Prediction of Localized Necking Based on Crystal Plasticity: Comparison of Bifurcation and Imperfection Approaches

Abstract:

In the present work, a powerful modeling tool is developed to predict and analyze the onset of strain localization in polycrystalline aggregates. The predictions of localized necking are based on two plastic instability criteria, namely the bifurcation theory and the initial imperfection approach. In this tool, a micromechanical model, based on the self-consistent scale-transition scheme, is used to accurately derive the mechanical behavior of polycrystalline aggregates from that of their microscopic constituents (the single crystals). The mechanical behavior of the single crystals is developed within a large strain rate-independent constitutive framework. This micromechanical constitutive modeling takes into account the essential microstructure-related features that are relevant at the microscale. These microstructural aspects include key physical mechanisms, such as initial and induced crystallographic textures, morphological anisotropy and interactions between the grains and their surrounding medium. The developed tool is used to predict sheet metal formability through the concept of forming limit diagrams (FLDs). The results obtained by the self-consistent averaging scheme, in terms of predicted FLDs, are compared with those given by the more classical full-constraint Taylor model. Moreover, the predictions obtained by the imperfection approach are systematically compared with those given by the bifurcation analysis, and it is demonstrated that the former tend to the latter in the limit of a vanishing size for the initial imperfection.

• Periodical: Key Engineering Materials (Volume 716)
• Pages: 779-789
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.716.779
• Online since: October 2016
• Authors: Holanyo K. Akpama, Mohammed Bettaieb, Farid Abed-Meraim*
• Keywords: Bifurcation Theory, Crystal Plasticity, Forming Limit Diagram (FLD), Imperfection Approach, Microstructure-Ductility Relationships, Plastic Instabilities, Self-Consistent Scale Transition

References

[1] S.P. Keeler, W.A. Backofen, Plastic instability and fracture in sheets stretched over rigid punches, Trans. ASM 56 (1963) 25-48.

[2] G.M., Goodwin, Application of strain analysis to sheet metal forming problems in press shop, Metallurgica Italiana 60 (1968) 767-744.

[3] R. Hill, On discontinuous plastic states, with special reference to localized necking in thin sheets, J. Mech. Phys. Solids 1 (1952) 19-30.

DOI: 10.1016/0022-5096(52)90003-3

[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

[5] E. Schmid, W. Boas, Plasticity of Crystals, Chapman and Hall, London, (1935).

[6] P. Lipinski, M. Berveiller, E. Reubrez, J. Morreale, Transition theories of elastic-plastic deformation of metallic polycrystals, Arch. Appl. Mech. 65 (1995) 291-311.

DOI: 10.1007/bf00789222

[7] J.R. Rice, The localization of plastic deformation, in: 14th International Congress of Theoretical and Applied Mechanics, 1976, pp.207-220.

[8] 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, Int. J. Num. Meth. Eng (2016) doi: 10. 1002/nme. 5215.

DOI: 10.1002/nme.5215

[9] R. Hill, Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids 13 (1965) 89-101.

DOI: 10.1016/0022-5096(65)90023-2

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

DOI: 10.1016/j.ijplas.2013.02.001

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

DOI: 10.1016/j.ijplas.2014.09.003