On capturing rate-dependent anisotropic behavior of sheet metal forming using a viscoplastic computational framework

References

• B. Smith, A. Spulber, S. Modi, and T. Fiorelli, Technology Roadmaps: Intelligent Mobility Technology, Materials and Manufacturing Processes, and Light Duty Vehicle Propulsion, Center for Automotive Research, Ann Arbor, MI, 2017.
   Google Scholar
• Chang, K.-H., Product manufacturing and cost estimating using CAD/CAE, Elsevier, pp. 134–135, 2015.
   Google Scholar
• D. Banabic, Sheet Metal Forming Process: Constitutive Modelling and Numerical Simulation, Springer, 2010. doi:10.1007/978-3-540-88113-1
   Google Scholar
• H.-C. Wu, Anisotropic plasticity for sheet metals using the concept of combined isotropic-kinematic hardening, Int. J. Plast., vol. 18, no. 12, pp. 1661–1682, 2002. DOI: 10.1016/S0749-6419(01)00060-2.
   Web of Science ®Google Scholar
• J. Coer, H. Laurent, M. C. Oliveira, P.-Y. Manach, and L. F. Menezes, Detailed experimental and numerical analysis of a cylindrical cup deep drawing: Pros and cons of using solid-shell elements, Int. J. Mater. Form., vol. 11, no. 3, pp. 357–373, 2018. DOI: 10.1007/s12289-017-1357-4.
   Web of Science ®Google Scholar
• Z. Chen, J. Zhao, and G. Fang, Finite element modeling for deep-drawing of aluminum alloy sheet 6014-T4 using anisotropic yield and non-AFR models, Int. J. Adv. Manuf. Technol., vol. 104, no. 1–4, pp. 535–549, 2019. DOI: 10.1007/s00170-019-03921-w.
   Web of Science ®Google Scholar
• B. Wu, H. Wang, T. Taylor, and J. Yanagimoto, A non-associated constitutive model considering anisotropic hardening for orthotropic anisotropic materials in sheet metal forming, Int. J. Mech. Sci., vol. 169, p. 105320, 2020. DOI: 10.1016/j.ijmecsci.2019.105320.
   Web of Science ®Google Scholar
• B. Wu, K. Ito, N. Mori, T. Oya, T. Taylor, and J. Yanagimoto, Constitutive equations based on non-associated flow rule for the analysis of forming of anisotropic sheet metals, Int. J. Precis. Eng. Manuf.-Green Tech., vol. 7, no. 2, pp. 465–480, 2020. DOI: 10.1007/s40684-019-00032-5.
   Web of Science ®Google Scholar
• Z. He, K. Zhang, H. Zhu, Y. Lin, M. W. Fu, and S. Yuan, An anisotropic constitutive model for forming of aluminum tubes under both biaxial tensión and pure shear stress states, Int. J. Plast., vol. 152, p. 103259, 2022. DOI: 10.1016/j.ijplas.2022.103259.
   Web of Science ®Google Scholar
• H. Rong, P. Hu, L. Ying, W. Hou, and M. Dai, Modeling the anisotropic plasticity and damage of AA7075 alloy in hot forming, Int. J. Mech. Sci., vol. 215, p. 106951, 2022. DOI: 10.1016/j.ijmecsci.2021.106951.
   Web of Science ®Google Scholar
• D. C. Ahn, J. W. Yoon, and K. Y. Kim, Modeling of anisotropic plastic behavior of ferritic stainless Steel sheet, Int. J. Mech. Sci., vol. 51, no. 9–10, pp. 718–725, 2009. DOI: 10.1016/j.ijmecsci.2009.08.003.
   Web of Science ®Google Scholar
• M. Dzoja, V. Cvitanic, M. Safaei, and L. Krstulovic-Opara, Modelling the plastic anisotropy evolution of AA5754-H22 sheet and implementation in predicting cylindrical cup drawing process, Eur. J. Mech./A Solids, vol. 77, p. 103806, 2019. DOI: 10.1016/j.euromechsol.2019.103806.
   Web of Science ®Google Scholar
• S. Kalpakjian and S. R. Schmid, Manufacturing Engineering and Technology-Sixth Edition in SI Units, Prentice Hall, 2009.
   Google Scholar
• J. L. Chaboche, A review of some plasticity and viscoplasticity constitutive theories, Int. J. Plast., vol. 24, no. 10, pp. 1642–1693, 2008. DOI: 10.1016/j.ijplas.2008.03.009.
   Web of Science ®Google Scholar
• S. Bodner and Y. Partom, Constitutive equations for elastic viscoplastic strain-hardening materials, Trans. ASME, J. Appl. Mech., vol. 42, no. 2, pp. 385–389, 1975. DOI: 10.1115/1.3423586.
   Web of Science ®Google Scholar
• F. Zerilli and R. Armstrong, Dislocation mechanics based constitutive relations for material dynamics calculations, J. Appl. Phys., vol. 61, no. 5, pp. 1816–1825, 1987. DOI: 10.1063/1.338024.
   Web of Science ®Google Scholar
• G. Johnson and W. Cook, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng. Fract. Mech., vol. 21, no. 1, pp. 31–48, 1985. DOI: 10.1016/0013-7944(85)90052-9.
   Web of Science ®Google Scholar
• S. Cowper and P. Symonds, Strain hardening and strain-rate effects in the impact loading of cantiléver beams, Technical Report No. 28, Division of Applied Mathematics Brown University, 1957.
   Google Scholar
• S. Nemat-Nasser and Y. Li, Flow stress of FCC polycrystals with application to OFHC Cu, Acta Mater., vol. 46, no. 2, pp. 565–577, 1998. DOI: 10.1016/S1359-6454(97)00230-9.
   Web of Science ®Google Scholar
• G. Voyiadjis and A. Almasri, A physically based constitutive model for FCC metals with applications to dynamic hardness, Mech. Mater., vol. 40, no. 6, pp. 549–563, 2008. DOI: 10.1016/j.mechmat.2007.11.008.
   Web of Science ®Google Scholar
• E. Voce, The relationship between stress and strain for homogeneous deformation, J. Inst. Met., vol. 74, pp. 537–546, 1948.
   Google Scholar
• U. Kocks and H. Mecking, Physics and phenomenology of strain hardening: The FCC case, Prog. Mater. Sci., vol. 48, no. 3, pp. 171–273, 2003. DOI: 10.1016/S0079-6425(02)00003-8.
   Web of Science ®Google Scholar
• D. Steinberg, S. Cochran, and M. Guinan, A constitutive model for strain rates from 10−4 to 106 s−1, J. Appl. Phys., vol. 51, no. 3, pp. 1498–1504, 1980. DOI: 10.1063/1.327799.
   Web of Science ®Google Scholar
• R. Austin and D. McDowell, A dislocation-based constitutive model for viscoplastic deformation of FCC metals at very high strain rates, Int. J. Plast., vol. 27, no. 1, pp. 1–24, 2011. DOI: 10.1016/j.ijplas.2010.03.002.
   Web of Science ®Google Scholar
• B. Tang and Y. Lou, Effect of anisotropic yield functions on the accuracy of material flow and its experimental verification, Acta Mech. Solida Sin., vol. 32, no. 1, p. 50, 2019. DOI: 10.1007/s10338-018-0043-5.
   Web of Science ®Google Scholar
• J. Lee, H. J. Bong, D. Kim, Y.-S. Lee, Y. Choi, and M.-G. Lee, Mechanical properties and formability of heat-treated 7000-series high-strength aluminum alloy: Experiments and finite element modeling, Met. Mater. Int., vol. 26, no. 5, pp. 682–694, 2020. DOI: 10.1007/s12540-019-00353-9.
   Web of Science ®Google Scholar
• R. Hill, A theory of yielding and plastic flow anisotropic metals, Proc. R. Soc. Lon. A, vol. 193, pp. 281–297, 1948.
   Web of Science ®Google Scholar
• J. J. Skrzypek, Plasticity and Creep, R. B. Hetnarski (ed.), London CRC Press Inc, 2000.
   Google Scholar
• J. L. Chaboche and G. Rousselir, On the plastic and viscoplastic constitutive equations: Part I – Rules developed with internal variable concept, Trans. ASME, J. Press. Vessel Technol., vol. 105, no. 2, pp. 153–158, 1983. DOI: 10.1115/1.3264257.
   Web of Science ®Google Scholar
• F. Dunne and N. Petrinic, Introduction to Computational Plasticity, Oxford University Press, 2005.
   Google Scholar
• C. Hernandez, A. Maranon, I. A. Ashcroft, and J. P. Casas-Rodriguez, A computational determination of the Cowper-Symonds parameters from a single Taylor test, Appl. Math. Modell., vol. 37, no. 7, pp. 4698–4708, 2013. DOI: 10.1016/j.apm.2012.10.010.
   Web of Science ®Google Scholar
• S. Yuen and G. Nurick, Experimental and numerical studies on the response of quadrangular stiffened plates: Part I: Subjected to uniform blast load, Int. J. Impact Eng., vol. 31, no. 1, pp. 55–83, 2005. DOI: 10.1016/j.ijimpeng.2003.09.048.
   Web of Science ®Google Scholar
• G. Nurick and J. Martin, Deformation of thin plates subjected to impulsive loading – a review Part II: Experimental studies, Int. J. Impact Eng., vol. 8, no. 2, pp. 171–186, 1989. DOI: 10.1016/0734-743X(89)90015-8.
   Web of Science ®Google Scholar
• M. Olson, G. Nurick, and J. Fagnan, Deformation and rupture of blast loaded square plates – predictions and experiments, Int. J. Impact Eng., vol. 13, no. 2, pp. 279–292, 1993. DOI: 10.1016/0734-743X(93)90097-Q.
   Web of Science ®Google Scholar
• K. Ramajeyathilagam, C. P. Vendhan, and V. Bhujanga Rao, Non-linear transient dynamic response of rectangular plates under shock loading, Int. J. Impact Eng., vol. 24, no. 10, pp. 999–1015, 2000. DOI: 10.1016/S0734-743X(00)00018-X.
   Web of Science ®Google Scholar
• Y. Yuan and P. Tan, Deformation and failure of rectangular plates subjected to impulsive loadings, Int. J. Impact Eng., vol. 59, pp. 46–59, 2013. DOI: 10.1016/j.ijimpeng.2013.03.009.
   Web of Science ®Google Scholar
• A. Skrlec and J. Klemenc, Estimating the strain-rate-dependent parameters of the Cowper-Symonds and Johnson-Cook material models using Taguchi arrays, SV-JME, vol. 62, no. 4, pp. 220–230, 2016. DOI: 10.5545/sv-jme.2015.3266.
   Google Scholar
• Dassault Systemes Simulia Corp., Abaqus 6.12 documentation, 2012.
   Google Scholar
• A. Bhaduri, Mechanical Properties and Working of Metals and Alloys, Springer Series in Material Science, Vol. 264, Springer Nature, Singapore, 2018.
   Google Scholar
• E. E. Michaelis, The r and n test for every day testing in the sheet metal industry, Sheet Met Ind., vol. 56, no. 10, pp. 936–941, 1979.
   Google Scholar
• S.P. Keeler, Properties related to forming, Sheet Met. Ind., vol. 48, no. 7, pp. 511–517, 1971.
   Google Scholar
• J. Willis, J. C. Blade, A proposed earing test for sheet metal, Sheet Met Ind., vol. 4, pp. 316, 1966.
   Google Scholar
• O. H. Kemmis, The assessment of the drawing and forming qualitites of sheet metal by the Swift Cup-Forming Test, Sheet Met Ind., vol. 34, pp. 203, 1957.
   Google Scholar
• S. L. Semiatin, Metalworking: Bulk Forming, ASM Handbook, ASM International, Materials Park, OH, 2005.
   Google Scholar
• L. S. Lasdon, A. D. Waren, A. Jain, and M. Ratner, Design and testing of generalized reduced gradient code for non-linear programming, ACM Trans. Math. Softw., vol. 4, no. 1, pp. 34–50, 1978. DOI: 10.1145/355769.355773.
   Google Scholar
• A. Maia, E. Ferreira, M. C. Oliveira, L. F. Menezes, and A. Andrade-Campos, Numerical optimization strategies for springback compensation in sheet metal forming, Comput. Methods Prod. Eng., pp. 51–82, 2017.
   Google Scholar
• A. Afdhal, L. Gunawan, S. P. Santosa, I. S. Putra, and H. Huh, Measurement of mechanical properties of St 37 material at high strain rates using a split Hopkinson pressure bar, AMM, vol. 660, pp. 562–566, 2014. DOI: 10.4028/www.scientific.net/AMM.660.562.
   Google Scholar
• N. Jones, Structural Impact, Cambridge University Press, 2003.
   Google Scholar
• D. D. Fuller, Theory and Practice of Lubrication for Engineers, 2nd ed., Wiley-Interscience, 1984.
   Google Scholar