Model of formation of porosity of sponge titanium briquettes at the sintering stage

Leonid Klymenko, Vyacheslav Andreev, Olexandr Sluchak, Oleg Pryshchepov, Oleg Shchesiuk

Abstract


This article examines the peculiarities of the formation of interparticle connections in porous products based on titanium powders using sponge titanium as an example, which are used in the aviation industry and airfield management. The developed model is based on the results of a previous study, where the structure of cuboctahedral and inverse cuboctahedral clusters of packing spherical powder particles was determined at the most dense packing. During the study, a model of the fusion of particles at the points of pressing deformation due to recrystallization under the influence of high temperatures in a vacuum was developed. 4 main stages of powder briquette sintering were considered, and a mathematical model was developed for each of them. Thus, the stage of liquid evaporation is considered from the viewpoint of the cavitation effect of boiling on the surface of particles and boiling of plasticizers. Euler's film boiling formula was used to describe the forces acting on the particle surface; Tolubinsky's formula was used for bubble boiling; convective heat exchange was considered part of the final stage of sintering. The stage of the formation of metallic bonds is modeled on the basis of the results of practical studies in the REV 5.5 furnace, recrystallization based on differential scanning colorimetry on the NETZSCH STA 449F1 Proteus device, and determining the change in grain size according to the E19 ASTM scales using the Jeffers method. The diffusion stage is modeled on the basis of the approximation of the particle deformation model in the contact zones at the pressing stage using the Frenkel formula. Linear shrinkage is modeled based on direct measurement of sample sizes before and after sintering. The developed model has a certain versatility when applied to simulate the interaction of particles of metal powders under the conditions of the formation of porous briquettes, especially if the shape of the particles is close to round or spongy. The obtained result will make it possible to more accurately evaluate such a factor as the adhesion between the particles of the pressing and predict the tensile strength of the material. Additionally, due to the mathematical characterization of the peculiarities of the formation of corpuscular porosity under the conditions of sintering in a vacuum, we can design materials with differentiated porosity, as well as lay the foundations for powder 3D printing of such materials, by assembling grain by grain, or layer by layer with the adjustment of the force of particle compression one into the other.

Keywords


titanium; titanium sponge; corpuscular porosity; sintering; particle packing; diffusion; recrystallization; pressing

References


Kiselev, A. Korpuskulyarnaya struktura adsorbentov geley. In. Book Metody issledovaniya struktury vysokodispersnykh i poristykh tel. Moscow, Izd-vo AN SSSR Publ., 1958, pp. 47–59.

Klymenko, L., Andrieiev, V., Sluchak, O., Pryshchepov, O., Shchesiuk, O. Cluster model of the porosity of spongy titanium briquettes at the stage of pressing. Eastern-European Journal of Enterprise Technologies, 2020, vol. 3, iss. 6 (105), pp. 42-52. DOI: 10.15587/1729-4061.2020.206715.

Ferguson, S., Hales, T. A formulation of the Kepler conjecture, 2002. Available at: https://arxiv.org/pdf/math/9811072.pdf. (accessed 12.12.2022).

Froes, Francis H. (Sam)., Qian, Ma. 31 - A perspective on the future of titanium powder metallurgy. Titanium Powder Metallurgy, 2015, pp. 601–608. DOI: 10.1016/B978-0-12-800054-0.00031-9.

Gab I., Stetsiuk T., Kostiuk B., Martyniuk S., Naidich Yu. Adheziyno-mekhanichne zʺyednannya oksydnykh materialiv z metalamy [Adhesive-mechanical connection of oxide materials with metals]. Adheziya rozplaviv i payka materialiv – Adhesion of melts and soldering materials, 2015, no. 48, pp. 117–124. Available at: http://www.materials.kiev.ua/

article/1878. (accessed 12.12.2022).

Liu, Na., Wang, Ying., He, Wei-jun., Li, Jun., Chapuis, Adrien et al. Microstructure and textural evolution during cold rolling and annealing of commercially pure titanium sheet. Transactions of Nonferrous Metals Society of China, 2018, vol. 28, iss. 6, pp. 1123-1131. DOI: 10.1016/S1003-6326(18)64748-X.

Annur, D., Rokhmanto, F., Thaha, Y. N., Kartika, I., Dimyati, A., Supriadi, S., Suharno, B. Processing and Characterization of Porous Titanium for Orthopedic Implant Prepared by Argon-atmospheric Sintering and Arc Plasma Sintering. Materials Research, 2021, vol. 24, iss. 6. DOI: 10.1590/1980-5373-MR-2021-0122.

Zabolotnyi, O., Povstyanoi, O., Somov, D., Sychuk, V., Svirzhevskyi, K. Technology of Obtaining Long-Length Powder Permeable Materials with Uniform Density Distributions. World Congress on Engineering and Technology; Innovation and its Sustainability 2018. WCETIS 2018. EAI/Springer Innovations in Communication and Computing. Springer, Cham, 2020, pp. 63-78. DOI: 10.1007/978-3-030-20904-9_5.

Marchenko, Tu., Petrik, Ya., Ovchynnikov, A., Skrebtsov, A. Puti povisheniya svoistv zahotovok detaley HTD iz zharoprochnykh titanovykh splavov, po-luchennykh metodom priamoho lazernoho vyra-shchivania [Ways to increase the properties of blots of gas turbine engine parts from heat-resistant titanium alloys obtained by direct laser growth]. Aviacijno-kosmicna tehnika i tehnologia – Aerospace technic and technology, 2021, no. 5 (175), pp. 53-59. DOI: 10.32620/aktt.2021.5.07.

Wenjie Hu, Sergii Markovych, Kun Tan, Oleksandr Shorinov, Tingting Cao. Issledovaniye iznosostoykogo pokrytiya aviatsionnykh detaley iz titanovogo splava po tekhnologii kholodnogo napyleniya [Research on wear resistance coating of aircraft titanium alloy parts by cold spraying technology]. Aviacijno-kosmicna tehnika i tehnologia – Aerospace technic and technology, 2020, no. 6 (166), pp. 61-71. DOI: 10.32620/aktt.2020.6.07.

Kobashi, Makoto., Kanetake, Naoyuki. Novel Processing of Porous Titanium Composite for Producing Open Cell Structure. Materials Science Forum, 2007, vol. 539-543, pp. 1004-1009. DOI: 10.4028/www.scientific.net/MSF.539-543.1004.

Khunger, G. Y. Izbrannye metody issledovanyia v metallove-denii [Selected research methods in metallurgy]. Moscow, Metallurgiya Publ., 1985. 416 p.

McCracken, C., Motchenbacher, C., Barbis, D. Review of titanium powder-production methods. International Journal of Powder Metallurgy, 2010, vol. 46, iss. 5, pp. 19-26.

Frenkel’, Ya. Osvobozhdeniye vnutriatomnoy energii [Release of intra-atomic energy]. Moscow, Akad. nauk SSSR Publ., 1946. 124 p.




DOI: https://doi.org/10.32620/aktt.2023.1.03