A Review of Analytical Methods for Evaluating the Stress-strain State of Workpieces During the Processing of Semi-finished Pipe Products
DOI:
https://doi.org/10.32515/2664-262X.2026.13(44).117-127Keywords:
distribution, cylindrical workpiece, equilibrium equation, hardening, wall thicknessAbstract
This study reviews analytical modeling methods for the division of tubular cylindrical blanks and identifies the primary factors influencing the stress-strain state of blank walls. The objective is to establish a mathematical model for the asymmetric deformation of bell-shaped products.
The work provides a critical analysis of existing analytical models of the process of dividing a cylindrical blank with conical punches. It is shown that this processing method is used in various industries and is sufficiently studied from a theoretical point of view. Some researchers focus on calculating the components of the stress tensor. They explicitly identify technological process factors that affect the quality of the final product. Other researchers pay more attention to the deformed state of the blank and, based on the obtained dependencies, calculate changes in the radius of the semi-finished product along the forming conical surface and wall thinning in the deformed part. Various theoretical approaches are used: sheet metal stamping theory, theory of shells of rotation, deformation theory of plasticity, and theory of plastic flow. The obtained dependencies have closed solutions, which are obtained by direct integration of the equilibrium conditions of the workpiece element with the plasticity conditions. But there are solutions that are proposed to be integrated numerically. This integration approach somewhat reduces the informativeness of the final formulas and does not allow for investigating the weight of each parameter of the technological process in relation to its regulation. However, the development of digital calculation tools and computer programs allows the creation of a powerful tool for analyzing the processes of distributing cylindrical semi-finished products based on the equation database.
Questions regarding the loss of stability of both the deformed and undeformed parts of the workpiece remain open. The same applies to the destruction of the walls of the samples. Based on the presented solutions, these questions can be determined by introducing the criteria for loss of stability and destruction. For further research on this topic, taking into account the previous work of various researchers, it is necessary to apply a synergistic approach that will take into account the best practices of methods for theoretical analysis of sheet metal stamping and the technical theory of shells.
References
Список літератури
1. Tan C.J. End Formation of a Round Tube into a Square Section with Reduced Forming Loads. Applied Mechanics and Materials. 2013. Vol. 395-396. P. 945–948. Doi: 10.4028/www.scientific.net/amm.395-396.945.
2. Пузир Р.Г., Троцко О.В., Черкащенко В.Ю. Вплив геометричних параметрів циліндричної заготовки на напружено деформований стан при роздачі конічними пуансонами. Обробка матеріалів тиском: збірник наукових праць. Краматорськ: 2012. № 4 (33). С. 114-121.
3. Karrech A., Seibi A. Analytical model for the expansion of tubes under tension. Journal of Materials Processing Technology. 2010. Vol. 210, №. 2. P. 356–362. Doi: 10.1016/j.jmatprotec.2009.09.024.
4. Yang J., Luo M., Hua Yu., Lu Xu. Energy absorption of expansion tubes using a conical–cylindrical die: Experiments and numerical simulation. International Journal of Mechanical Sciences. 2010. Vol. 52, №. 5. Р. 716–725. Doi: 10.1016/j.ijmecsci.2009.11.015.
5. Keeler S.P. Sheet Metal Stamping Technology ‒ Need for Fundamental Understanding. Mechanics of Sheet Metal Forming. Springer. Boston: MA, 1978. Р. 3–18. Doi: 10.1007/978-1-4613-2880-3_1.
6. Wang N.M. A mathematical model of drawbead forces in sheet metal forming. J. Applied Metalworking. 1982. Vol. 2. Р. 193–199. Doi: 10.1007/BF02834037.
7. Thomsen E.G., Yang C.T., Kobayashi S. Plastic Deformation in Metal Processing. Macmillan, 1965. 486 р.
8. Nádai A. Theory of Flow and Fracture of Solids. McGraw-Hill, 1950. 572 p.
9. Johnson W., Mellor P.B. Plasticity for mechanical engineers. D. Van Nostrand Company LTD, 1962. 412 p.
10. Hill R. The Mathematical Theory of Plasticity. Oxford University Press, New York, 1950. 407 р.
11. Пузир Р. Г., Левченко Р. В., Сіра Ю. Б., Лелюх С. Н. Чисельне моделювання втрати стійкості трубної заготовки під час роздачі сполучних перехідників. Вісник Національного технічного університету «ХПІ». Серія: «Інноваційні технології та обладнання обробки матеріалів у машинобудуванні та металургії». 2019. № 12 (1337). С. 51–56.
12. Пузир Р. Г. Визначення довжини хвилі загасання згинального моменту при роздачі циліндричної заготовки. Вісник Кременчуцького національного університету імені Михайла Остроградського. 2012. № 5 (76), С. 64–66.
13. Al-Abri O.S. Analytical and numerical solution for lardge plastic deformation of solid expandable tubular. SPE International. 2011. 152370. P. 1 – 13.
References
1. Tan, C.J. (2013). End Formation of a Round Tube into a Square Section with Reduced Forming Loads. Applied Mechanics and Materials, 395-396, 945–948. Doi: 10.4028/www.scientific.net/amm.395-396.945.
2. Puzyr, R.G., Trocko, O.V. & Cherkashenko, V.Yu. (2012). Vpliv geometrichnih parametriv cilindrichnoyi zagotovki na napruzheno deformovanij stan pri rozdachi konichnimi puansonami. Obrobka materialiv tiskom: zbirnik naukovih prac. Kramatorsk: 4 (33), 114-121. [in Ukrainian].
3. Karrech, A. & Seibi, A. (2010). Analytical model for the expansion of tubes under tension. Journal of Materials Processing Technology, 210, 2, 356–362. Doi: 10.1016/j.jmatprotec.2009.09.024.
4. Yang, J., Luo, M., Hua, Yu, & Lu, Xu. (2010). Energy absorption of expansion tubes using a conical–cylindrical die: Experiments and numerical simulation. International Journal of Mechanical Sciences, 52, 5, 716–725. Doi: 10.1016/j.ijmecsci.2009.11.015.
5. Keeler, S.P. (1978). Sheet Metal Stamping Technology ‒ Need for Fundamental Understanding. Mechanics of Sheet Metal Forming. Springer. Boston: MA, 3–18. Doi: 10.1007/978-1-4613-2880-3_1.
6. Wang, N.M. (1982). A mathematical model of drawbead forces in sheet metal forming. J. Applied Metalworking, 2, 193–199. Doi: 10.1007/BF02834037.
7. Thomsen, E.G., Yang, C.T. & Kobayashi S. (1965). Plastic Deformation in Metal Processing. Macmillan.
8. Nádai, A. (1950). Theory of Flow and Fracture of Solids. McGraw-Hill.
9. Johnson, W. & Mellor, P.B. (1962). Plasticity for mechanical engineers. D. Van Nostrand Company LTD.
10. Hill, R. (1950). The Mathematical Theory of Plasticity. Oxford University Press, New York.
11. Puzyr, R. G., Levchenko, R. V., Sira, Yu. B. & Lelyuh, S. N. (2019). Chiselne modelyuvannya vtrati stijkosti trubnoyi zagotovki pid chas rozdachi spoluchnih perehidnikiv. Visnik Nacionalnogo tehnichnogo universitetu «HPI». Seriya: «Innovacijni tehnologiyi ta obladnannya obrobki materialiv u mashinobuduvanni ta metalurgiyi», 12(1337), 51–56. [in Ukrainian].
12. Puzyr, R. G. (2012). Viznachennya dovzhini hvili zagasannya zginalnogo momentu pri rozdachi cilindrichnoyi zagotovki. Visnik Kremenchuckogo nacionalnogo universitetu imeni Mihajla Ostrogradskogo, 5 (76), 64–66. [in Ukrainian].
13. Al-Abri, O.S. (2011). Analytical and numerical solution for lardge plastic deformation of solid expandable tubular. SPE International, 152370, 1–13.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Ruslan Puzyr, Rostyslav Kozlov
This work is licensed under a Creative Commons Attribution 4.0 International License.
