Finite-element modeling of super-plastic forming processes
Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 55-71.

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The present work is devoted to the development of the production of three-layered hollows structures made of VT6 titanium alloy by means of superplastic forming (SPF) and pressure welding. Finite-element modeling can be successfully applied to optimize the forming process, if the adequate constitutive relations would be defined and the friction at the contact surface of the material with the die would be specified. To find the friction coefficient and the parameters of the constitutive relations for metal forming process, test experiments are conducted to the forming of sheet into dies of various shapes. In such test experiments, a biaxial loading is realized, as in the actual processes of fabricating complicated structures from sheet by SPF. To this end, Finite-element modeling of the SPF process of sheet forming into dies of two types is performed: (i) into wedge die having cross section in the form of equilateral triangle, and (ii) cone die. Recommendations are given for the choice of the optimum angle at the vertex, determining the geometry of the dies, which results in the constancy of the stresses during forming at constant pressure. The methodology for estimating the coefficient of friction on the contact surface between sheet and die is given. Finite-element modeling of the SPF process of three-layer hollow structures is carried out using the parameters of the constitutive relations obtained by the proposed methods. Technological constraints on the geometric parameters of structures, such as the angle of inclination of the stiffening ribs and the thickness ratio of outer to inner sheet thicknesses are established, which provides forming without the formation of folds on the shell and the minimum variability of ribs thickness.
Keywords: superplastic forming, die, three-layered hollow structure, finite element method.
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A. Kh. Akhunova; R. R. Mulyukov; R. V. Safiullin. Finite-element modeling of super-plastic forming processes. Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 55-71. http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a4/

[1] Bonet J., Gil A., Wood R. D., Said R., Curtis R. V., “Simulating superplastic forming”, Computer Methods in Applied Mechanics and Engineering, 195:48–49 (2006), 6580–6603 | DOI | MR | Zbl

[2] Pradeep P., Ayyanar S., Balasubramanian M., Ramanathan K., Senthilkumar V. S., “Advanced Finite Element Analysis and Simulation in Superplastic Forming Process of Stepped Semispherical Die”, Journal of Applied Sciences, 12:10 (2012), 1048–1052 | DOI | MR

[3] Strength analysis system Fidesys, 2012 (Accessed 5 August 2017)

[4] Levin V.A., Zingerman K.M., Exact and approximate analytical solutions for finite deformations and their imposition, Fizmatlit, M., 2016

[5] Levin V.A., Kalinin V.V., Zingerman K.M., Vershinin A.V., Development of defects in finite deformations. Computer and physical modeling, Fizmatlit, M., 2007, 392 pp.

[6] Levin V.A., Morozov Ye.M., Matviyenko Yu.G., Selected nonlinear problems of fracture mechanics, Fizmatlit, M., 2004, 407 pp.

[7] Akhunova A., Dmitriev S., Kruglov A., Safiullin R., “Constitutive relations for superplastic flow modeling from two axial loading experiments”, Key Engineering Materials, 433 (2010), 319–323 | DOI

[8] Levin V.A., Zingerman K.M., “On the construction of effective constitutive relations for porous elastic materials subjected to finite deformations including the case of their superposition”, Doklady RAN, 382:4 (2002), 482–487

[9] Simulation designed for designers, https://www.sim4design.com/en/index

[10] Lederich R. J., Sastry S. M. L., Hayase M., Mackay T. L., “Superplastic formability testing”, Journal of Metals, 34:8 (1982), 16–20

[11] Ghosh A. K., Hamilton C. H., “On constant membrane stress test for superplastic metals”, Metallurgical Transactions A, 11:11 (1980), 1915–1918 | DOI

[12] Akhunova A.Kh., Dmitriev S.V., “Optimization of the shape of dies for test superplastic forming of sheet”, Russian metallurgy (Metally), 2009, no. 11, 40–44

[13] Akhunova A.Kh., Dmitriev S.V., Kruglov A.A., Safiullin R.V., “Superplastic forming of sheet into wedge die”, Russian metallurgy (Metally), 2010, no. 9, 38–41

[14] Panchenko Ye.V., Alekseyev P.A., “Effect of contact friction on the formation of thin-walled shells in the superplasticity regime”, Forging and Stamping Production. Material Working by Pressure, 2012, no. 7, 37–40

[15] Akhunova A.Kh., Dmitriev S.V., Kruglov A.A., Safiullin R.V., “Method for estimating the friction coefficient for superplastic forming of sheet into cone die”, Forging and Stamping Production. Material Working by Pressure, 2009, no. 6, 15–19

[16] Petrov Ye.N., Rodionov V.V., Kuz'min E.N., Lutfullin R.Ya., Safiullin R.V., Cellular structures, RFYATS-VNIITF, Snezhinsk, 2008, 176 pp.

[17] Safiullin R.V., “Superplastic forming and pressure welding of multilayer hollow structures. Part I. International experience”, Letters on materials, 2:1(5) (2012), 32–35

[18] Safiullin R.V., “Superplastic forming and pressure welding of multilayer hollow structures. Part II. Experience of IMSP RAS”, Letters on materials, 2:1(5) (2012), 36–39

[19] Morozov M.A., Trifonov V.G., Kharin S.A., Safiullin R.V., Mulyukov R.R., Manapov I.U., Inozemtsev A.A., Pavlinich S.P., Artyukhov A.V., Method of manufactured hollow fan blade, Pat. No 2555274, B21D 53/78, Institute for Metals Superplasticity Problems RAS, UEC-Aviadvigatel, 2015

[20] Temis Yu.M., Khudyakov A.P., “Mathematical modeling of isothermal stamping and superplastic forming operations for manufacturing a hollow fan blade”, Vestnik UGATU, 19:3(69) (2015), 50–60

[21] Akhunova A.Kh., Dmitriyev S.V., Kruglov A.A., Safiullin R.V., “Modeling of the process of superplastic forming of hollow structures with goffred filler produced from titanium alloy Ti-6Al-4V”, Journal of Advanced Materials, 2011, no. 12, 42–44

[22] Akhunova A.Kh., Dmitriyev S.V., Kruglov A.A., Safiullin R.V., “Modeling of the process of superplastic forming of three-layer hollow structures for determining constraints on their geometric parameters”, Russian metallurgy (Metally), 2012, no. 11, 38–41

[23] Akhunova A.Kh., Pshenichnyuk A.I., Dmitriyev S.V., Safiullin A.R., Safiullin R.V., “Optimization of parameters of superplastic forming of hollow three-layer structures”, Russian metallurgy (Metally), 2013, no. 7, 33–38

[24] Safiullin A. R., Safiullin R. V., Safin F. F., Akhunova A. Kh., Dmitriyev S. V., “Optimization of the process of superplastic forming of three-layer hollow structures”, Journal of advanced materials, 2013, no. 15, 114–118