[en] This work presents an elastoplastic characterization of a rolled C11000-H2 99.90% pure
copper sheet considering the orthotropic non-associated Hill-48 criterion together with a modified
Voce hardening law. One of the main features of this material is the necking formation at small
strains levels causing the early development of non-homogeneous stress and strain patterns
in the tested samples. Due to this fact, a robust inverse calibration approach, based on an
experimental–analytical–numerical iterative predictor–corrector methodology, is proposed to obtain
the constitutive material parameters. This fitting procedure, which uses tensile test measurements
where the strains are obtained via digital image correlation (DIC), consists of three steps aimed at,
respectively, determining (a) the parameters of the hardening model, (b) a first prediction of the
Hill-48 parameters based on the Lankford coefficients and, (c) corrected parameters of the yield and
flow potential functions that minimize the experimental–numerical error of the material response.
Finally, this study shows that the mechanical characterization carried out in this context is capable of
adequately predicting the behavior of the material in the bulge test.
Disciplines :
Mechanical engineering
Author, co-author :
Pacheco, Matias; Universidad de Santiago de Chile, USACH
Garcia-Herrera, Claudio; Universidad de Santiago de Chile, USACH
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Bibliography
Manopulo, N.; Raemy, C.; Hora, P. A flexible modelling approach for capturing plastic anisotropy and strength differential effects exhibited by commercially pure titanium. Int. J. Solids Struct. 2017, 151, 91–98. [CrossRef]
Xue, X.; Liao, J.; Vincze, G.; Sousa, J.; Barlat, F.; Gracio, J. Modelling and sensitivity analysis of twist springback in deep drawing of dual-phase steel. Mater. Des. 2016, 90, 204–217. [CrossRef]
Wang, W.; Huang, L.; Tao, K.; Chen, S.; Wei, X. Formability and numerical simulation of AZ31B magnesium alloy sheet in warm stamping process. Mater. Des. 2015, 87, 835–844. [CrossRef]
El Sherbiny, M.; Zein, H.; Abd-Rabou, M.; El Shazly, M. Thinning and residual stresses of sheet metal in the deep drawing process. Mater. Des. 2014, 55, 869–879. [CrossRef]
Hähner, P.; Soyarslan, C.; Cakan, B.G.; Bargmann, S. Determining tensile yield stresses from Small Punch tests: A numerical-based scheme. Mater. Des. 2019, 182, 107974. [CrossRef]
Ha, J.; Baral, M.; Korkolis, Y. Ductile fracture of an Al-Si-Mg die-casting aluminum alloy. Procedia Eng. 2017, 207, 2024–2029. [CrossRef]
Chen, K.; Scales, M.; Kyriakides, S. Material hardening of a high ductility aluminum alloy from a bulge test. Int. J. Mech. Sci. 2018, 138–139, 476–488. [CrossRef]
Ha, J.; Baral, M.; Korkolis, Y.P. Plastic anisotropy and ductile fracture of bake-hardened AA6013 aluminum sheet. Int. J. Solids Struct. 2018, 55, 123–139. [CrossRef]
Džoja, M.; Cvitanić, V.; Safaei, M.; Krstulović-Opara, L. Modelling the plastic anisotropy evolution of AA5754-H22 sheet and implementation in predicting cylindrical cup drawing process. Eur. J. Mech. A Solids 2019, 77, 103806. [CrossRef]
Kohar, C.P.; Brahme, A.; Hekmat, F.; Mishra, R.K.; Inal, K. A computational mechanics engineering framework for predicting the axial crush response of aluminum extrusions. Thin-Walled Struct. 2019, 140, 516–532. [CrossRef]
Gotoh, M. A theory of plastic anisotropy based on yield function of fourth order (plane stress state)-II. Int. J. Mech. Sci. 1977, 19, 513–520. [CrossRef]
Banabic, D.; Kuwabara, T.; Balan, T.; Comsa, D.S.; Julean, D. A new yield criterion for orthotropic sheet metals under plane–stress conditions. Int. J. Mech. Sci. 2003, 45, 797–811. [CrossRef]
Barlat, F.; Brem, J.C.; Yoon, J.W.; Chung, K.; Dick, R.E.; Lege, D.J.; Pourboghrat, F.; Choi, S.H.; Chu, E. Plane stress yield function for aluminum alloy sheets–Part 1: Theory. Int. J. Plast. 2003, 19, 1297–1319. [CrossRef]
Aretz, H.; Barlat, F. New convex yield functions for orthotropic metal plasticity. Int. J. Non-Linear Mech. 2013, 51, 97–111. [CrossRef]
Baral, M.; Hama, T.; Knudsen, E.; Korkolis, Y.P. Plastic deformation of commercially-pure titanium: Experiments and modeling. Int. J. Plast. 2018, 105, 164–194. [CrossRef]
Yang, H.; Li, H.; Ma, J.; Zhang, Z.; Chen, J. Constitutive modeling related uncertainties: Effects on deformation prediction accuracy of sheet metallic material. Int. J. Mech. Sci. 2019, 157–158, 574–598. [CrossRef]
Stoughton, T.B. A non-associated flow rule for sheet metal forming. Int. J. Plast. 2002, 18, 687–714. [CrossRef]
Stoughton, T.B.; Yoon, J.W. Anisotropic hardening and non-associated flow in proportional loading of sheet metals. Int. J. Plast. 2009, 25, 1777–1817. [CrossRef]
Rahmaan, T.; Bardelcik, A.; Imbert, J.; Butcher, C.; Worswick, M.C. Effect of strain rate on flow stress and anisotropy of DP600, TRIP780, and AA5182-O sheet metal alloys. Int. J. Impact Eng. 2016, 288, 72–90. [CrossRef]
Ciemiorek, M.; Chrominski, W.; Olejnik, L.; Lewandowska, M. Evaluation of mechanical properties and anisotropy of ultra-fine grained 1050 aluminum sheets produced by incremental ECAP. Mater. Des. 2017, 130, 392–402. [CrossRef]
Cheng, C.; Meng, B.; Han, J.Q.; Wan, M.; Wu, X.D.; Zhao, R. A modified Lou–Huh model for characterization of ductile fracture of DP590 sheet. Mater. Des. 2017, 118, 89–98. [CrossRef]
Acosta, C.A.; Hernandez, C.; Maranon, A.; Casas-Rodriguez, J.P. Validation of material constitutive parameters for the AISI 1010 steel from Taylor impact tests. Mater. Des. 2016, 110, 324–331. [CrossRef]
Moussa, C.; Bartier, O.; Hernot, X.; Mauvoisin, G.; Collin, J.M.; Delattre, G. Mechanical characterization of carbonitrided steel with spherical indentation using the average representative strain. Mater. Des. 2016, 89, 1191–1198. [CrossRef]
Zribi, T.; Khalfallah, A.; BelHadjSalah, H. Experimental characterization and inverse constitutive parameters identification of tubular materials for tube hydroforming process. Mater. Des. 2013, 49, 866–877. [CrossRef]
Kobayashi, S.; Caddell, S.; Hosford, W.F. Examination of Hill’s latest yield criterion using experimental data for various anisotropic sheet metals. Int. J. Mech. Sci. 1985, 27, 509–517. [CrossRef]
Khan, A.S.; Cheng, P. An anisotropic elastic-plastic constitutive model for single and polycrystalline metals. ii-experiments and predictions concerning thin-walled tubular ofhc copper. Int. J. Plast. 1998, 14, 209–226. [CrossRef]
Suwas, S.; Singh, A.K.; Narasimha Rao, K.; Singh, T. Effect of modes of rolling on evolution of texture in pure copper and some copper base alloys. Z. Met. 2003, 94, 1313–1319. [CrossRef]
Alexander, D.J.; Beyerlein, I.J. Anisotropy in mechanical properties of high-purity copper processed by equal channel angular extrusion. Mater. Sci. Eng. A 2005, 410–411, 480–484. [CrossRef]
Haouaoui, M.; Karaman, I.; Maier, H.J. Flow stress anisotropy and bauschinger effect in ultrafine grained copper. Acta Mater. 2006, 54, 5477–5488. [CrossRef]
Molotnikov, A.; Lapovok, R.; Gu, C.F.; Davies, C.H.J.; Estrin, Y. Size effects in micro cup drawing. Mater.Sci. Eng. A 2012, 550, 312–319. [CrossRef]
Fu, M.W.; Yang, B.; Chan, W.L. Experimental and simulation studies of micro blanking and deep drawing compound process using copper sheet. J. Mater. Process. Technol. 2013, 213, 101–110. [CrossRef]
Gong, F.; Chen, Q.; Yang, Z.; Shu, D.; Zhang, S. Micro deep drawing of C1100 conical-cylindrical cups. Procedia Eng. 2014, 81, 1457–1462. [CrossRef]
ASTM E8/E8M-16a, Standard Test Methods for Tension Testing of Metallic Materials; Standard, ASTM International: West Conshohocken, PA, USA, 2016. [CrossRef]
Celentano, D.; Cabezas, E.; García–Herrera, C.; Monsalve, A. Characterization of the mechanical behaviour of materials in the tensile test: Experiments and simulation. Model. Simul. Mater. Sci. Eng. 2004, 12, 425–444. [CrossRef]
Pacheco, M.; Celentano, D.; García–Herrera, C.; Méndez, J.; Flores, F. Numerical simulation and experimental validation of a multi-step deep drawing process. Int. J. Mater. Form. 2017, 10, 15–27. [CrossRef]
Yan, Y.; Wang, H.; Li, Q. The inverse parameter identification of Hill 48 yield criterion and its verification in press bending and roll forming process simulations. J. Manuf. Process. 2015, 20, 46–53. [CrossRef]
Kim, J.H.; Serpantie, A.; Barlat, F.; Pierron, F.; Lee, M.G. Characterization of the post-necking strain hardening behavior using the virtual fields method. Int. J. Solids Struct. 2013, 50, 3829–3842.
Rees, D.W.A. The Mechanics of Engineering Structures, 1st ed.; Imperial College Press: London, UK, 2015.
Banabic, D. Sheet Metal Forming Processes, 1st ed.; Springer: Berlin/Heidelberg, Germany, 2010.
Moré, J.J. The Levenberg-Marquardt algorithm: Implementation and theory. In Numerical Analysis. Lecture Notes in Mathematics; Watson, G.A., Ed.; Springer: Berlin/Heidelberg, Germany, 1978; Volume 630.
Ichikawa, K.; Kuwabara, T.; Coppieters, S. Forming simulation considering the differential work hardening behavior of a cold rolled interstitial-free steel sheet. In Material Forming ESAFORM 2014, Key Engineering Materials; Trans Tech Publications Ltd.: Stäfa-Zurich, Switzerland, 2014; Volume 611, pp. 56–61.
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