Theoretical Analysis of the Effects of Hardening Laws, Normal and Through Thickness Shear Stresses on Forming Limit Curves of AA6016-T4

Document Type : Research Article

Authors

Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran

Abstract

Forming limit Curves are one of the common tools to predict the necking in various forming processes. In this study, the Marciniak-Kuczynski instability theory by applying the Gotoh yield function is utilized to estimate the forming limit curves for the AA6016-T4 aluminum sheet in plane stress conditions. Also, the effect of three different hardening models including Swift, Voce, and a linear combination of the Swift and Voce models to determine the limit curves are investigated. The comparison between the theoretical forming limit curves and experimental results from the Nakajima test determines the accuracy of the hardening models in predicting the limit strains. Since in many new forming processes such as hydroforming and incremental sheet forming processes, investigation of the process in plane stress state is not an exact assumption, Therefore, in continuation of the paper, generalized forming limit curves are plotted based on the developed Marciniak-Kuczynski model by extending the Gotoh yield function, and the effect of compressive normal stress and through-thickness shear stress on forming limits of the sheet are investigated. The results indicated that by applying the compressive normal stress and through-thickness shear stresses, the limit strains increase, and the formability is improved, in contrast, limit stresses move down in the diagram.

Keywords

Main Subjects

References

[1] S.P. Keeler, W.A. Backhofen, Plastic instability and fracture in sheets stretched over rigid punches, Transactions of American Society of Metals, 56 (1964) 25–48.
[2] Z. Marciniak, K. Kuczyński, Limit strains in the processes of stretch-forming sheet metal, International journal of mechanical sciences, 9(9) (1967) 609-620.
[3] M. Ganjiani, A. Assempour, An improved analytical approach for determination of forming limit diagrams considering the effects of yield functions, Journal of materials processing technology, 182(1-3) (2007) 598-607.
[4] H.-b. WANG, W. Min, Y. Yu, Effect of flow stress—strain relation on forming limit of 5754O aluminum alloy, Transactions of Nonferrous Metals Society of China, 22(10) (2012) 2370-2378.
[5] Q.-T. Pham, S.-H. Oh, Y.-S. Kim, An efficient method to estimate the post-necking behavior of sheet metals, The International Journal of Advanced Manufacturing Technology, 98(9) (2018) 2563-2578.
[6] K. Young-Suk, L. Bong-Hyun, Y. Seung-Han, Prediction of forming limit curve for pure titanium sheet, Transactions of Nonferrous Metals Society of China, 28(2) (2018) 319-327.
[7] J. Zhang, R. Wang, Y. Zeng, Hydroforming rules and quality control parameters analysis for metal bipolar plate, Engineering Failure Analysis, 132 (2022) 105919.
[8] D. Banabic, S. Soare, On the effect of the normal pressure upon the forming limit strains, in:  Hora P (ed) Proceedings of the 7th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, 2008, pp. 199-204.
[9] J.M. Allwood, D.R. Shouler, Generalised forming limit diagrams showing increased forming limits with non-planar stress states, International journal of Plasticity, 25(7) (2009) 1207-1230.
[10] P. Eyckens, A. Van Bael, P. Van Houtte, Marciniak–Kuczynski type modelling of the effect of through-thickness shear on the forming limits of sheet metal, International Journal of Plasticity, 25(12) (2009) 2249-2268.
[11] A. Assempour, H.K. Nejadkhaki, R. Hashemi, Forming limit diagrams with the existence of through-thickness normal stress, Computational Materials Science, 48(3) (2010) 504-508.
[12] M. Nurcheshmeh, D.E. Green, Influence of out-of-plane compression stress on limit strains in sheet metals, International journal of material forming, 5(3) (2012) 213-226.
[13] R. Hashemi, K. Abrinia, Analysis of the extended stress-based forming limit curve considering the effects of strain path and through-thickness normal stress, Materials & Design (1980-2015), 54 (2014) 670-677.
[14] F. Zhang, J. Chen, J. Chen, X. Zhu, Forming limit model evaluation for anisotropic sheet metals under through-thickness normal stress, International Journal of Mechanical Sciences, 89 (2014) 40-46.
[15] A. Fatemi, B. Mollaei Dariani, Forming limit prediction of anisotropic material subjected to normal and through thickness shear stresses using a modified M–K model, The International Journal of Advanced Manufacturing Technology, 80(9) (2015) 1497-1509.
[16] S. Mirfalah-Nasiri, A. Basti, R. Hashemi, Forming limit curves analysis of aluminum alloy considering the through-thickness normal stress, anisotropic yield functions and strain rate, International Journal of Mechanical Sciences, 117 (2016) 93-101.
[17] S.M. Nasiri, A. Basti, R. Hashemi, A. Darvizeh, Effects of normal and through-thickness shear stresses on the forming limit curves of AA3104-H19 using advanced yield criteria, International Journal of Mechanical Sciences, 137 (2018) 15-23.
[18] Q. Hu, X. Li, J. Chen, Forming limit evaluation by considering through-thickness normal stress: theory and modeling, International Journal of Mechanical Sciences, 155 (2019) 187-196.
[19] S. Sojodi, A. Basti, S.R. Falahatgar, S.M.M. Nasiri, Investigation on the forming limit diagram of AA5754-O alloy by considering strain hardening model, strain path, and through-thickness normal stress, The International Journal of Advanced Manufacturing Technology, 113(9) (2021) 2495-2511.
[20] C. Wang, Y. Yi, S. Huang, F. Dong, H. He, K. Huang, Y. Jia, Experimental and theoretical investigation on the forming limit of 2024-O aluminum alloy sheet at cryogenic temperatures, Metals and Materials International, 27(12) (2021) 5199-5211.
[21] R. Uppaluri, D. Helm, A convex fourth order yield function for orthotropic metal plasticity, European Journal of Mechanics-A/Solids, 87 (2021) 104196.
[22] S.M. Mirfalah Nasiri, A. Basti, R. Hashemi, Numerical analysis of the effect of advanced yield criterion on prediction of strains and stresses in anisotropic aluminum sheets, Modares mechanical engineering, 15(8) (2015) 393-401(in persian).
[23] W. Hu, An orthotropic yield criterion in a 3-D general stress state, International Journal of Plasticity, 21(9) (2005) 1771-1796.
[24] M. Erfanian, R. Hashemi, A comparative study of the extended forming limit diagrams considering strain path, through-thickness normal and shear stress, International Journal of Mechanical Sciences, 148 (2018) 316-326.
Amirkabir Journal of Mechanical Engineering
Volume 54, Issue 6
September 2022
Pages 1391-1408

Files

Share

How to cite

Statistics