Method for determining the deep drawing limit coefficients taking into account the workpiece nonlinear plasticity and thickness alteration

Widespread use of the drawing processes in manufacture of the aviation parts using the metal forming methods substantiates the relevance of this study The research problem is related to assessing the thin-walled product limit state during elastoplastic deformation, taking into account the material nonlinear plasticity, large deformations and compressibility. The paper cosiders a method for determining the deep drawing limit coefficient of the thin-walled axisymmetric parts from a flat sheet workpiece, taking into account the nonlinear law of hardening and the workpiece thickness alteration. The problem is solved using the deformation theory of plasticity. Numerical methodology is based on the method of variable elastic parameters and the forming limit diagrams (FLD) to assess the workpiece stress-strain state and predict its destruction. Based on the research results, the workpiece deformed state was analyzed at various stages of loading with FLD diagrams, Hill-Swift and Storen-Rice limit deformation curves. Results of applying the numerical methodology in assessing the upper and lower levels of permissible drawing coefficients showed good agreement with the reference data.
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References

[1] Chumadin A.S. Teoriya i raschety protsessov listovoy shtampovki [Theory and calculations of sheet forging processes]. Moscow, Eksservis «VIP» Publ., 2014. 216 p. (In Russ.).

[2] Nakazima K., Kikuma T. Forming limits under biaxial stretching of sheet metals. Testu-to Hagane, 1967, vol. 53, pp. 455–458.

[3] Marciniak Z., Kucznski K. Limit strain in the process of stretch forming sheet metal. Int. J. Mech. Sci., 1967, vol. 9, no. 9, pp. 609–620, doi: https://doi.org/10.1016/0020-7403(67)90066-5

[4] Feoktistov S.I., Chzho Z.S. Determination of the limiting drawing ratio of titanium and aluminum alloys by FLD-diagrams. Kuznechno-shtampovochnoe proizvodstvo. Obrabotka materialov davleniem [Forging and stamping production. processing of materials by pressure], 2019, no. 5, pp. 27–34. (In Russ.).

[5] Storozhev M.V., Popov E.A. Teoriya obrabotki metallov davleniem [Theory of metal processing by pressure]. Moscow, Mashinostroenie Publ., 1977. 423 p. (In Russ.).

[6] Popov E.A. Osnovy teorii listovoy shtampovki [Fundamentals of the theory of sheet forging]. Moscow, Mashinostroenie Publ., 1977. 278 p. (In Russ.).

[7] Nepershin R.I. Modelling of deep drawing of thin-walled axisymmetric shells. Teoreticheskaya i prikladnaya mekhanika, 2016, no. 31, pp. 11–16. (In Russ.).

[8] Birger I.A. Kruglye plastinki i obolochki vrashcheniya [Round plates and shells of rotation]. Moscow, Oborongiz Publ., 1961. 368 p. (In Russ.).

[9] Malinin N.N. Prikladnaya teoriya plastichnosti i polzuchesti [Applied theory of plasticity and creep]. Moscow, Mashinostroenie Publ., 1975. 400 p. (In Russ.).

[10] Feoktistov S.I., Chzho Z.S. Determination of the limiting expanding ratio by FLD-diagrams. Kuznechno-shtampovochnoe proizvodstvo. Obrabotka materialov davleniem [Forging and stamping production. processing of materials by pressure], 2019, no. 9, pp. 3–7. (In Russ.).

[11] Feoktistov S.I., Andrianov I.K. Equations of joint logarithmic deformations in Euler coordinates for solving axisymmetric pressure metal processes. Uchenye zapiski Komsomolskogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta [Scientific Notes of Komsomolsk-on-Amour State Technical University], 2021, no. 7, pp. 26–30, doi: https://doi.org/10.17084/20764359-2021-55-26 (in Russ.).

[12] Feoktistov S.I., Andrianov I.K., Tkhet L. Modeling of the stress-strain state of thick-walled cylindrical shells taking into account physical nonlinearity of the material. Uchenye zapiski Komsomolskogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta [Scientific Notes of Komsomolsk-on-Amour State Technical University], 2022, no. 3, pp. 12–20, doi: https://doi.org/10.17084/20764359-2022-59-12 (in Russ.).

[13] Feoktistov S.I. Raschet na EVM formozadayushchikh elementov osnastki dlya gibki listovykh i profilnykh zagotovok [Computer calculation of forming elements of tooling for bending of sheet and profile blanks]. Komsomolsk-na-Amure, Khabarov. politekh. in-t Publ., 1984. 59 p. (In Russ.).

[14] Swift H.W. Plastic instability under plane stress. J. Mech. Phys. Solids, 1952, vol. 1, no. 1, pp. 1–18, doi: https://doi.org/10.1016/0022-5096(52)90002-1

[15] Hill R. On discontinuous plastic states, with special reference to localized necking in thin sheets. J. Mech. Phys. Solids, 1952, vol. 1, no. 1, pp. 19–30, doi: https://doi.org/10.1016/0022-5096(52)90003-3

[16] Stoughton T., Zhu X. Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD. Int. J. Plasticity, 2004, vol. 20, no. 8–9, pp. 1463–1486, doi: https://doi.org/10.1016/j.ijplas.2003.11.004

[17] Paul S.K. Theoretical analysis of strain- and stress-based forming limit diagrams. J. Strain Anal. Eng. Des., 2013, vol. 48, no. 3, pp. 177–188, doi: https://doi.org/10.1177/0309324712468524

[18] Storen S., Rice J.R. Localized necking in thin sheets. J. Mech. Phys. Solids, 1975, vol. 23, no. 6, pp. 421–441, doi: https://doi.org/10.1016/0022-5096(75)90004-6

[19] Chumadin A.S. On one approach to calculation of ultimate deformation in sheet forging. Kuznechno-shtampovochnoe proizvodstvo, 1990, no. 6, pp. 10–13. (In Russ.).

[20] Chumadin A.S. Metody rascheta predelnykh deformatsiy v operatsiyakh listovoy shtampovki [Methods of calculation of limit deformations in sheet forging operations]. Moscow, MATI Publ., 2002. 53 p. (In Russ.).

[21] Filimonov V.I., Mishchenko O.V. Teoriya obrabotki metallov davleniem [Theory of metal processing by pressure]. Ulyanovsk, UlGTU Publ., 2012. 208 p. (In Russ.).

[22] Hollomon J.H. Tensile deformation. Trans. ASME, 1945, vol. 162, pp. 268–277. (In Russ.).

[23] Romanovskiy V.P. Spravochnik po kholodnoy shtampovke [Handbook on cold forging]. Leningrad, Mashinostroenie Publ., 1979. 520 p. (In Russ.).

[24] Tumanov A.T., ed. Aviatsionnye materialy. T. 5. Magnievye i titanovye splavy [Aviation materials. Т. 5. Magnesium and titanium alloys]. Moscow, VIAM Publ., 1973. 583 p. (In Russ.).