Numerical simulation of high-speed forming of plates from light alloys taking into account the localization of plastic deformation and the evolution of damage
Vladimir V. Skripnyak, Sergey A. Zelepugin, Alexander E. Kiryushkin, Natalia V. Skripnyak, Vladimir A. Skripnyak
Author details
- National Research Tomsk State University, Tomsk, Russian Federation
- National Research Tomsk State University, Tomsk, Russian Federation
- National Research Tomsk State University, Tomsk, Russian Federation
- National Research Tomsk State University, Tomsk, Russian Federation
- National Research Tomsk State University, Tomsk, Russian Federation
Abstract
This paper presents the results of a numerical study of plastic deformation and crack formation processes during the pressing a hemispherical punch at speeds of 5 and 10 m/s into AMg2 aluminum alloy plates and MA2-1 magnesium alloy plates, which belong to different isomechanical groups of light alloys. The aim of the study was to investigate the adequacy of the predictions of numerical modeling of plastic deformation and crack formation in light alloy plates during high-speed stamping without preheating. To describe the mechanical behavior of the alloys, modifications of the Zerilli-Armstrong models for alloys with a face-centered cubic crystal lattice and a hexagonal close-packed lattice, as well as the Gurson-Tvergaard-Needleman model of damage and destruction of deformable media were used. It is shown that the modifications of the models allow predicting the features of deformation localization development during high-speed stamping, which lead to the formation of localized zones of damage to light alloys and cracks, using numerical simulation. The simulation results indicate the possibility of increasing plastic deformations in alloy plates before their destruction at room temperature with increasing stamp speed. The effect of increasing the ultimate plastic deformations under biaxial high-speed tension is realized when extruding alloy plates with a hemispherical punch at a speed of 10 m/s. The obtained results substantiate the possibility of using the considered modifications of the models for computer design of high-speed stamping technologies without heating of light alloys related to the FCC and HCP isomechanical groups, which expands the potential of using dynamic stamping for the production of products from light alloy sheet metal.
Keywords
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ВЫСОКОСКОРОСТНОГО ФОРМОВАНИЯ ПЛАСТИН ИЗ ЛЕГКИХ СПЛАВОВ С УЧЕТОМ ЛОКАЛИЗАЦИИ ПЛАСТИЧЕСКОЙ ДЕФОРМАЦИИ И ЭВОЛЮЦИИ ПОВРЕЖДЕННОСТИ
В данной работе представлены результаты исследования процессов пластической деформации и образования трещин при вдавливании полусферического пуансона со скоростями 5 и 10 м/с в пластины сплавов АМг2 и МА2-1, относящихся к разным изомеханическим группам легких сплавов. Цель исследования состояла в изучении адекватности прогнозов численного моделирования пластической деформации и образования трещин в пластинах легких сплавов при высокоскоростной штамповке без предварительного нагрева. Для описания механического поведения сплавов применялись модификации моделей Зерилли-Армстронга для материалов с гранецентрированной кубической кристаллической решеткой и гексагональной плотноупакованной решеткой, а также модель повреждения и разрушения деформируемых сред Гурсона-Твергаарда-Нидлмана. Показано, что при численном моделировании модификации моделей позволяют прогнозировать особенности развития локализации деформации в пластинах при высокоскоростной штамповке, приводящие к формированию зон повреждения легких сплавов и образования трещин. Результаты моделирования свидетельствуют о возможности увеличения пластических деформаций в пластинах сплавов с ростом скорости штампа при комнатной температуре. При продавливании пластин сплавов полусферическим пуансоном со скоростью 10 м/с в условиях двухосного высокоскоростного растяжения реализуется эффект увеличения предельных пластических деформаций. Полученные результаты указывают на адекватность рассмотренных модификаций моделей для компьютерного проектирования технологий высокоскоростной штамповки без нагрева и расширяют потенциальные возможности использования динамической штамповки для производства изделий из листового проката легких сплавов.
Ключевые слова
Bibliography
- 1.Avrillaud G., Mazars G., Cantergiani E., Beguet F., Cuq-Lelandais J.-P., Deroy J. Examples of how increased formability through high strain rates can be used in electro-hydraulic forming and electromagnetic forming industrial applications, Journal of Manufacturing and Materials Processing, 2021, no 5, 96. doi:10.3390/jmmp5030096 Scholar
- 2.Chen D-Y., Xu Y., Zhang S.-H., Ma Y., El-Aty A. A., Banabic D., Pokrovsky A. I., Bakinovskaya A. A. A novel method to evaluate the high strain rate formability of sheet metals under impact hydroforming, Journal of Materials Processing Technology, 2019, vol. 287, 116553. doi:10.1016/j.jmatprotec.2019.116 Scholar
- 3.Kopec M., Politis D.J. Advances in sheet metal forming processes of lightweight alloys?, Materials, 2023, vol. 16, 3293. doi:10.3390/ma16093293 Scholar
- 4.Mamutov A. V., Golovashchenko S. F., Mamutov V. S. Experimental-analytical method of analyzing performance of coils for electromagnetic forming and joining operations, Journal of Materials Processing Technology, 2018, vol. 255, pp. 86–95. doi:10.1016/j.jmatprotec.2017.11.050 Scholar
- 5.Liu D. H., Yu H. P., Li C.F. Experimental Observations of Quasi-Static-Dynamic Formability in Bi axially Strained AA5052-O, Journal of Materials Engineering & Performance, 2011, vol. 20, pp. 223–230, doi:10.1007/s11665-010-9676-3] Scholar
- 6.Smerd R., Winkler S., Salisbury C., Worswick M., Lloyd D., Finn M. High strain rate tensile testing of automotive aluminum alloy sheet, International Journal of Impact Engineering , 2005, vol. 32, pp. 541–560. doi:10.1016/j.ijimpeng.2005.04.013 Scholar
- 7.Ma H., Wang P., Huang X., Mao W., Gong Z., Zhang M., Zhu H. Study on the flow behavior of 5052 aluminum alloy over a wide strain-rate range with a constitutive model based on the arrhenius model extension, Metals, 2023, vol.13, 1948. doi: 10.3390/met13121948 Scholar
- 8.Skripnyak V.A., Chirkov M.O., Skripnyak V.V. Mechanical behavior of aluminum alloy 1520 under tension in the range of strain rates from 10-1 to 103 s-1. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics, 2023, no. 86, pp. 120–135. doi: 10.17223/19988621/86/9 Scholar
- 9.Ravindranadh B., Vemuri M., Ashok K. G. Tensile behaviour of aluminium 7017 alloy at various temperatures and strain rates, Journal of Materials Research and Technology. – 2016. – Vol. 5. –pp. 190–197. doi:10.1016/j.jmrt.2015.12.002 Scholar
- 10.Murugesan M., Yu J.-H., Chung W., Lee C.-W. Warm deformation behavior and flow stress modeling of AZ31B magnesium alloy under tensile deformation, Materials, 2023, vol. 16, 5088. doi:10.3390/ma16145088 Scholar
- 11.Lee W.-S., Chou C.-W. Dynamic deformation behaviour and dislocation substructure of az80 magnesium alloy over a wide range of temperatures, EPJ Web of Conferences DYMAT, 2018, vol.183, - 03010 / doi: 10.1051/epjconf/201818303010 Scholar
- 12.Skripnyak V.A., Skripnyak V.V., Kozulin A.A., Iohim K.V. The influence of stress concentrators on the magnesium alloy mechanical behavior under deformation at high strain rates in the temperature range from 295 to 673 K, PNRPU Mechanics Bulletin, 2019, no. 1, pp. 151-160. doi: 10.15593/perm.mech/2019.1.13 Scholar
- 13.Joun M. S., Razali M. K., Jee C. W., Byun J. B., Kim M. C., Kim K. M. A review of flow characterization of metallic materials in the cold forming temperature range and its major issues, Materials, 2022, vol.15, no 8, 2751. doi: 10.1063/5.0119350 Scholar
- 14.Madhusudhana, H. K., Gaitonde, V. N., Jangali, S. G. A review on lightweight metal component forming and its application, Journal of Physics: Conference Series 2021, 2021, vol. 2070, - 012246. doi:10.1088/1742-6596/2070/1/012246 Scholar
- 15.Pereira R., Peixinho N., Costa S.L. A Review of Sheet Metal Forming Evaluation of Advanced High-Strength Steels (AHSS), Metals, 2024, vol. 14. - 394. doi:10.3390/met14040394 Scholar
- 16.Prakash V., Digavalli R.K., Lenzen M., Hagenah H., Merklein M. Numerical simulation of sheet metal forming of an Al-Mg alloy incorporating plane strain properties in the yield criterion. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture. -2024. -Vol. 238, No. 3. - pp. 373-384. https://doi.org/10.1177/09544054221135388 Scholar
- 17.El-Aty A. A., Xu Y., Hou Y., Zhang S.-H., Ha S., Xia L., Alzahrani B., Ali A., Ahmed M.M.Z., Shokry A. Modelling the flow behaviour of al alloy sheets at elevated temperatures using a modifid Zerilli-Armstrong model and phenomenological-based constitutive models.// Materials, 2024, vol.17, 1584. doi:10.3390/ma17071584 Scholar
- 18.Petrov M.A., Matveev A.G., Petrov P.A. Modelirovanie processa shtampovki c kruchenien v programme ABAQUS [Modeling the process of stamping with torsion in the ABAQUS program], Technology of light alloys, 2022, no. 1, pp. 45-53. Scholar
- 19.Frost H. J., Ashby M. F. Deformation-mechanism maps: the plasticity and creep of metals and ceramics. Pergamon Press: Oxford, UK. -1982. -166 p. Scholar
- 20.Shokry A., Gowid S., Kharmanda G. An improved generic Johnson-Cook model for the flow prediction of different categories of alloys at elevated temperatures and dynamic loading conditions, Materials Today Communication, 2021, vol. 27, 102296. Scholar
- 21.Skripnyak V.V., Skripnyak V.A. Residual stresses in alpha titanium alloy sheet after punching at moderate strain rate // Journal of Materials Engineering and Performance. - 2024, vol. 33, - pp. 3885-3898. doi:10.1007/s11665-023-09055-1 Scholar
- 22.Sokovikov M., Uvarov S., Simonov M., Chudinov V., Naimark O. Metastability, adiabatic shear bands initiation and plastic strain localization in the AMg6 alloy under dynamic loading, Fracture and Structural Integrity, 2024, vol 18, no. 68, pp. 255-266 . doi: 10.3221/IGF-ESIS.68.17 Scholar
- 23.Lucon, E., Benzing, J., Hrabe, N. Development and validation of small punch testing at NIST, National Institute of Standards and Technology USA. Interagency or Internal Report 8303, 2020, 55 p. doi:10.6028/NIST.IR.8303 Scholar
- 24.Skripnyak V.V., Skripnyak N.V., Zagorodkin O.N., Skripnyak V.A. Vyazkoe razrushenie splava Mg-3Al-1Zn pri dinamicheskih nagruskah [Ductile fracture of Mg-3Al-1Zn alloy under dynamic loads], Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika - Tomsk State University Journal of Mathematics and Mechanics, 2025, no 95. -pp.164-179, doi: 10.17223/19988621/95/14 Scholar
- 25.Skripnyak V.V. Programma dlya rascheta deformacii I razrusheniya 3D elementov konstrukcii iz legkih splavov v usloviyah dinamicheskih vozdeistvii [Program for calculating the deformation and failure of 3D structural elements made of light alloys under dynamic effects.] Certificate of registration of the computer program RU 2024617669, 04.04.2024. Application No. 2024615724 dated 22.03.2024. Scholar
- 26.Skripnyak N.V., Skripnyak V.V., Skripnyak E.G., Skripnyak V.A., Vaganova I.K. Programma dlya modelirovaniya processa vyazkogo razrusheniya splavov pri kvazistaticheskom I dinamicheskih vozdeistviyah [Program for modeling the process of viscous fracture of alloys under quasi-static and dynamic effects.] Certificate of registration of the computer program RU 2020612860, 05.03.2020. Application No. 2020611898 dated 27.02.2020 Scholar
- 27.Curran D.R., Seaman L., Shockey D.A. Dynamic failure of solids, Physics Reports, 1987, vol.146, pp. 253-388. doi:10.1016/0370-1573(87)90049-4 Scholar
- 28.Zhang T., Lu K., Mano A., Yamaguchi Y., Katsuyama J., Li Y. A novel method to uniquely determine the parameters in Gurson - Tvergaard - Needleman model, Fatigue and Fracture of Engineering Materials and Structures, 2021, vol.44, no. 12, pp. 3399-3415. doi: 10.1111/ffe.13568 Scholar
- 29.Espeseth V., Morin D., Tekoglu C., Borvik T., Hopperstad O.S. Ductile tearing of aluminium plates: experiments and modeling, International Journal of Fracture, 2023, vol. 242, pp. 39-70. doi:10.1007/s10704-023-00701-2 Scholar
- 30.Tize Mha, P., Tongne, A., Pantale, O. A generalized non-linear flow law based on modified Zerilli-Armstrong model and its implementation into Abaqus/Explicit FEM Code, World Journal of Engineering and Technology, 2022, vol. 10, pp. 334-362. doi:10.4236/wjet.2022.102021 Scholar
- 31.Song P., Li W.-B., Wang X.-M. A study on dynamic plastic deformation behavior of 5052 aluminum alloy, Key Engineering Materials, 2019, vol. 812, pp. 45-52. Scholar
- 32.Jin F., Gu M., Hong H. High - strain - rate forming performance of an aluminum alloy, Materials and technology, 2020, vol.54, no. 5, pp. 627-632. doi:10.17222/mit.2019.255 Scholar
- 33.Du Z., Cui X., Yang H., Xia W. Deformation and fracture behavior of 5052 aluminum alloy by electromagnetic-driven stamping, The International Journal of Advanced Manufacturing Technology, 2022, vol.123, pp.:3955-3968. doi:10.1007/s00170-022-10446-2 Scholar
- 34.Loginov Yu. N., Zamaraeva Yu. V. Modelirovanie shtampovki bimetallicheskogo shara s obolochkoi iz magniya [Modeling of stamping of a bimetallic ball with a magnesium shell]// Metal forming, 2022, no. 2, pp. 75-82. DOI: 10.24412/0321-4664-2022-2-75-82 Scholar
- 35.Petrov P.A., Fam V.N. Vybor matematicheskoy funkcii dlya opisaniya soprotivleniya deformacii alyuminiyevih slavov sistemy Al- Mg [Selection of a mathematical function for describing the deformation resistance of aluminum alloys of the Al-Mg system], Automated design in mechanical engineering, 2022, no. 12, pp. 25-28. Scholar
- 36.Rulin S.P., Petrov P.A. Mayematicheskoe modelirovanie operacii pryamogo vydvalivaniya osesimmetrichnoi zagotovki iz alyumini evogo splava v sfericheskuyu matritsu, [Mathematical modeling of the operation of direct extrusion of an axisymmetric billet from an aluminum alloy into a spherical matrix], Mechanical Engineering: a network electronic scientific journal, 2025, vol. 12, no. 1, pp. 53-57. Scholar
- 1.Examples of how increased formability through high strain rates can be used in electro-hydraulic forming and electromagnetic forming industrial applications / G. Avrillaud, G. Mazars, E. Cantergiani, F. Beguet, J.-P. Cuq-Lelandais, J. Deroy // Journal of Manufacturing and Materials Processing – 2021. – Vol. 5. – Art. 96. DOI: 10.3390/jmmp5030096 Scholar
- 2.A novel method to evaluate the high strain rate formability of sheet metals under impact hydroforming / D-Y. Chen, Y. Xu, S.-H. Zhang, Y. Ma, A.A. El-Aty, D. Banabic, A.I. Pokrovsky, A.A. Bakinovskaya // Journal of Materials Processing Technology. – 2019. – Vol. 278. – 116553. DOI: 10.1016/j.jmatprotec.2019.116 Scholar
- 3.Kopec, M. Advances in sheet metal forming processes of lightweight alloys / M. Kopec, D.J. Politis // Materials. – 2023. – Vol. 16. – Art. 3293. DOI: 10.3390/ma16093293 Scholar
- 4.Mamutov, A.V. Experimental-analytical method of analyzing performance of coils for electromagnetic forming and joining operations / A.V. Mamutov, S.F. Golovashchenko, V.S. Mamutov // Journal of Materials Processing Technology. – 2018. – Vol. 255. – P. 86–95. DOI: 10.1016/j.jmatprotec.2017.11.050 Scholar
- 5.Liu, D.H. Experimental observations of quasi-static-dynamic formability in bi axially strained AA5052-O / D.H. Liu, H.P. Yu, C.F. Li // Journal of Materials Engineering & Performance. – 2011. – Vol. 20. – P. 223–230. DOI: 10.1007/s11665-010-9676-3 Scholar
- 6.High strain rate tensile testing of automotive aluminum alloy sheet / R. Smerd, S. Winkler, C. Salisbury, M. Worswick, D. Lloyd, M. Finn // International Journal of Impact Engineering Fifth International Symposium on Impact Engineering. – 2005. – Vol. 32. – P. 541–560. DOI: 10.1016/j.ijimpeng.2005.04.013 Scholar
- 7.Study on the flow behavior of 5052 aluminum alloy over a wide strain-rate range with a constitutive model based on the Arrhenius model extension / H. Ma, P. Wang, X. Huang, W. Mao, Z. Gong, M. Zhang, H. Zhu // Metals. – 2023. – Vol. 13. – 1948. DOI: 10.3390/met13121948 Scholar
- 8.Скрипняк, В.А. Механическое поведение алюминиевого сплава 1520 при растяжении в диапазоне скоростей деформации от 10-1 до 10-3 с-1 / В.А. Скрипняк, М.О. Чирков, В.В. Скрипняк // Вестник Томского государственного университета. Математика и механика. –2023. –№ 86. – С. 120–135. Scholar
- 9.Ravindranadh, B. Tensile behaviour of aluminium 7017 alloy at various temperatures and strain rates / B. Ravindranadh, M. Vemuri, K.G. Ashok // Journal of Materials Research and Technology. – 2016. – Vol. 5. – P. 190–197. DOI: 10.1016/j.jmrt.2015.12.002 Scholar
- 10.Warm deformation behavior and flow stress modeling of AZ31B magnesium alloy under tensile deformation / M. Murugesan, J.-H. Yu, W. Chung, C.-W. Lee // Materials. – 2023. – Vol. 16. – 5088. DOI: 10.3390/ma16145088 Scholar
- 11.Lee, W.-S. Dynamic deformation behaviour and dislocation substructure of AZ80 magnesium alloy over a wide range of temperatures / W.-S. Lee, C.-W. Chou // EPJ Web of Conferences DYMAT. – 2018. – Vol. 183. – 03010. DOI: 10.1051/epjconf/201818303010 Scholar
- 12.Влияние концентраторов напряжений на механическое поведение магниевого сплава при высокоскоростной деформации в температурном диапазоне от 295 К до 673 К / В.А. Скрипняк, В.В. Скрипняк, А.А. Козулин, К.В. Иохим // Вестник Пермского национального исследовательского политехнического университета. Механика. – 2019. – № 1. – С. 151–160. DOI: 10.15593/perm.mech/2019.1.13 Scholar
- 13.A review of flow characterization of metallic materials in the cold forming temperature range and its major issues / M.S. Joun, M.K. Razali, C.W. Jee, J.B. Byun, M.C. Kim, K.M. Kim // Materials. – 2022. – Vol. 15(8). – 2751. DOI: 10.1063/5.0119350 Scholar
- 14.Madhusudhana, H.K. A review on lightweight metal component forming and its application / H.K. Madhusudhana, V.N. Gaitonde, S.G. Jangali // Journal of Physics: Conference Series. – 2021. – 2021. – Vol. 2070. – 012246. DOI: 10.1088/1742-6596/2070/1/012246 Scholar
- 15.Pereira, R. A Review of Sheet Metal Forming Evaluation of Advanced High-Strength Steels (AHSS) / R. Pereira, N. Peixinho, S.L. Costa // Metals. – 2024. – Vol. 14. – 394. DOI: 10.3390/met14040394 Scholar
- 16.Numerical simulation of sheet metal forming of an Al-Mg alloy incorporating plane strain properties in the yield criterion. Proceedings of the Institution of Mechanical Engineers, Part B / V. Prakash, R.K. Digavalli, M. Lenzen, H. Hagenah, M. Merklein // Journal of Engineering Manufacture. – 2024. – Vol. 238, no. 3. – P. 373–384. DOI: 10.1177/09544054221135388 Scholar
- 17.Modelling the flow behaviour of al alloy sheets at elevated temperatures using a modified Zerilli–Armstrong model and phenomenological-based constitutive models / A.A. El-Aty, Y. Xu, Y. Hou, S.-H. Zhang, S. Ha, L. Xia, B. Alzahrani, A. Ali, M.M.Z. Ahmed, A. Shokry // Materials. –2024. – Vol. 17. – 1584. DOI: 10.3390/ ma17071584 Scholar
- 18.Петров, М.А. Моделирование процесса штамповки с кручением в программе ABAQUS / М.А. Петров, А.Г. Матвеев, П.А. Петров // Технология легких сплавов. – 2022. – № 1. – С. 45–53. Scholar
- 19.Frost, H.J. Deformation-mechanism maps: the plasticity and creep of metals and ceramics / H.J. Frost, M.F. Ashby. – Pergamon Press: Oxford, UK. – 1982. – 166 p. Scholar
- 20.Shokry, A. Modified Fields-Backofen and Zerilli-Armstrong constitutive models to predict the hot deformation behavior in titanium-based alloys / A. Shokry // Science Report. – 2024. – Vol. 14. – 8359. DOI: 10.1038/s41598-024-58568-9 Scholar
- 21.Skripnyak, V.V. Residual stresses in alpha titanium alloy sheet after punching at moderate strain rate / V.V. Skripnyak, V.A. Skripnyak // Journal of Materials Engineering and Performance. – 2024. – Vol. 33. – P. 3885–3898. DOI: 10.1007/s11665-023-09055-1 Scholar
- 22.Metastability, adiabatic shear bands initiation and plastic strain localization in the AMg6 alloy under dynamic loading / M. Sokovikov, S. Uvarov, M. Simonov, V. Chudinov, O. Naimark // Fracture and Structural Integrity. – 2024. – Vol. 18, no 68. – P. 255–266. DOI: 10.3221/IGF-ESIS.68.17 Scholar
- 23.Lucon, E. Development and validation of small punch testing at NIST / E. Lucon, J. Benzing, N. Hrabe // National Institute of Standards and Technology USA. Interagency or Internal Report 8303. – 2020. – 55 p. DOI: 10.6028/NIST.IR.8303 Scholar
- 24.Вязкое разрушение магниевого сплава Mg-3Al-1Zn при динамических нагрузках / В.В. Скрипняк, Н.В. Скрипняк, О.Н. Загородкин, В.А. Скрипняк // Вестник Томского государственного университета. Математика и механика. –2025. – № 95. – С. 164–179. Scholar
- 25.Скрипняк В.В. Программа расчета деформации и разрушения 3D-элементов конструкций из легких сплавов в условиях динамических воздействий. Свидетельство о регистрации программы для ЭВМ RU 2024617669, 04.04.2024. Заявка № 2024615724 от 22.03.2024. Scholar
- 26.Скрипняк Н.В., Скрипняк В.В., Скрипняк Е.Г., Скрипняк В.А., Ваганова И.К. Программа для моделирования процесса вязкого разрушения сплавов при квазистатических и динамических воздействиях. Свидетельство о регистрации программы для ЭВМ RU 2020612860, 05.03.2020. Заявка № 2020611898 от 27.02.2020 Scholar
- 27.Curran, D.R. Dynamic failure of solids / D.R. Curran, L. Seaman, D.A. Shockey // Physics Reports. – 1987. – Vol. 147, iss. 5–6. – P. 253–388. DOI: 10.1016/0370-1573(87)90049-4 Scholar
- 28.A novel method to uniquely determine the parameters in Gurson – Tvergaard – Needleman model / T. Zhang, K. Lu, A. Mano, Y. Yamaguchi, J. Katsuyama, Y. Li // Fatigue and Fracture of Engineering Materials and Structures. – 2021. – Vol. 44 (12). – P. 3399–3415. DOI: 10.1111/ffe.13568 Scholar
- 29.Ductile tearing of aluminium plates: experiments and modeling / V. Espeseth, D. Morin, C. Tekoglu, T. Borvik, O.S. Hopperstad // International Journal of Fracture. – 2023. – Vol. 242. – P. 39–70. DOI: 10.1007/s10704-023-00701-2 Scholar
- 30.Tize Mha, P. A generalized non-linear flow law based on modified Zerilli-Armstrong model and its implementation into Abaqus/Explicit FEM Code / P. Tize Mha, A. Tongne, O. Pantalé // World Journal of Engineering and Technology. – 2022. – Vol. 10. – P. 334–362. DOI: 10.4236/wjet.2022.102021 Scholar
- 31.Song, P. A study on dynamic plastic deformation behavior of 5052 aluminum alloy / P. Song, W.-B. Li, X.-M. Wang // Key Engineering Materials. – 2019. – Vol. 812. – P. 45–52. Scholar
- 32.Jin, F. High – strain – rate forming performance of an aluminum alloy / F. Jin, M. Gu, H. Hong // Materials and technology. – 2020. – Vol. 54 (5). – P. 627–632. DOI: 10.17222/mit.2019.255 Scholar
- 33.Du, Z.-Deformation and fracture behavior of 5052 aluminum alloy by electromagnetic-driven stamping / Z. Du, X.-Cui, H. Yang, W. Xia // The International Journal of Advanced Manufacturing Technology. – 2022. – Vol. 123. – P. 3955–3968. DOI: 10.1007/s00170-022-10446-2 Scholar
- 34.Логинов, Ю.Н. Моделирование штамповки биметаллического шара с оболочкой из магния / Ю.Н. Логинов, Ю.В. Замараева // Обработка металлов давлением. – 2022. – № 2. – С. 75–82. DOI: 10.24412/0321-4664-2022-2-75-82 Scholar
- 35.Петров, П.А. Выбор математической функции для описания сопротивления деформации алюминиевых сплавов системы Al-Mg / П.А. Петров, В.Н. Фам // Автоматизированное проектирование в машиностроении. – 2022. –№ 12. – С. 25–28. Scholar
- 36.Рулин, С.П. Математическое моделирование операции прямого выдавливания осесимметричной заготовки из алюминиевого сплава в сферическую матрицу / С.П. Рулин, П.А. Петров // Машиностроение: сетевой электронный научный журнал. – 2025. – Т. 12, № 1. – С. 53–57. Scholar
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Article information
- Published
- 17 December 2025
- Issue date
- 17 December 2025
- Issue
- No. 5 (2025)