Superplastic deformation of thin sheets is widely used in aerospace, automotive and other industries. In this paper, a mathematical model of plane strain superplastic pressure forming of a sheet specimen into a die is proposed. A die under consideration has a shape of a long box with an isosceles trapezoid cross section, but the model can be generalized for more complex die shapes. It is assumed that sticking happens between a shell and a die and thickness remains unchanged once contact occurs. The process of forming was divided into different phases, which are determined by the die geometry. For each phase, ordinary differential equations for thickness were derived along with the initial conditions. Solutions of obtained ODEs allow estimating the shell thickness at any point of a specimen as a function of coordinate along walls of the die and to determine the duration of each superplastic pressure forming phase for a given pressure-time function. Norton’s power law was used as a constitutive equation. Due to the simplicity of Norton`s law it is possible to solve some of ODEs analytically. The proposed model can be used with other types of constitutive relations, in particular with relations that include microstructure parameters etc. The superplastic forming of a Ti-6Al-4V titanium alloy sheet for the piecewise pressure-time function has been modelled. Some special cases of die geometry are analyzed.
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Among the practical applications of the phenomenon of superplasticity, the technique of superplastic forming (SPF) has acquired particular importance [1– 4]. Since the 1960s, superplastic forming of metal alloy sheets has become one of the main applications of superplasticity in various industries. The work by Jovane [5] appears to be the first research to analyze the bulging of a circular sheet clamped at its perimeter. The assumption of a uniform thickness for SPF of circular sheets, however, leads to a contradiction of the boundary conditions and hypothesis that the membrane holds the spherical shape at the deformation, as was observed by researchers (see, for example [1]). Furthermore, the thickness non-uniformity remains one of the important technical problems concerning SPF. A number of studies are devoted to solving the axisymmetric problem of the SPF of a round membrane (see, for example, [5 –19]). These SPF studies include analytical, experimental and FEM analyses.
Список литературы
1. K. A. Padmanabhan, R. A. Vasin, F. U. Enikeev, Superplastic Flow: Phenomenology and mechanics, Berlin-Heidelberg: Springer-Verlag, Berlin, 2001, 363 p. DOI: 10.1007/978-3-662-04367-7
2. Р. А. Васин, Ф. У. Еникеев, Введение в механику сверхпластичности. Т1, Гилем, Уфа, 2001, 280 с.
3. Н. Н. Малинин, Ползучесть в обработке металлов, Машиностроение, Москва, 1986, 222 с.
4. D. Sorgente, Superplasticity and Superplastic Forming, Metals 11 (2021) 946. DOI: 10.3390/met11060946
5. F. Jovane, An approximate analysis of the superplastic forming of a thin circular diaphragm: Theory and experiments, International Journal of Mechanical Sciences 10, 5 (1968) 403 - 427. DOI: 10.1016/0020-7403(68)90005-2
6. N. Chandra, D. Kannan, Superplastic sheet metal forming of a generalized cup. Part I: Uniform thinning, JMEP 1 (1992) 801- 810. DOI: 10.1007/BF02658264
7. N. Chandra, D. Kannan, Superplastic sheet metal forming of a generalized cup. Part II: Nonuniform thinning, JMEP 1 (1992) 813 - 822. DOI: 10.1007/BF02658265
8. А. А. Круглов, В. Р. Ганиева, О. П. Тулупова, Ф. У. Еникеев, Методы расчета продолжительности сверхпластической формовки круглой мембраны, Изв. ВУЗов, Цвет. Мет. 2 (2017) 66 - 75. DOI: 10.17073/0021-3438-2017-2-66-75
9. D. L. Holt, An analysis of the bulging of a superplastic sheet by lateral pressure, Int. Journal of Mech. Sci. 12, 6 (1970) 491- 497. DOI: 10.1016/0020-7403(70)90076-7
10. P. Guglielmi, D. Sorgente, A. Lombardi, G. Palumbo, A new experimental approach for modelling the constitutive behaviour of sheet metals at elevated temperature through interrupted bulge tests, Int. Journal of Mech. Sci. 184 (2020) 105839. DOI: 10.1016/j.ijmecsci.2020.105839
11. Т. А. Белякова, И. А. Гончаров, Влияние микроструктуры металлического сплава на распределение толщины в круглой пластине при сверхпластической формовке давлением, Вестн. СамУ, Естественнонаучн. сер. 26, 2 (2020) 50 - 62. DOI: 10.18287/2541-7525-2020-26-2-50-62
12. L. García-Barrachina, D. Sorgente, L. Tricarico, A. J. Gámez, A method for estimating superplastic material parameters via free-inflation tests, JMRT 11 (2021) 1387 -1395. DOI: 10.1016/j.jmrt.2021.01.116
13. R. V. Safiullin, V. A. Valitov, R. Y. Lutfullin, E. V. Galieva, E. Y. Klassman, Superplastic forming of EK61 nickel-based superalloy with ultrafine-grained structure, Lett. Mater. 12, 4s (2022) 439 - 444. DOI: 10.22226/2410-3535-2022-4-439-444
14. M. R. Shagiev, A. A. Kruglov, O. A. Rudenko, M. A. Murzinova, Superplastic forming of titanium alloys at 700°C, Lett. Mater. 12, 4 (2022) 332 - 335. DOI: 10.22226/2410-3535-2022-4-332-335
15. G. R. Murzina, V. R. Ganieva, A. A. Kruglov, F. U. Enikeev, Modeling of the process of superplastic forming of hemispherical shells from blanks of different profiles, Lett. Mater. 11, 4s (2021) 548 - 552. DOI: 10.22226/2410-3535-2021-4-548-552
16. Г. Р. Мурзина, В. Р. Ганиева, Ф. У. Еникеев, О. П. Тулупова, Программное средство для расчета технологических и геометрических характеристик процесса сверхпластической формовки, Int. Journal of Open Inf. Tech. 12, 11 (2024) 35 - 40.
17. I. Zakhariev, Numerical simulation of superplastic bulge forming test, J. Phys.: Conf. Ser. 1740 (2021) 012021. DOI: 10.1088/1742-6596/1740/1/012021
18. O. Tulupova, C. Gumerova, V. Ganieva, A. Kruglov, F. Enikeev, Improving the accuracy of finite element modeling of superplastic forming processes, Lett. Mater. 12, 2 (2022) 142 -147. DOI: 10.22226/2410-3535-2022-2-142-147
19. A. A. Kruglov, O. P. Tulupova, N. V. Olimpieva, V. R. Ganieva, F. U. Enikeev, Superplastic forming of hemispheres out of AZ61 magnesium alloy, IOP Conference Series: Mat. Sci. and Engineering, Ufa, 1008 (2020) 012050. DOI: 10.1088/1757-899X/1008/1/012050
20. A. R. Ragab, Thermoforming of superplastic sheet in shaped dies, Metals Technology 10, 1 (1983) 340 - 348. DOI: 10.1179/030716983803291262
21. R. A. Vasin, F. U. Enikeev, R. V. Safiullin, Mathematical Modeling of Superplastic Forming of a Long Rectangular Box Section, Mater. Sci. Forum 304 - 306 (1999) 765 - 770. DOI: 10.4028/www.scientific.net/MSF.304-306.765
22. R. A. Vasin, F. U. Enikeev, M. Tokuda, R. V. Safiullin, Mathematical modelling of the superplastic forming of a long rectangular sheet, Int. Journal of Non-Linear Mech. 38 (2003) 799 - 807. DOI: 10.1016/S0020-7462(01)00134-2
23. N. Chandra, K. Chandy, Superplastic process modeling of plane strain components with complex shapes, J. Mat. Shaping Technology 9 (1991) 27 - 37. DOI: 10.1007/BF02833630
24. L. Carrino, G. Giuliano, Analysis of Superplastic Testing by Using Constant Pressure in Prismatic Die, MSF 357 - 359 (2001) 219 - 224. DOI: 10.4028/www.scientific.net/MSF.357-359.219
25. A. Kh. Akhunova, S. V. Dmitriev, A. A. Kruglov, R. V. Safiullin, Superplastic forming of sheet into wedge die, Russian metallurgy (Metally) (2010) 9 38 - 41.
26. G. R. Murzina, A. R. Zharmukhametova, V. R. Ganieva, F. U. Enikeev, Method for calculating the parameters of superplasticity of titanium alloys based on the results of test forming into a rectangular matrix at constant pressure, Bulletin of the south Ural state university, 16, 1 (2023) 96 -107. DOI: 10.14529/mmp230108
27. А. Р. Горонкова, Ф. У. Еникеев, А. А. Круглов, Применение модели Пэжины для моделирования процесса сверхпластической формовки прямоугольной мембраны, Кузнечно-штамповочное производство, Обработка материалов давлением 9 (2016) 11-18.
28. А. А. Круглов, Ф. У. Еникеев, Конечноэлементное моделирование процесса сверхпластической формовки прямоугольной мембраны, Кузнечно-штамповочное производство, Обработка материалов давлением 2 (2019) 31- 40.
29. F. S. Jarrar, M. A. Nazzal, Inclination Angle Effect on the Thickness Distribution in a Superplastic Formed Long Rectangular Pan, MSF 735 (2012) 155 -161. DOI: 10.4028/www.scientific.net/MSF.735.155
30. R. Trân, F. Reuther, S. Winter, V. Psyk, Process Development for a Superplastic Hot Tube Gas Forming Process of Titanium (Ti-3Al-2.5V) Hollow Profiles, Metals 10 (2020) 1150. DOI: 10.3390/met10091150
31. M. N. Postnikova, A. D. Kotov, A. I. Bazlov, A. O. Mosleh, S. V. Medvedeva, A. V. Mikhaylovskaya, Effect of Boron on the Microstructure, Superplastic Behavior, and Mechanical Properties of Ti-4Al-3Mo-1V Alloy, Materials 16 (2023) 3714. DOI: 10.3390/ma16103714
32. A. D. Kotov, M. N. Postnikova, A. O. Mosleh, A. V. Mikhaylovskaya, Effect of Co addition on the microstructure evolution and superplastic behavior of Ti-4Al-3Mo-1V-0.1B alloy, Materials Research Proceedings 32 (2023) 181-188. DOI: 10.21741/9781644902615-20
33. N. Tian, X. Song, W. Ye, S. Hui, Superplastic Deformation Behavior of A β-rich α+β Titanium Alloy, JMRT 25 (2023) 1150 -1163. DOI: 10.1016/j.jmrt.2023.05.276
34. Y. Mi, Y. Lu, D. Wang, Y. Zhao, Y. Dong, H. Chang, I. V. Alexandrov, A Study of the Superplastic Deformation Behavior of Low-Cost Ti-2Fe-0.1B Alloys, Materials 17 (2024) 1282.
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- Имаев Ренат Мазитович (Директор)
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