Main Article Content

Davood Hashempoor


In this paper, deep drawing process of functionally graded sheet is investigated analytically and using finite element method. Using equations for deep drawing of isotropic sheets and governing equations of functionally graded materials, equations for deep drawing of functionally graded sheets are derived. Mechanical properties of the functionally graded sheet vary through the thickness of it according to the exponential law distribution. Punch force and axial stresses at the wall are calculated by this analytical method. Also, using this force in abaqus software, axial stresses at the wall are determined. The results of two methods were compared with each other and good agreement was obtained.

Article Details


Deep drawing, FGM, Exponential law distribution, Finite element

[1] R. Lapovok, H.P. Ng, D. Tomus, Y. Estrin. Bimetallic copper–aluminium tube by severe plastic deformation. Scripta Materialia. 66 (2012) 1081-4.
[2] L. Ghalandari, M. Moshksar. High-strength and high-conductive Cu/Ag multilayer produced by ARB. Journal of Alloys and Compounds. 506 (2010) 172-8.
[3] M. Abbasi, M.R. Toroghinejad. Effects of processing parameters on the bond strength of Cu/Cu roll-bonded strips. Journal of Materials Processing Technology. 210 (2010) 560-3.
[4] S. Ohsaki, S. Kato, N. Tsuji, T. Ohkubo, K. Hono. Bulk mechanical alloying of Cu–Ag and Cu/Zr two-phase microstructures by accumulative roll-bonding process. Acta Materialia. 55 (2007) 2885-95.
[5] H. Akramifard, H. Mirzadeh, M. Parsa. Cladding of aluminum on AISI 304L stainless steel by cold roll bonding: Mechanism, microstructure, and mechanical properties. Materials Science and Engineering: A. 613 (2014) 232-9.
[6] I.-K. Kim, S.I. Hong. Effect of heat treatment on the bending behavior of tri-layered Cu/Al/Cu composite plates. Materials & Design. 47 (2013) 590-8.
[7] K. Wu, H. Chang, E. Maawad, W. Gan, H. Brokmeier, M. Zheng. Microstructure and mechanical properties of the Mg/Al laminated composite fabricated by accumulative roll bonding (ARB). Materials Science and Engineering: A. 527 (2010) 3073-8.
[8] L. Jiang, M.T. Pérez-Prado, P. Gruber, E. Arzt, O.A. Ruano, M. Kassner. Texture, microstructure and mechanical properties of equiaxed ultrafine-grained Zr fabricated by accumulative roll bonding. Acta Materialia. 56 (2008) 1228-42.
[9] D. Terada, S. Inoue, N. Tsuji. Microstructure and mechanical properties of commercial purity titanium severely deformed by ARB process. Journal of Materials Science. 42 (2007) 1673-81.
[10] E. Karajibani, R. Hashemi, M. Sedighi. Experimental determination of forming limit diagram in Aluminum-Copper twolayer metallic sheets. Science and Technology of Composites. 2 (2016) 45-50.
[11] L. Lang, J. Danckert, K.B. Nielsen. Multi-layer sheet hydroforming: Experimental and numerical investigation into the very thin layer in the middle. Journal of Materials Processing Technology. 170 (2005) 524-35.
[12] H. Tsukamoto. Impact compressive behavior of deep-drawn cups consisting of aluminum/duralumin multi-layered graded structures. Materials Science and Engineering: B. 198 (2015) 25-34.
[13] K. Bandyopadhyay, S. Panda, P. Saha, G. Padmanabham. Limiting drawing ratio and deep drawing behavior of dual phase steel tailor welded blanks: FE simulation and experimental validation. Journal of materials processing technology. 217 (2015) 48-64.
[14] C. Li, C. Chi, P. Lin, H. Zhang, W. Liang. Deformation behavior and interface microstructure evolution of Al/Mg/Al multilayer composite sheets during deep drawing. Materials & Design. 77 (2015) 15-24.
[15] A. Jalil, M.H. Gollo, M.M. Sheikhi, S.H. SEYEDKASHI. Hydrodynamic deep drawing of double layered conical cups. Transactions of Nonferrous Metals Society of China. 26 (2016) 237-47.
[16] M. Harhash, A. Carradò, H. Palkowski. Mechanical properties and forming behaviour of laminated steel/polymer sandwich systems with local inlays–Part 2: Stretching and deep drawing. Composite Structures. 160 (2017) 1084-94.
[17] W.F. Hosford, R.M. Caddell. Metal forming: mechanics and metallurgy. Cambridge University Press2011.
[18] M. Alinia, S. Ghannadpour. Nonlinear analysis of pressure loaded FGM plates. Composite Structures. 88 (2009) 354-9.
[19] A.G. Khiabani, R. Babazadeh. Design of robust fractional-order lead–lag controller for uncertain systems. IET Control Theory & Applications. 10 (2016) 2447-55.
[20] O.A. Ranjbar, A.N. Volkov. Kinetic and hydrodynamic simulations of laser-induced plume expansion. Early Career Tech J. (2016) 160-7.
[21] S. Esmaeili, M. Nasiri, N. Dadashi, H. Safari. Wave function properties of a single and a system of magnetic flux tube (s) oscillations. Journal of Geophysical Research: Space Physics. 121 (2016) 9340-55.
Mechanical Engineering

How to Cite

Hashempoor, D. (2019). Simulation and Analysis of Deep Drawing Process of the Functionally Graded Sheet. Mapta Journal of Mechanical and Industrial Engineering (MJMIE), 3(1), 1-8.