A Comparative Study of Forming Limit Diagrams Predicted by Two Different Plasticity Theories Involving Vertex Effects

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The main objective of this contribution is to compare the Forming Limit Diagrams (FLDs) predicted by the use of two different vertex theories. The first theory is micromechanical and is based on the use of the Schmid law, within the framework of crystal plasticity coupled with the Taylor scale-transition scheme. The second theory is phenomenological and is based on the deformation theory of plasticity. For both theories, the mechanical behavior is formulated in the finite strain framework and is assumed to be isotropic and rate-independent. The theoretical framework of these approaches will be presented in details. In the micro-macro modeling, the isotropy is ensured by considering an isotropic initial texture. In the phenomenological modeling, the material parameters are identified on the basis of micro-macro simulations of tensile tests.

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Key Engineering Materials (Volumes 651-653)

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21-26

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July 2015

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© 2015 Trans Tech Publications Ltd. All Rights Reserved

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[1] A. Considère, Mémoire sur l'emploi du fer et de l'acier dans les constructions, Ann. Ponts et Chausées. 9 (1885), 574-775.

Google Scholar

[2] D.C. Drucker, Some implications of work hardening and ideal plasticity, Q. Appl. Math. 7 (1950), 411-418.

DOI: 10.1090/qam/34210

Google Scholar

[3] R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, J. Mech. Phys. Solids. 6 (1958), 239-249.

Google Scholar

[4] Z. Marciniak, K. Kuczynski, Limit strains in processes of stretch-forming sheet metal, Int. J. Mech. Sci. 9 (1967), 609-620.

DOI: 10.1016/0020-7403(67)90066-5

Google Scholar

[5] S. Stören, J.R. Rice, Localized necking in thin sheets, J. Mech. Phys. Solids 23 (1975), 421-441.

DOI: 10.1016/0022-5096(75)90004-6

Google Scholar

[6] M. Ben Bettaieb, F. Abed-Meraim, Investigation of localized necking in substrate-supported metal layers: Comparison of bifurcation and imperfection analyses, International Journal of Plasticity 65 (2015), 168-190.

DOI: 10.1016/j.ijplas.2014.09.003

Google Scholar

[7] J.W. Hutchinson, K.W. Neale, Sheet necking – II. Time-independent behavior. In: Koistinen, D.P., Wang, N.M. (Eds. ), Mechanics of Sheet Metal Forming. Plenum, 1978, pp.127-153.

DOI: 10.1007/978-1-4613-2880-3_6

Google Scholar

[8] K. Yoshida, M. Kuroda, Numerical investigation on a key factor in superior stretchability of face-centered cubic polycrystalline sheets, Int. J. Mech. Sci., 58 (2012), 47-56.

DOI: 10.1016/j.ijmecsci.2012.02.009

Google Scholar

[9] G. Franz, F. Abed-Meraim, M. Berveiller, Strain localization analysis for single crystals and polycrystals: Towards microstructure–ductility linkage, International Journal of Plasticity 48 (2013), 1-33.

DOI: 10.1016/j.ijplas.2013.02.001

Google Scholar

[10] J.W. Hutchinson, V. Tvergaard, Shear band formation in plane-strain, Int. J. Solids Struct., 17 (1981), 451-470.

DOI: 10.1016/0020-7683(81)90053-6

Google Scholar

[11] H.K. Akpama, M. Ben Bettaieb, F. Abed-Meraim, Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms, submitted to Comput. Meth. Appl. Mech. Eng.

DOI: 10.1002/nme.5215

Google Scholar

[12] C. Miehe, J. Schröder, J. Schotte, 1999. Computational homogenization analysis in finite plasticity. Simulation of texture development in polycrystalline materials. Comput. Meth. Appl. Mech. Eng. 171, 387-418.

DOI: 10.1016/s0045-7825(98)00218-7

Google Scholar