Kinematic Characteristics of Deformed Porous Structures

Author(s): Veselovska N.1, Sivak R.2, Paladiychuk Y.1, Bandura V.3, Telyatnik I.1, Bohatiuk M.1, Savkiv V.1, Edl M.4*

Affiliation(s):
1 Vinnytsia National Agrarian University, 3, Sonyachna St., 21000 Vinnytsia, Ukraine;
2 Polissia National University, 7, Staryi Blvd., 10002 Zhytomyr, Ukraine;
3 National University of Life and Environmental Sciences of Ukraine, 15, Heroiv Oborony St., 03041 Kyiv, Ukraine;
4 University of West Bohemia, 2732/8, Univerzitní St., 301 00, Pilsen, Czech Republic

*Corresponding Author’s Address: [email protected]

Issue: Volume 11, Issue 1 (2024)

Dates:
Submitted: September 18, 2023
Received in revised form: February 15, 2024
Accepted for publication: March 1, 2024
Available online: March 14, 2024

Citation:
Veselovska N., Sivak R., Paladiychuk Y., Bandura V., Telyatnik I., Bohatiuk M., Savkiv V., Edl M. (2024). Kinematic characteristics of deformed porous structures. Journal of Engineering Sciences (Ukraine), Vol. 11(1), pp. D44–D53. https://doi.org/10.21272/jes.2024.11(1).d6

DOI: 10.21272/jes.2024.11(1).d6

Research Area: Dynamics and Strength of Machines

Abstract. Experimental and computational methods of studying the stress state in the plastic region are characterized by various methods and accuracy of measurements, methods of mathematical processing of experimental information, and interpretation of results. The experimentally determined kinematics as a starting point is the most widely used method to study the stress-strain state in the plastic region. When studying the process of plastic deformation of porous blanks, the model of a rigid-plastic isotropic-strengthening porous body with a loading surface that has the shape of an ellipsoid with semi-axes. It depends on the amount of porosity and the ratio of the associated flow law as a mechanical model of the material. In the axisymmetric extrusion of porous blanks, the viscoplasticity method was used to determine the field of flow velocities based on the results of experimental studies. R-functions were applied to approximate experimentally obtained values. The problem of finding approximations was formulated in a variational statement. Cubic splines of one argument were used to interpolate functions. As a result, an approach was proposed, which consists of a particular sequence of calculating the derivatives of the coordinates of the nodes in time in combination with the R-functions approach. All the calculations were performed in Euler variables, eliminating the need to switch from Lagrangian variables and simplifying the solution. Additionally, this method allowed for working with an irregular and non-rectangular grid in areas with any shape of boundaries. This approach is more effective from the point of view of the approximation’s accuracy and the speed of calculations. Finally, the equation for calculating the porosity in the volume of the deformable workpiece based on the information about the distortion of the dividing grid elements was obtained. For stationary axisymmetric processes, a technique was developed that allowed for replacing the calculation of the accumulated deformation of the base material along the deformation trajectory by integration over the region. A technique was developed for determining the stress-strain state at unstable and stable stages of axisymmetric plastic deformation of porous blanks. The calculation results were compared based on the proposed experimental and calculation techniques and the finite element method.

Keywords: porous body, spline interpolation, non-stationary state, axisymmetric deformation, visioplasticity method, Euler coordinates, Lagrangian coordinates.

References:

  1. Grushko, A., Kukhar, V., Slobodyanyuk, Y. (2017). Phenomenological model of low-carbon steels hardening during multistage drawing. Solid State Phenomena, Vol. 265, pp. 114–123. https://doi.org/10.4028/www.scientific.net/SSP.265.114
  2. Puzyr, R., Shchetynin, V., Vorobyov, V., Skoriak, Y., Negrebetskyi, I. (2021). Improving the technology for manufacturing hollow cylindrical parts for vehicles by refining technological estimation dependencies. Eastern-European Journal of Enterprise Technologies, Vol. 6(1(114)), pp. 56–64. https://doi.org/10.15587/1729-4061.2021.244241
  3. Hrudkina, N., Markov, O., Shapoval, A., Titov, V., Aliyev, I., Abhari, P., Malii, K. (2022). Mathematical and computer simulation for the appearance of dimple defect by cold combined extrusion. FME Transactions, Vol. 50(1), pp. 90–98. https://doi.org/10.5937/fme2201090H
  4. Hosford, W. F., Caddell, R. M. (2007). Metal Forming: Mechanics and Metallurgy. Cambridge University Press, Cambridge, UK.
  5. Baldinozzi, G., Pontikis, V. (2022). Phenomenological potentials for the refractory metals Cr, Mo and W. Journal of Physics: Condensed Matter, Vol. 34(31), pp. 315–702. https://doi.org/10.1088/1361-648X/ac73ce
  6. Jia, X., Hao, K., Luo, Z., Fan, Z. (2022). Plastic deformation behavior of metal materials: A review of constitutive models. Metals, Vol. 12(12), 2077. https://doi.org/10.3390/met12122077
  7. Knudsen, T. (2008). An Experimental Study of Plastic Deformation of Materials. PhD thesis, Technical University of Denmark, Roskilde, Denmark.
  8. Kronsteiner, J., Horwatitsch, D., Hinterer, A., Gusenbauer, C., Zeman, K. (2016). Experimental determination of plastic strain in the extrusion process. AIP Conference Proceedings, Vol. 1769, 140001. https://doi.org/10.1063/1.4963538
  9. Kulagin, R., Beygelzimer, Y., Bachmaier, A., Pippan, R., Estrin, Y. (2019). Benefits of pattern formation by severe plastic deformation. Applied Materials Today, Vol. 15, pp. 236–241. https://doi.org/10.1016/j.apmt.2019.02.007
  10. Prager, W., (1995). The theory of plasticity: A survey of recent achievements. Proceedings of the Institution of Mechanical Engineers, Vol. 169(1), pp. 41–57. https://doi.org/10.1243/PIME_PROC_1955_169_015_02
  11. Versino, D., Tonda, A., Bronkhorst, C. A. (2017). Data driven modeling of plastic deformation. Computer Methods in Applied Mechanics and Engineering, Vol. 318, pp. 981–1004. https://doi.org/10.1016/j.cma.2017.02.016
  12. Hah, Z.-H., Youn, S.-K. (2015). Eulerian analysis of bulk metal forming processes based on spline-based meshfree method. Finite Elements in Analysis and Design, Vol. 106, pp. 1–15. https://doi.org/10.1016/j.finel.2015.07.004
  13. Schröder, J., Balzani, D., Brands, D. (2011). Approximation of random microstructures by periodic statistically similar representative volume elements based on lineal-path functions. Archive of Applied Mechanics, Vol. 81, pp. 975–997. https://doi.org/10.1007/s00419-010-0462-3
  14. Gogaev, K. A., Voropaev, V. S., Podrezov, Yu. N., Lugovskoi, Yu. F., Nazarenko, V. A., Koval, A. Yu., Yevych, Ya. I. (2017). Mechanical and fatigue properties of powder titanium strips, obtained by asymmetric rolling. Powder Metallurgy and Metal Ceramics, Vol. 56(1–2), pp. 69–77. https://doi.org/10.1007/s11106-017-9871-y
  15. Dell, H., Gese, H., Oberhofer, G. (2007). CrachFEM – A comprehensive approach for the prediction of sheet metal failure. AIP Conference Proceedings, Vol. 908, pp. 165–170. https://doi.org/10.1063/1.2740806
  16. Veselovska, N., Shargorodsky, S., Rutkevych, V., Iskovych-Lototsky, R., Omiotek, Z., Mamyrbaev, O., Zhunissova, U. (2021). Analysis of the Character of Change of the Profilogram of Micro Profile of the Processed Surface. In: Mechatronic Systems II. Applications in Material Handling Processes and Robotics, pp. 165–174. Routledge Taylor & Francis Group, New York, NY, USA.
  17. Papadopoulos, P., Lu, J. (2001). On the formulation and numerical solution of problems in anisotropic finite plasticity. Computer Methods in Applied Mechanics and Engineering, Vol. 190(37–38), pp. 4889–4910. https://doi.org/10.1016/S0045-7825(00)00355-8
  18. Bašić, H., Demirdzic, I., Muzaferia, S. (2005). Finite volume method for simulation of extrusion processes. International Journal for Numerical Methods in Engineering, Vol. 62(4), pp. 475–494. https://doi.org/10.1002/nme.1168
  19. Weselowska, N., Turych, V., Rutkevych, V., Ogorodnichuk, G. Kisała, P., Yeraliyeva, B., Yusupova, G. (2021). Investigation of Interaction of a Tool with a Part in the Process of Deforming Stretching with Ultrasound. In: Mechatronic Systems II. Applications in Material Handling Processes and Robotics, pp. 175–184. Routledge Taylor & Francis Group, New York, NY, USA.
  20. Veselovska, N. R., Shargorodsky, S. A., Larysa, E. Nykyforova, L. E, Omiotek, Z., Baglan, I., Kozhamberdiyeva, M. (2022). Efficiency Assessment Functioning of Vibration Machines for Biomass Processing. In Biomass as Raw Material for Production of Biofuels and Chemicals, pp. 53–60. Routledge Taylor & Francis Group, London, UK.
  21. Pokras, V, Rvachev, M. (1996). Application of the R-functions method to visioplastic analysis in metal forming. Journal of Materials Processing Technology, Vol. 60(1–4), pp. 493–500. https://doi.org/10.1016/0924-0136(96)02376-X
  22. Ogorodnikov, V. A., Dereven’ko, I. A., Sivak, R. (2018). On the influence of curvature of the trajectories of deformation of a volume of the material by pressing on its plasticity under the conditions of complex loading. Materials Science, Vol. 54(3), pp. 326–332. https://doi.org/10.1007/s11003-018-0188-x
  23. Nalobina, О. O., Vasylchuk, N. V., Bundza, О. Z., Holotiuk, M. V., Veselovska, N. R., Zoshchuk, N. V. (2019). А new technical solution of a header for sunflower harvesting. INMATEH-Agricultural Engineering, Vol. 58(2), pp. 129–136.
  24. Shatokhin, V., Ivanchuk, Y., Dvirna, O., Veselovskaya, N., Jurczak, W. (2022). Dynamic processes modeling in a peristaltic pump with a hydraulic drive for the Bingham fluid. Advances in Science and Technology Research Journal, Vol. 16(4), pp. 256–269. https://doi.org/10.12913/22998624/152944
  25. Sivak, R., Kulykivskyi, V., Savchenko, V., Minenko, S., Borovskyi, V. (2023). Determination of porosity functions in the pressure treatment of iron-based powder materials in agricultural engineering. Scientific Horizons, Vol. 26(3), pp. 124–134. https://doi.org/10.48077/scihor3.2023.124
  26. Shtern, M., Mikhailov, O., Mikhailov, A. (2021). Generalized continuum model of plasticity of powder and porous materials. Powder Metallurgy and Metal Ceramics, Vol. 60(1–2), pp. 20–34. https://doi.org/10.1007/s11106-021-00211-7
  27. Aliyeva, L., Hrudkina, N., Aliyev, I., Zhbankov, I., Markov, O. (2020). Effect of the tool geometry on the force mode of the combined radial-direct extrusion with compression. Eastern-European Journal of Enterprise Technologies, Vol. 2(1(104)), pp. 15–22. https://doi.org/10.15587/1729-4061.2020.198433

Full Text

© 2024 by the author(s).

This work is licensed under Creative Commons Attribution-Noncommercial 4.0 International License