Modares Mechanical Engineering

Modares Mechanical Engineering

Investigation of formability limit of metallic sheets subjected to non-proportional biaxial loading based on anisotropic diffuse and vertex localized plastic instability models

Authors
Asghar Zajkani
Ali Bandizaki
- Department of Mechanical Engineering, Imam Khomeini International University, Qazvin, Iran
Abstract
In this paper, an analytical path-dependent plastic instability model is proposed for the thin metallic sheets through considering a linear pre-straining path for the both diffuse and localized necking. The model is introduced by extending a modified maximum force (MMFC) that the MMFC considers the strain hardening on the diffuse necking as well as the loading conditions. Also, the vertex criterion will be used to prediction of localized necking. The vertex criterion presented by Sto ̈ren and Rice are usually based on the J_2 deformation theory of classical plasticity, which explores the localized necking through the rate discontinuity assumption at the necking band. Both models will be combined with the strain path effect through a linear adoption of an equivalent strain. It will be investigated by applying a pre-strain in the major and minor directions for prediction of the formability in the non-proportional loading. Moreover, a dependent to yield criterion (DYC) - angle is used for prediction of the necking band angle in the vertex theory. Finally, the quadratic Hill criterion is used to investigate the anisotropy effect. The model is verified by experimental results presented by other authors.
Keywords
Plastic instability
Diffuse and localized necking
Vertex model
MMFC model
Strain path
[1] M. Considère, L’emploi du fer et de l’acier dans les constructions, Ann. des ponts chaussées, Vol. 1, pp. 574–775, 1885.
[2] H. W. Swift, Plastic instability under plane stress, Journal of the Mechanics and Physics of Solids, Vol. 1, No. 1, pp. 1–18, 1952.
[3] P. Hora, L. Tong, B. Berisha, Modified maximum force criterion, a model for the theoretical prediction of forming limit curves, International Journal of Material Forming, Vol. 6, No. 2, pp. 267–279, 2013.
[4] R. Hill, On discontinuous reference plastic states, with special to localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, Vol. 1, No. 2, pp. 19–30, 1952.
[5] Z. Marciniak, K. Kuczyński, Limit strains in the processes of stretch-forming sheet metal, International Journal of Mechanical Sciences, Vol. 9, No. 9, pp. 609IN1613-612IN2620, 1967.
[6] M. Aghaie-Khafri, R. Mahmudi, Predicting of plastic instability and forming limit diagrams, Interernational Journal of Mechanical Sciences, Vol. 46, No. 9, pp. 1289–1306, 2004.
[7] M. Hosseinpour Gollo, S.M.H. Seyedkashi, N. Valian Iraj, The effects of Hosford, Hill’s quadratic and non-quadratic yield criteria on prediction of forming limit diagrams based on MK Model, Modares Mechecanical Engineering, Vol. 14, No. 5, pp. 137-146, 2014 (In Persian)
[8] M. Saradar, A. Basti, M. Zaeimi, Numerical study of the effect of strain rate on damage prediction by dynamic forming limit diagram in high velocity sheet metal forming, Modares Mechecanical Engineering, Vol. 14, No. 16, pp. 212–222, 2015. (In Persian فارسی(
[9] R. Hashemi, K. Abrinia, Analysis of the extended stress-based forming limit curve considering the effects of strain path and through-thickness normal stress, Material and Design, Vol. 54, No. 1, pp. 670–677, 2014.
[10] S. Stören, J. R. Rice, Localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, Vol. 23, No. 6, pp. 421–441, 1975.
[11] A. Graf, W. Hasford, The influence of strain-path changes on forming limit diagrams of a1 6111 t4, International Journal of Mechanical Sciences, Vol. 36, No. 10, pp. 897–910, 1994.
[12] H. Li, G. Li, G. Gao, W. Zhang, X. Wu, A formability evaluation method for sheet metal forming with non-linear strain path change, International Journal of Material Forming, pp. 1–13, 2017.
[13] D. S. Comsa, G. Dragos, L. Paraianu, D. Banabic, Prediction of the forming limit band for steel sheets using a new formulation of hora ’ s criterion (MMFC), American Institute physics, International Confrence on Advances in Materials and Proccesing Technology, Vol. 1315, No. 1, pp. 425–431, 2011.
[14] X. Zhu, K. Weinmann, A. Chandra, A unified bifurcation analysis of sheet metal forming limits, Journal of Engineering Material Technology, Vol. 123, No. 3, pp. 329, 2001.
[15] A. Zajkani, A. Bandizaki, An efficient model for diffusion to localized necking evolution in rate dependent bifurcation analysis of metallic sheets, International Journal of Mechanical Sciences, Vol. 58, No. 7, pp. 794–803, 2017.
[16] M. W. Fu, W. L. Chan, Micro-scaled Products Development via Microforming, Springer series in advanced manufacturing, Springer, London. Vol. 10, No. 1007, pp. 978-1, 2014.
Modares Mechanical Engineering
Volume 18, Issue 1
March 2018
Pages 211-218