Tula State University (Tula, Russia)

V. I. Platonov, Associate Professor of the Department of Mechanics and Processes of Plastic Shaping, Candidate of Technical Sciences, pvi_1@rambler.ru
S. N. Larin, Head of the Department of Mechanics and Processes of Plastic Shaping, Doctor of Technical Sciences, mpf-tula@rambler.ru

The paper investigates the process of isothermal backward extrusion of products made from high-strength, low-ductility materials. The necessity of accounting for the viscoplastic behavior of the material, including creep and stress relaxation occurring under hot deformation conditions, is substantiated to ensure accurate determination of forming loads and assessment of the integrity of finished products. The deformation process is assumed to be axisymmetric, with the deforming material in a viscoplastic state. The theoretical analysis is based on a variational approach employing the upperbound energy theorem of plasticity. A discontinuous velocity field is developed to describe the material flow kinematics. A distinctive feature of the proposed model is the consideration of the rotation of velocity discontinuity surfaces during extrusion, which generates additional normal velocity components and contributes to the overall energy balance. Based on the balance between the power of external and internal forces, an expression for the forming pressure is derived that accounts for both the strain level and the punch velocity. Relationships are obtained for predicting the final material integrity (damage accumulation) of the deforming billet using both energybased and strain-based fracture criteria. The proposed equations are applied to aluminum alloy AMg6 and titanium alloy VT6S. The results show that reducing the deformation rate decreases the forming pressure due to stress relaxation and, for certain materials, also reduces damage accumulation. It is demonstrated that the allowable degree of deformation should be determined using the proposed fracture criteria while considering the initial and critical material integrity. Both the pressure and the loss of material integrity are shown to depend on the operation rate. The results have been applied to the design of industrial manufacturing processes, as confirmed by examples of finished products.

1. Yakovlev S. S. Forging and stamping : study guide. Vol. 4. Sheet stamping. Moscow : Mashinostroeniye, 2010. 732 p.
2. Golenkov V. А., Yakovlev S. P., Golovin S. А., Yakovlev S. S., Kukhar V. D. Theory of metal pressure treatment. Moscow : Mashinostroeniye, 2009. 442 p.
3. Malinin N. N. Creep in metalworking. Moscow : Yurait, 2023. 221 p.
4. Kolmogorov V. L. Mechanics of metalworking by pressure. Moscow : Metallurgiya, 1986. 688 p.
5. Dwight G. B. Tables of integrals and other mathematical formulas. Moscow : Nauka, 1973. 228 p.
6. Yakovlev S. S., Yakovlev S. P., Chudin V. N. et al. Isothermal shaping of anisotropic materials with a rigid tool in the pre-creep mode. Moscow : Mashinostroeniye, 2009. 412 p.
7. Yakovlev S. P., Yakovlev S. S., Andreichenko V. A. Pressure treatment of anisotropic materials. Chișinău : Kvant, 1997. 331 p.
8. Platonov V. I. On the calculation of distribution stresses under conditions of visco-plasticity. Izvestiya Tulskogo gosudarstvennogo universiteta. Tekhnicheskiye nauki. 2022. No. 8. pp. 497–500.
9. Platonov V. I., Chudin V. N. Power mode of crimping with heating. Zagotovitelnye proizvodstva v mashinostroenii. 2022. Vol. 20, No. 7. pp. 311–314.
10. Ji H., Li Y., Huang X., Dong S., Li Y., Xiao W. Study on formability of duplex steel expansion pipe and its threaded joints. Measurement. 2023. Vol. 206, No. 1. 112308.
11. Tan B., Yao S., Zhang L., Xu P., Che Q. A novel deformation mode of expansion tubes accounting for extra contact. International Journal of Mechanical Sciences. 2023. Vol. 242, No. 3. 108024.
12. Shinkin V. N. Simple analytical dependence of elastic modulus on high temperatures for some steels and alloys. CIS Iron and Steel Review. 2018. Vol. 15. pp. 32–38.
13. Paul S. K. The effect of deformation gradient on necking and failure in hole expansion test. Manufacturing Letters. 2019. Vol. 21, No. 8. pp. 50–55.
14. Lu R., Zheng S., Teng J., Hu J., Fu D., Chen J., Zhao G., Jiang F., Zhang H. Microstructure, mechanical properties and deformation characteristics of Al-Mg-Si alloys processed by a continuous expansion extrusion
approach. Journal of Materials Science and Technology. 2021. Vol. 80, No. 7. pp. 150–162.
15. Shinkin V. N., Kolikov A. P. Engineering calculations for processes involved in the production of large-diameter pipes by the SMS Meer technology. Metallurgist. 2012. Vol. 55, No. 11-12. pp. 833–840.
16. Wu M. Z., Zhang X. W., Zhang Q. M. A new model for the expansion tube considering the stress coupling: Theory, experiments and simulations. Defence Technology. 2022. Vol. 18, No. 7. pp. 1190–1204.
17. Li J., Xie Z., Yu Y., Gong X., Gao G. Experimental and numerical study on the crashworthiness performance of a hybrid energy absorber with expanding-splitting-bending process. Thin-Wall Structures. 2022. Vol. 181, No. 12. 110122.
18. Shinkin V. N., Kolikov A. P. Simulation of the shaping of blanks for largediameter pipe. Steel in Translation. 2011. Vol. 41, No. 1. pp. 61–66.
19. Moreno C., Beaumont R., Hughes D. J., Williams T., Dashwood R. Quasi-static and dynamic testing of splitting, expansion and expansion-splitting hybrid tubes under oblique loading. International Journal of Impact Engineering. 2017. Vol. 100, No. 2. pp. 117–130.
20. Li J., Gao G., Dong H., Xie S., Guan W. Study on the energy absorption of the expanding-splitting circular tube by experimental investigations and numerical simulations. Thin-Wall Structures. 2016. Vol. 103, No. 6. pp. 105–114.
21. Demin V. A., Chernyaev A. V., Platonov V. I., Korotkov V. A. Experimental technique for determining the mechanical properties of metal under stretching at high temperature. Tsvetnye Metally. 2019. No. 5. pp. 66–73.
22. Chernyaev A. V., Usenko N. A., Korotkov V. A., Platonov V. I. Understanding how deformation rate influences the resistance to deformation under static tension at high temperature. Tsvetnye Metally. 2019. No. 5. pp. 60–65.