Assessment of the upper and lower levels of permissible strains in the manufacture of sheet and thin-walled parts based on the forming limit diagram

S. I. Feoktistov   ; I. K. Andrianov

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 86 (2023), pp. 136-148

Résumé

Forming limit diagrams (FLDs) are currently widely used in the analysis of sheet metal forming without destruction and in assessing the technological capabilities of metal forming. This paper is devoted to the FLD-based assessment of the maximum and minimum limiting strains of the forming of thin-walled workpieces. Theoretical analysis of well-known criteria is used, including the criteria for the occurrence of scattered and localized necks, the so-called energy (static) criteria, as well as the criterion of abrupt local thinning of the sheet, the so-called kinematic criterion. This paper considers a two-way analysis of the forming limits of thin-walled workpieces according to FLDs, which allows one to determine the upper and lower estimates of the limiting strains of the forming. The analysis is based on the FLD study results obtained by various authors and published both in Russia and abroad. The presented research results can be used as a first-order analysis tool for evaluating and predicting the technological capabilities of the molded material in the manufacture of thin-walled parts. They are also relevant to metal processing by pressure and plastic forming of thin-walled sheets.

Détail

Keywords: forming limit diagram, Hill-Swift criterion, Storen-Rice criterion, upper and lower estimates of the forming limits.

Bibliographie

[1] Stoughton T.B., “General forming limit criterion for sheet metal forming”, International Journal of Mechanical Science, 42 (2000), 1–27 | DOI | Zbl

[2] Kazantsev A.V., Osnovy LS-DYNA. Diagramma predelnykh deformatsii (FLD). Sozdanie i verifikatsiya modelei povedeniya materialov, metod. posobie, Perm, 2018 http://dpm.pstu.ru>images/R/NZh>_Osnovy_LS-DYNA_v1.1.pdf

[3] Sanay B., Prediction of Plastic Instability and Forming Limits in Sheet Metal Forming, A Thesis Submitted to the Graduate School of Natural and Applied Sciences of Middle East Technical University in Partial Fullfilment of the Requirements for the Degree of Master of Science in Mechanical Engineering, 2010

[4] Paul S.K., “Theoretical analysis of strain- and stress-based forming limit diagrams”, Strain Analysis, 48:3 (2013), 177–188 | DOI

[5] Marciniak Z., Kuczynski K., “Limit strains in the processes of stretch-forming sheet metal”, International Journal of Mechanical Science, 1967, no. 9, 609–620 | DOI

[6] Marciniak Z., Kuczynski K., Pokora T., “Influence of the plastic properties of a material on the forming limit curve for sheet metal in tension”, Int. J. Mech. Sci., 1973, no. 15, 789–805 | DOI

[7] Nakazima K., Kikuma T., “Forming Limits under biaxial stretching of sheet metals”, Testu-to Hagane, 53 (1967), 455–458

[8] Nakazima K., Kikuuma T., Hasuka K., Study on the formability of steel sheets, Yawata Technical Report No 264, 1968, 141–154

[9] Izosimova S.V., “Issledovanie vliyaniya formy zagotovki na tochnost postroeniya dia grammy predelnykh deformatsii”, Studencheskaya nauchnaya vesna 2013: Mashinostroitelnye tekhnologii, vseros. nauch.-tekhn. konf. studentov, 2013 http://studvesna.ru/db_files/articles/810/article.pdf

[10] ISO 12004-2:2021. Metallic materials - Determination of forming-limit curves for sheet and strip - Part 2: Determination of forming-limit curves in the laboratory

[11] Swift H.W., “Plastic instability under plane stress”, Journal of the Mechanics and Physics of Solids, 1952, no. 1, 1–18 | DOI

[12] Hill R., “On discontinuous plastic states with special reference to localized necking in thin sheets”, Journal of the Mechanics and Physics of Solids, 1952, no. 1, 19–30 | DOI | MR

[13] Storen S., Rice J.R., “Localized necking in thin sheets”, Journal of the Mechanics and Physics of Solids, 23 (1975), 421–441 | DOI | Zbl

[14] Chumadin A.S., “Ob odnom podkhode k raschetu predelnogo deformirovaniya pri listovoi shtampovke”, Kuznechno-shtampovochnoe proizvodstvo, 1990, no. 6, 10–13

[15] Chumadin A.S., Metody rascheta predelnykh deformatsii v operatsiyakh listovoi shtampovki, ucheb. posobie, Izd-vo MATI, M., 2002

[16] Chumadin A.S., Teoriya i raschety protsessov listovoi shtampovki, dlya inzhenerov, 2-e izd., Eksposervis «VIP», M., 2014

[17] Marciniak Z., Kuczynski K., Pokora T., “Influence of the plastic properties of a material on the forming limit curve for sheet metal in tension”, International Journal of Mechanical Science, 1973, no. 15, 789–805 | DOI

[18] Marciniak Z., Kuczynski K., “Limit strains in the processes of stretch forming sheet steel”, Journal of the Mechanics and Physics of Solids, 1967, no. 1, 609–620

[19] Filimonov V.I., Mischenko O.V., Teoriya obrabotki metallov davleniem, ucheb. posobie, UlGTU, Ulyanovsk, 2012

[20] Stoughton T.B., Zhu X., “Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD”, International Journal of Plasticity, 20 (2004), 1463–1486 | DOI | Zbl

[21] Malinin N.N., Prikladnaya teoriya plastichnosti i polzuchesti, Mashinostroenie, M., 1975

[22] Shalin R.E., Aviatsionnye materialy, spravochnik dlya inzhenerno-tekhnicheskikh i nauchnykh rabotnikov, v 9 t., v. 4, Alyuminievye i berillievye splavy, ch. 1: Deformiruemye alyuminievye splavy i splavy na osnove berilliya, 6-e izd. pererab. i dop., ed. R.E. Shalin, VIAM, M., 1982