Cluster model of the porosity of spongy titanium briquettes at the stage of pressing
DOI:
https://doi.org/10.15587/1729-4061.2020.206715Keywords:
composites, powder metallurgy, spongy titanium, packing of particles, pressing, types of poresAbstract
The main factors of the formation of porosity of pressed products based on spongy titanium were studied. Three types of pores were studied and separated – cluster (in the place of particles), inter-cluster, and natural pores of the material. The cluster models of particles packing at the stages of pressing were developed (from bulk density, or the formation of temporary structures to the formation of stable structures). The number of cluster faces in the models depends on coordination number λ, which means tetrahedral (λ=4) clusters at the initial stage and cuboctahedral (λ=12) at the later ones. Based on the Gaussian rule, for spheres packing, it was found that the most correct form of clusters for later pressing stages is cuboctahedral, as the pores between the spheres at the maximum tight packing with the coordination number of 12 have the shape close to cuboctahedrons and octahedrons, but with concave faces. Based on the difference between the volume of spheres, for which particles and clusters in the model were accepted, based on calculated volumes of intercluster octahedrons and cuboctahedrons, the volume of pores in the shape of the Steiner octahedron or cuboctahedron was calculated. In calculating the strength of adhesion between the particles, the proper porosity of spongy titanium is determined through the assumption that a part of the powder is a conglomerate that is formed from hollow spheres of the regular shape at the stage of titanium reduction by the magnesium thermal method. Accordingly, in the formula for calculating the strength of adhesion, the force that influences a particle will consist of the difference between forces of elastic deformation and the destruction of hollow spheres contained in the deformed volume. The developed models were proved by the results of practical research. Actual measurements show the average exponential ratio of the porosity to pressing pressure, which makes it possible to calculate s maximum inter-cluster porosity at the maximum compaction of 66 % and the compression factor of the studied material of 0.15References
- Krivoruchko, Y. S., Lerman, L. B., Shkoda, N. G. (2013). Models of porouse medias. Poverhnost', 5, 34–47. Available at: http://nbuv.gov.ua/UJRN/Pov_2013_5_6
- Kiselev, A. V. (1958). Korpuskulyarnaya struktura adsorbentov geley. Metody issledovaniya struktury vysokodispersnyh i poristyh tel. Moscow, 47–59.
- Pałka, K., Pokrowiecki, R. (2018). Porous Titanium Implants: A Review. Advanced Engineering Materials, 20 (5), 1700648. doi: https://doi.org/10.1002/adem.201700648
- Naidich, Y. V., Krasovskii, V. P. (2015). Use of Interfacial Exothermic Effect in the Wetting Process, Production of Composites, and Soldering of Ceramic Materials. Powder Metallurgy and Metal Ceramics, 54 (5-6), 331–339. doi: https://doi.org/10.1007/s11106-015-9718-3
- Zabolotnyi, O., Sychuk, V., Somov, D. (2018). Obtaining of Porous Powder Materials by Radial Pressing Method. Advances in Design, Simulation and Manufacturing, 186–198. doi: https://doi.org/10.1007/978-3-319-93587-4_20
- Romero, C., Yang, F., Bolzoni, L. (2018). Fatigue and fracture properties of Ti alloys from powder-based processes – A review. International Journal of Fatigue, 117, 407–419. doi: https://doi.org/10.1016/j.ijfatigue.2018.08.029
- Hadadzadeh, A., Whitney, M. A., Wells, M. A., Corbin, S. F. (2017). Analysis of compressibility behavior and development of a plastic yield model for uniaxial die compaction of sponge titanium powder. Journal of Materials Processing Technology, 243, 92–99. doi: https://doi.org/10.1016/j.jmatprotec.2016.12.004
- Titov, V. G., Zalazinsky, A. G., Kryuchkov, D. I., Nesterenko, A. V. (2019). Multi-criteria optimization by the «ideal point» method of raw material composition for composite blank manufacturing. Izvestiya Vuzov. Poroshkovaya Metallurgiya i Funktsional’nye Pokrytiya (Universitiesʹ Proceedings. Powder Metallurgy Аnd Functional Coatings), 2, 49–56. doi: https://doi.org/10.17073/1997-308x-2019-2-49-56
- Berezin, I. M., Zalazinskii, A. G., Nesterenko, A. V., Bykova, T. M. (2019). Simulation of metal powder bidirectional compression in a pressing tool with a floating die. PNRPU Mechanics Bulletin, 3, 5–16. doi: https://doi.org/10.15593/perm.mech/2019.3.01
- Berezin, I., Nesterenko, A., Kovacs, G., Zalazinskii, A. (2017). Influence of Stress State Conditions on Densification Behavior of Titanium Sponge. Acta Polytechnica Hungarica, 14 (6), 153–168.
- Zalazinskii, A. G., Nesterenko, A. V., Berezin, I. M. (2019). Study of the process of titanium-containing furnace charging material compaction by an experimental-analytical method. Izvestiya Vuzov Tsvetnaya Metallurgiya (Proceedings of Higher Schools Nonferrous Metallurgy, 4, 16–22. doi: https://doi.org/10.17073/0021-3438-2019-4-16-22
- Savich, V. V., Taraykovich, A. M., Sheko, G. A., Bedenko, S. A. (2017). Increase in homogenization of bidisperse mixture of spongy titanium powders and reduction in energy consumption during its preparation in the production of thin permeable elements. Metal Powder Report, 72 (5), 327–330. doi: https://doi.org/10.1016/j.mprp.2016.04.006
- Savich, V. V., Pronkevich, S. A., SHeluhina, A. I., Gorohov, V. M. (2013). Modelirovanie deformatsii chastitsy nesfericheskogo poroshka titana pri odnostoronnem pressovanii puansonom, plakirovany elastichnoy oblitsovkoy. Poroshkovaya metallurgiya: Inzheneriya poverhnosti, novye poroshkovye kompozitnye materialy, svarka. Sbornik dokladov 8-go Mezhdunarodnogo simpoziuma. Minsk, 314–320.
- Klymenko, L. P., Andrieiev, V. I., Prishchepov, O. F., Shuhai, V. V., Sluchak, O. I. (2017). Modification of construction and composite mixture in custing forms for cylinders of ICE. Internal Combustion Engines, 1, 43–46. doi: https://doi.org/10.20998/0419-8719.2017.1.08
- Andreeva, N. V., Radomysel'skiy, I. D., Scherban', N. I. (1975). Issledovanie uplotnyaemosti poroshkov. Poroshkovaya metallurgiya, 6, 32–42.
- Ferguson, S. P., Hales, T. C. (1998). A formulation of the Kepler conjecture. arXiv. Available at: https://arxiv.org/pdf/math/9811072.pdf
- Konvey, Dzh., Sloen, N. (1990). Upakovki sharov, reshetki i gruppy. Moscow: Mir, 415.
- Conway, J. H., Sloane, N. J. A. (1998). Sphere Packings, Lattices and Groups. Springer. doi: https://doi.org/10.1007/978-1-4757-2016-7
- Donets', A. G. (2000). Pro zvazhenu zadachu Shteynera. Matematychni mashyny i systemy, 1, 28–37.
- Johnson, K. L. (1985). Contact Mechanics. Cambridge University Press. doi: https://doi.org/10.1017/cbo9781139171731
- Batyanovskiy, E. I., Leonovich, I. A., Leonovich, A. A. (2010). Rezhimy pressovaniya materialov, porizovannyh mikrosferami. Novye materialy i tekhnologii v mashinostroenii: materialy XII Mezhdunar. nauch. Internetkonf. Bryansk: BGITA, 12, 151–155.
- Lichtenecker, K. (1926). Die Dielectrizitatskonstante naturlicher und Kunstlicher Mischkorper. Physik Z, 27, 115–255.
- Shneyder, P. (1960). Inzhenernye problemy teploprovodnosti. Moscow: Izdatel'stvo inostrannoy literatury, 478.
- Thomson, W. (1887). LXIII. On the division of space with minimum partitional area. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 24 (151), 503–514. doi: https://doi.org/10.1080/14786448708628135
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 Leonid Klymenko, Vyacheslav Andreev, Olexandr Sluchak, Oleg Pryshchepov, Oleg Shchesiuk
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.