A Comparative Study on the Formability Prediction of Two-Layer Metallic Sheets

Document Type: Research Paper


Arak University of Technology


Two-layer metallic sheets have wide applications in aerospace, marine, automotive and domestic industries due to their superlative characteristics. In this paper, the formability of two-layer sheet is investigated through analytical, experimental and numerical approaches. An analytical model is developed based on Marciniak-Kuczynski method associated Hill’s non-quadratic yield criterion. Forming limit diagrams are also obtained numerically based on finite element method using Bifurcation theory and ductile fracture criteria. Furthermore, experiments are carried out on Al3105-St14 two-layer sheet. Theoretical results from various methods are compared with results obtained from experiments to evaluate the competency of discussed analytical and numerical methods to predict the formability of two-layer sheets. The results show that analytical and numerical approaches discussed in this paper have good capabilities to predict the formability of two-layer sheets. However, the analytical method based on M-K model and numerical approach based on bifurcation theory are more suitable to determine the forming limit diagram of Al3105-St14 two-layer sheets.


[1] S. P. Keeler, Circular grid system – a valuable aid for evaluating sheet metal formability, SAE Technical Paper, 77 (1968) 371–379.
[2] G. M. Goodwin, Application of strain analysis to sheet metal forming problems in press shop, SAE Transactions, 77 (1968) 380–387.
[3] S. L. Semiatin, H. R. Piehler, Formability of sandwich sheet materials in plane strain compression and rolling, Metallurgical Transactions A, 10 (1979), 97–107.
[4] S. L. Semiatin, H. R. Piehler, Deformation of sandwich sheet materials in uniaxial tension, Metallurgical Transactions A, 10 (1979) 85–96.
[5] T. Mori, S. Kurimoto, Press-formability of stainless steel and aluminum clad sheet, Journal of Materials Processing Technology, 56 (1996) 242–253.
[6] F. Yoshida, R. Hino, Forming limit of stainless steel-clad aluminum sheets under plane stress condition, Journal of Materials Processing Technology, 63 (1997) 66–71.
[7] -A. Jalali Aghchai, M. Shakeri, B. Mollaei Dariani, Theoretical and experimental formability study of two-layer metallic sheet Al1100/St12, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering manufacture, 222 (9) (2008) 1131–1138.
[8] -A.Jalali Aghchai, M. Shakeri, B. Mollaei Dariani, Influences of material properties of components on formability of two-layer metallic sheets, International Journal of Advanced Manufacturing Technoloogy, 66 (2012) 809–823.
[9] Z. Marciniak, K. Kuczynski, Limit strains in the processes of stretch-forming sheet metal, International Journal of Mechanical Sciences, 9 (1967) 609–620.
[10] J.Z. Gronostajski, Z. Zimniak, Theoretical simulation of sheet behavior in forming processes, Journal of Materials Processing Technology, 34 (1992) 457–464.
[11] M. Shakeri, A. Sadough, B.M. Dariani, Theoretical and Experimental Analysis of Sheet Metal Formability Limit, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering manufacture, 214 (2000) 821–827.
[12] -A.Assempour, M. Nurcheshmeh, The influence of material properties on the shape and level of the forming limit diagram, SAE Technical Paper, 01 (2003) 1149.
[13] R. Hill, Theoretical plasticity of textured aggregates, Mathematical Proceedings of the Cambridge Philosophical Society, 85 (1979) 179–620.
[14] M. Pishbin, P.P. Gillis, Forming limit diagrams calculated using Hill’s non-quadratic yield criterion Metallurgical Transactions A, 23 (1992) 1992-2817.
[15] J. Gronostajski, The effect of strain path on the plastic instability, Proceedings of the 3rd International Conference on the Technology of Plasticity, Kyoto, Japan, (1990), Vol. 3, 49-50.
[16] S. S. Hecker, A cup test for assessing stretchability, Metals Engineering Quarterly, 14, (1974), 30-36.
[17] S. Storen, J.R. Rice, Localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, 23 (1975) 421-441.
[18] -A.Petek, T. Pepelnjak, K. Kuzman, An improved method for determining forming limit diagram in digital environment, Journal of Mechanical Engineering, 51 (2005) 330-345.
[19] T. Pepelnjak, A. Petek, K. Kuzman, Analysis of the forming limit diagram in digital environmrnt, Advanced Material Research, 6-8 (2005) 697-704.
[20] M.G. Cockcroft, D.J. Latham, Ductility and the Workability of Metals, Journal of the Institute of Metals, 96 (1968) 33–39.
[21] S. I. Oh, C. C. Chen, S. Kobayashi, Ductile Fracture in Axisymmetric Extrusion and Drawing, Journal of Engineering for Industry-Transactions of the ASME, 101 (1979) 36-44.
[22] P. Brozzo, B. Deluca, R. Rendina, A New Method for the Prediction of Formability in Metal Sheets, Proceedings of the Seventh Biennial Conference of IDDRG on Sheet Metal Forming and Formability, (1972).