Modeling of density estimation during sintering of zirconium dioxide by the method of electroconsolidation
DOI (Low Temperature Physics):
https://doi.org/10.1063/10.0043203Ключові слова:
модель Скорохода–Олевського–Штерна, діоксид цирконію, електроконсолідація, ущільнення, спікання, моделюванняАнотація
Представлено результати чисельного моделювання процесів ущільнення та зростання зерна порошкових матеріалів на основі діоксиду цирконію ZrO2 при електроконсолідації. Як теоретичну основу використано модель Скорохода–Олевського–Штерна, яка описує кінетику ущільнення та еволюцію мікроструктури. Ідентифікацію параметрів моделі виконано на основі експериментальних даних щодо зміни температури, відносної щільності та осьового напруження зразків складу ZrO2+3 мол % Y2O3. Розроблено спеціалізовану комп’ютерну програму, яка дозволила виконати серію чисельних експериментів та зіставити результати моделювання з реальними даними спікання. Встановлено, що розраховані криві зміни щільності добре збігаються з експериментальними результатами, що підтверджує адекватність застосованої моделі. Показано, що на заключних стадіях процесу істотно впливає зростання зерна, проте остаточна щільність значною мірою визначається режимом ізотермічної витримки та рівнем тиску, що прикладається. Продемонстровано, що збільшення тиску дає змогу досягти високої щільності навіть без значного подовження часу процесу. Розроблений підхід забезпечує можливість прогнозування щільності, розмірів зерен та механічних характеристик спечених зразків. Практична значимість роботи полягає в тому, що запропонована методика може використовуватися для оптимізації режимів електроконсолідації, зниження енерговитрат та підвищення якості керамічних цирконієвих композитів.
Посилання
O. I. Getman, S. P. Rakitin, and V. V. Skorokhod, “Rheological and thermal activation analyses of the sintering kinetics of tungsten powders,” Powder Metall. Metal Cer. 23, 764 (1984). https://doi.org/10.1007/BF00792139
V. V. Skorokhod, “Mechanism of flow of material during sintering and superplasticity of polyc rystalline materials,” Powder Metall. Metal Cer. 17, 359 (1978). https://doi.org/10.1007/BF00795017
R. M. German, Sintering: From Empirical Observations to Scientific Principles (Elsevier, 2014).
O. Getman, “Application of skorokhod’s rheological theory of sintering to analyze the sintering kinetics of tungsten powders,” Powder Metall. Metal Cer. 58, 373 (2019). https://doi.org/10.1007/s11106-019-00088-7
B. T. Ratov, V. A. Mechnik, N. A. Bondarenko, V. M. Kolodnitskyi, E. S. Gevorkyan, V. P. Nerubaskyi, A. G. Gusmanova, B. V. Fedorov, N. A. Kaldibaev, M. T. Arshidinova, and V. G. Kulych, “Features structure of the cdiamond‒(WC‒Co)‒ZrO2 composite fracture surface as a result of impact loading,” J. Superhard Mater. 45, 348 (2023). https://doi.org/10.3103/S1063457623050088
M. Shtern, A. Kuzmov, V. Skorokhod, and E. Olevsky, “Influence of external constraints on the stability of sintering of bi-porous materials,” Modell. Simul. Mater, Sci. Eng. 19, 015001 (2011). https://doi.org/10.1088/0965-0393/19/1/015001
E. A. Olevsky, “Theory of sintering: From discrete to continuum,” Mater. Sci. Eng. R 23, 41 (1998), see http://www.ptl.sdsu.edu/articles_pics/review.pdf. https://doi.org/10.1016/S0927-796X(98)00009-6
C. Manière, L. Durand, G. Chevallier, and C. Estournès, “A spark plasma sintering densification modeling approach: From polymer, metals to ceramics,” J. Mater. Sci. 53, 7869 (2018). https://doi.org/10.1007/s10853-018-2096-8
M. Abouaf, J. L. Chenot, G. Raisson, and P. Bauduin, “Finite element simulation of hot isostatic pressing of metal powders,” Int. J. Numer. Methods Eng. 25, 191 (1988). https://doi.org/10.1002/nme.1620250116
H. Riedel, H. Zipse, and J. Svoboda, “Equilibrium pore surfaces, sintering stresses and constitutive equations for the intermediate and late stages of sintering — II. diffusional densification and creep,” Acta Metall. Mater. 42, 445 (1994). https://doi.org/10.1016/0956-7151(94)90499-5
M. Gasik and B. Zhang, “A constitutive model and FE simulation for the sintering process of powder compacts,” Comput. Mater. Sci. 18, 93 (2000). https://doi.org/10.1016/S0927-0256(00)00090-2
Y. Wang, F. Wang, and Y. Wang, “Numerical simulation and verification of hot isostatic pressing densification process of W–Cu powder,” Mater. Res. Express 9, 076503 (2022). https://doi.org/10.1088/2053-1591/ac7ea1
V. V. Skorokhod, E. A. Olevskii, and M. B. Shtern, “Continuum theory of sintering. I. phenomenological model. analysis of the effect of external forces on the kinetics of sintering,” Powder Metall. Metal Cer. 32, 21 (1993). https://doi.org/10.1007/BF00559728
M. B. Shtern, A. V. Kuzmov, V. V. Skorokhod, and E. Olevsky, “Sintering stability of biporous materials under kinematic constraints,” Powder Metall. Metal Cer. 49, 17 (2010). https://doi.org/10.1007/s11106-010-9196-6
R. L. Coble, “Sintering crystalline solids. I. intermediate and final state diffusion models,” J. Appl. Phys. 32, 787 (1961). https://doi.org/10.1063/1.1736107
C. Manière, L. Durand, A. Weibel, and C. Estournès, “Spark-plasma-sintering and finite element method: From the identification of the sintering parameters of a submicronic α-alumina powder to the development of complex shapes,” Acta Mater. 102, 169 (2016). https://doi.org/10.1016/j.actamat.2015.09.003
S.-J. L. Kang, Sintering: Densification, Grain Growth, and Microstructure (Elsevier Butterworth-Heinemann, 2005), see https://books.google.com.ua/books?id=uPWbuZohRmoC&printsec=frontcover&redir_esc=y#v=onepage&q&f=false.
Z.-Z. Du and A and C. F. Cocks, “Constitutive models for the sintering of ceramic components—I. Material models,” Acta Metall. Mater. 40, 1969 (1992). https://doi.org/10.1016/0956-7151(92)90183-F
R. M. German, P. Suri, and S. J. Park, “Review: Liquid phase sintering,” J. Mater. Sci. 44, 1 (2009). https://doi.org/10.1007/s10853-008-3008-0
R. K. Bordia, S.-J. L. Kang, and E. A. Olevsky, “Current understanding and future research directions at the onset of the next century of sintering science and technology,” J. Am. Cer. Soc. 100, 2314 (2017). https://doi.org/10.1111/jace.14919
E. S. Hevorkian, M. Rucki, R. V. Vovk, V. P. Nerubatskyi, D. Pieniak, and V. O. Chyshkala, “Comparative qualitative analysis of hot pressing of zirconium dioxide nanopowders,” Funct. Mater. 32, 134 (2025). https://doi.org/10.15407/fm32.01.134
J. P. Winczewski, S. Zeiler, S. Gabel, D. Maestre, B. Merle, J. G. E. Gardeniers, and A. Susarrey Arce, “Additive manufacturing of 3D yttria-stabilized zirconia microarchitectures,” Mater. Des. 238, 112701 (2024). https://doi.org/10.1016/j.matdes.2024.112701
E. S. Hevorkian, O. M. Morozova, V. P. Nerubatskyi, V. O. Chyshkala, D. S. Sofronov, S. Moya, A. Abarrategi, B. Arnaiz, M. A. Bondarenko, and R. V. Vovk, “Composite material based on zirconium dioxide partially stabilised with cerium oxide and aluminium oxide for bioengineering applications,” Funct. Mater. 31, 351 (2024). https://doi.org/10.15407/fm31.03.351
E. Volceanov, A. Volceanov, Ş. Motoc, Ş. Iacob, and R. Constantin, “Stabilisation of zirconium dioxide in the ZrO2–CeO2–SrO system,” Key Eng. Mater. 206–213, 1697 (2001). https://doi.org/10.4028/www.scientific.net/KEM.206-213.1697
E. Gevorkyan, V. Nerubatskyi, V. Chyshkala, and O. Morozova, “Revealing specific features of structure formation in composites based on nanopowders of synthesized zirconium dioxide,” East.-Eur. J. Enterp. Technol. 5, 12 (113), 6 (2021). https://doi.org/10.15587/1729-4061.2021.242503
V. P. Nerubatskyi, R. V. Vovk, E. S. Gevorkyan, D. A. Hordiienko, Z. F. Nazyrov, and H. L. Komarova, “Investigation of phase and structural states in nanocrystalline powders based on zirconium dioxide,” Low Temp. Phys. 49, 1277 (2023) [Fiz. Nyzk. Temp. 49, 1404 (2023)]. https://doi.org/10.1063/10.0021374
M. H. Ghaemi, S. Reichert, A. Krupa, M. Sawczak, A. Zykova, K. Lobach, S. Sayenko, and Y. Svitlychnyi, “Zirconia ceramics with additions of alumina for advanced tribological and biomedical applications,” Cer. Int. 43, 9746 (2017). https://doi.org/10.1016/j.ceramint.2017.04.150
D. Tovar-Vargas, E. Roitero, M. Anglada, E. Jiménez-Piqué, and H. Reveron, “Mechanical properties of ceria-calcia stabilized zirconia ceramics with alumina additions,” J. Eur. Cer. Soc. 41, 5602 (2021). https://doi.org/10.1016/j.jeurceramsoc.2021.05.006
C. Piconi and G. Maccauro, “Zirconia as a ceramic biomaterial,” Biomaterials 20, 1 (1999). https://doi.org/10.1016/S0142-9612(98)00010-6
Z. Meng, W. Qian, B. Ning, S. Wang, Y. Chen, Y. Zhang, N. Wang, Y. Li, W. Zhang, and G. Gao, “High-temperature crack resistance of yttria-stabilized zirconia coatings enhanced by interfacial stress transfer,” Appl. Surf. Sci. 682, 161688 (2025). https://doi.org/10.1016/j.apsusc.2024.161688
A. G. Mamalis, E. S. Hevorkian, V. P. Nerybatskyi, M. Rucki, Z. Krzysiak, and O. M. Morozova, “Effect of nanoadditives on the properties of partially stabilized zirconia,” Nanotechno. Percep. 19, 26 (2023), see https://nano-ntp.com/index.php/nano/article/view/325/235.
E. S. Gevorkyan, D. S. Sofronov, V. P. Nerubatskyi, V. O. Chyshkala, O. M. Morozova, O. M. Lebedynskyi, and P. V. Mateychenko, “A study on the formation and sintering of powders synthesized from ZrO2 micro- and nanoparticles from fluoride solutions,” J. Superhard Mater. 45, 31 (2023). https://doi.org/10.3103/S1063457623010057
Z. Krzysiak, E. Gevorkyan, V. Nerubatskyi, M. Rucki, V. Chyshkala, J. Caban, and T. Mazur, “Peculiarities of the phase formation during electroconsolidation of Al2O3–SiO2–ZrO2 powders mixtures,” Materials 15, 6073 (2022). https://doi.org/10.3390/ma15176073
I.-W. Chen and X.-H. Wang, “Sintering dense nanocrystalline ceramics without final-stage grain growth,” Nature 404, 168 (2000). https://doi.org/10.1038/35004548
B. T. Ratov, E. Hevorkian, V. A. Mechnik, N. A. Bondarenko, V. M. Kolodnitskyi, T. O. Prikhna, V. E. Moshchil, V. P. Nerubaskyi, A. B. Kalzhanova, R. U. Bayamirova, A. R. Togasheva, and M. D. Sarbopeeva, “Effect of the ZrO2 content on the strength characteristics of the matrix material of cdiamond–(WC–Co) composites synthesized by spark plasma sintering,” J. Superhard Mater. 46, 175 (2024). https://doi.org/10.3103/S1063457624030079
D. M. Hulbert, A. Anders, D. V. Dudina, J. Andersson, D. Jiang, C. Unuvar, U. Anselmi-Tamburini, E. J. Lavernia, and A. K. Mukherjee, “The absence of plasma in “spark plasma sintering”,” J. Appl. Phys. 104, 033305 (2008). https://doi.org/10.1063/1.2963701
E. S. Hevorkian, V. P. Nerubaskyi, V. O. Chyshkala, S. V. Lytovchenko, M. M. Prokopiv, W. Samociuk, and V. A. Mechnik, “Technological and innovative features of the electroconsolidation method as a kind of plasma sintering for refractory compounds,” J. Superhard Mater. 46, 364 (2024). https://doi.org/10.3103/S1063457624050046
A. G. Mamalis, E. S. Hevorkian, V. P. Nerubatskyi, Z. Krzysiak, O. M. Morozova, and L. Chalko, “Peculiarities of obtaining nanostructured materials compacted by the method of hot pressing due to the passage of direct electric current,” Nanotechnol. Percep. 20, 61 (2024), see https://nano-ntp.com/index.php/nano/article/view/336. https://doi.org/10.62441/nano-ntp.v20i7.3799
A. M. Laptev, M. Bram, D. Garbiec, J. Räthel, A. van der Laan, Y. Beynet, J. Huber, M. Küster, M. Cologna, and O. Guillon, “Tooling in spark plasma sintering technology: Design, optimization, and application,” Adv. Eng. Mater. 26, 2301391 (2024). https://doi.org/10.1002/adem.202301391
F. Nisar, J. Rojek, S. Nosewicz, K. Kaszyca, and M. Chmielewski, “Coupled thermo-electric discrete element model for spark plasma sintering,” Powder Technol. 458, 120957 (2025). https://doi.org/10.1016/j.powtec.2025.120957
E. Gevorkyan, M. Rucki, Z. Krzysiak, V. Chishkala, W. Zurowski, W. Kucharczyk, V. Barsamyan, V. Nerubatskyi, T. Mazur, D. Morozow, Z. Siemiątkowski, and J. Caban, “Analysis of the electroconsolidation process of fine-dispersed structures out of hot pressed Al2O3–WC nanopowders,” Materials 14, 6503 (2021). https://doi.org/10.3390/ma14216503
E. S. Gevorkyan, M. Rucki, A. A. Kagramanyan, and V. P. Nerubatskiy, “Composite material for instrumental applications based on micro powder Al2O3 with additives nano-powder SiC,” Inter. J Refract. Metals Hard Mate. 82, 336 (2019). https://doi.org/10.1016/j.ijrmhm.2019.05.010
C. Gautam, J. Joyner, A. Gautam, J. Raoc, and R. Vajtai, “Zirconia-based dental ceramics: Structure, mechanical properties, biocompatibility and applications,” Dalton Trans. 45, 19194 (2016). https://doi.org/10.1039/C6DT03484E
W. Huang, J. Zhou, C. Ren, F. Zhang, J. Tang, M. Omran, and G. Chen, “Sintering behavior and properties of zirconia ceramics prepared by pressureless sintering,” Cer. Int. 49, 27192 (2023). https://doi.org/10.1016/j.ceramint.2023.05.267
E. Hevorkian, A. G. Mamalis, V. Nerubatskyi, M. Rucki, W. Samociuk, and V. Chishkala, “Effect of electric current on phase formation in tungsten monocarbide in the process of electroconsolidation of nanopowders,” Evol. Mech. Eng. 5, EME.000615 (2024). https://doi.org/10.31031/EME.2024.05.000615
Z. Wu, N. Ye, H. Zhuo, J. Mao, W. Zhu, Z. Gong, X. Chen, and J. Tang, “High-pressure and high-temperature synthesis of binderless nanocrystalline WC cemented carbide: Microstructure and mechanical properties,” Cer. Int. 51, 7756 (2025). https://doi.org/10.1016/j.ceramint.2024.12.213
E. Gevorkyan, M. Rucki, T. Sałaciński, Z. Siemiątkowski, V. Nerubatskyi, W. Kucharczyk, Ja. Chrzanowski, Yu. Gutsalenko, and M. Nejman, “Feasibility of cobalt-free nanostructured WC cutting inserts for machining of a TiC/Fe composite,” Materials 14, 3432 (2021). https://doi.org/10.3390/ma14123432
V. A. Dutka, A. L. Maystrenko, V. G. Kulych, and O. I. Borymskyi, “Modeling the densification of boron carbide based ceramic materials under flash pressure sintering,” J. Superhard Mater. 46, 352 (2024). https://doi.org/10.3103/S1063457624050022
C. Manière, L. Durand, A. Weibel, and C. Estournès, “A predictive model to reflect the final stage of spark plasma sintering of submicronic α-alumina,” Cer. Int. 42, 9274 (2016). https://doi.org/10.1016/j.ceramint.2016.02.048
A. Nisar, C. Zhang, B. Boesl, and A. Agarwal, “Unconventional materials processing using spark plasma sintering,” Ceramics 4, 20 (2021). https://doi.org/10.3390/ceramics4010003
