barroqueiro, On the design of mechanical heterogeneous specimens using multilevel topology optimization, Adv. Eng. Softw. 175 (2023) 103314. https://doi.org/10.1016/j.advengsoft.2022.103314
[14] L. Chamoin, C. Jailin, M. Diaz, L. Quesada, Coupling between topology optimization and digital image correlation for the design of specimen dedicated to selected material parameters identification, Int. J. Solids. Struct. 193-194 (2020) 270-286. https://doi.org/10.1016/j.ijsolstr.2020.02.032
[15] P. Wang, F. Pierron, O.T. Thomsen, Identification of Material Parameters of PVC Foams using Digital Image Correlation and the Virtual Fields Method, Exp. Mech. 53 (2013) 1001-1015. https://doi.org/10.1007/s11340-012-9703-4
[16] P. Wang, F. Pierron, M. Rossi, P. Lava, O.T. Thomsen, Optimised Experimental Characterisation of Polymeric Foam Material Using DIC and the Virtual Fields Method, Strain 52 (2016) 59-79. https://doi.org/10.1111/str.12170
[17] M. Shifa, Strength of Aluminum Alloys Under Static Mixed-Mode I/II Loading Conditions, J. Test. Eval. 46 (2018) 294-304. https://doi.org/10.1520/JTE20160475
[18] A. Kumar, M.K. Singha, V. Tiwari, Structural response of metal sheets under combined shear and tension, Structures 26 (2020) 915-933. https://doi.org/10.1016/j.istruc.2020.05.006
[19] F. Ozturk, S. Toros, S. Kilic, Effects of Anisotropic Yield Functions on Prediction of Forming Limit Diagrams of DP600 Advanced High Strength Steel, Procedia Eng. 81 (2014) 760-765. https://doi.org/10.1016/j.proeng.2014.10.073
[20] Dassault Systèmes. Abaqus 2017 documentation, 2017
[21] R. Hill, A theory of the yielding and plastic flow of anisotropic metals, Proc. R. Soc. Lond. A 193 (1948) 281-297. https://doi.org/10.1098/rspa.1948.0045
[22] H. Takizawa, T. Kuwabara, K. Oide, J. Yoshida, Development of the subroutine library ‘UMMDp’ for anisotropic yield functions commonly applicable to commercial FEM codes, J. Phys.: Conf. Ser. 734 (2016) 032028. https://doi.org/10.1088/1742-6596/734/3/032028
[23] M. Guimarães Oliveira, S. Thuillier, A. Andrade-Campos, Analysis of Heterogeneous Tests for Sheet Metal Mechanical Behavior, Procedia Manuf. 47 (2020) 831-838. https://doi.org/10.1016/j.promfg.2020.04.259
[24] MatchID: Metrology beyond colors. MatchID version 2022.2, 2022.
[25] J. Henriques, M. Conde, A. Andrade-Campos, J. Xavier, Identification of Swift Law Parameters Using FEMU by a Synthetic Image DIC-Based Approach, Key Eng. Mater. 926 (2022) 2211-2221. https://doi.org/ 10.4028/p-33un7m
[26] S. Avril, M. Grédiac, F. Pierron, Sensitivity of the virtual fields method to noisy data, Comput. Mech. 34 (2004) 439-452. https://doi.org/10.1007/s00466-004-0589-6
[27] A. Marek, F.M. Davis, F. Pierron, Sensitivity-based virtual fields for the non-linear virtual fields method, Comput. Mech. 60 (2017) 409-43. https://doi.org/10.1007/s00466-017-1411-6
[28] J.M.P. Martins, S. Thuillier, A. Andrade-Campos, Calibration of Anisotropic Plasticity Models with an Optimized Heterogeneous Test and the Virtual Fields Method, Residual Stress, Thermomechanics & Infrared Imaging and Inverse Problems 6 (2020) 25-32. https://doi.org/10.1007/978-3-030-30098-2_5