Machine-learning method for the development of a Vickers microhardness predictive model of a hydroxyapatite-multi-walled carbon nanotube ceramic composite material

   The durability and wear resistance of ceramic implants, used under high operating loads largely, depend on their mechanical characteristics. Ceramic composite based on hydroxyapatite is considered as a promising biomaterial for reconstruction of damaged bone tissues and replacement bone defects due to its biocompatibility and ability to provide osseointegration with bone tissue. In this work, to increase mechanical strength, the hydroxyapatite ceramics was reinforced by multi-walled carbon nanotubes additives which have high physical and mechanical properties. The potential of such research lies in the use of these composites in implantation areas that experience significant mechanical loads. The effectiveness of nanotubes reinforcement depends on the ceramics composition, synthesis technology, and testing conditions, resulting in high variability in the final characteristics. At the same time, direct experimental study of the properties of each sample requires significant time-cost. The use of mathematical models based on machine learning methods to optimize the process of analysis the mechanical characteristics of composite materials is relevant study. This will allow us to predict Vickers microhardness depending on the indentation load. In this study, experimental microhardness tests were carried out by using Vickers method for six sets of ceramic materials which were exposed to indentation loads ranging from 0.98 N to 9.8 N. Three machine learning methods were used to predict the data obtained: neural network, random forest and gradient boosting. After averaging the values for all loads, it was determined that with the increasing the concentration of multi-walled carbon nanotubes to 0.5 wt. % the Vickers microhardness of the composite increases from 3.83 ± 0.39 GPa to 4.71 ± 0.40 GPa compared to hydroxyapatite without additives, and reinforcement becomes effective by 19 %. Thus, the greatest contribution to the increase in the microhardness of the composite was made by the additives of multi-walled carbon nanotubes with a concentration of 0.5 wt.%, while the addition of 1 and 2 wt.% led to a significant decrease in microhardness, which is associated with the appearance of multi-walled carbon nanotubes agglomeration in the ceramic hydroxyapatite matrix. The simulation results based on experimental data allowed us to determine the optimal machine learning method for constructing a predictive model of the microhardness of hydroxyapatite - multi-walled carbon nanotubes ceramic composite in a wide range of loads. In addition, it was possible to establish the relationship between the composition of the composite and its mechanical characteristics, which opens up new possibilities for designing strong and durable ceramic implants.

1. Fiume E., Magnaterra G., Rahdar A., Verné E., Baino F. Hydroxyapatite for biomedical applications : A short overview. Ceramics, 2021, vol. 4, no. 4, pp. 542–563. doi: 10.3390/ceramics4040039

2. Rahman M., Li Y., Wen C. HA coating on Mg alloys for biomedical applications : A review. Journal of Magnesium and Alloys, 2020, vol. 8, no. 3, pp. 929–943. doi: 10.1016/j.jma.2020.05.003

3. Gu Y.W., Loh N.H., Khor K.A., Tor S.B., Cheang P. Spark plasma sintering of hydroxyapatite powders. Biomaterials, 2002, vol. 23, no. 1, pp. 37–43. doi: 10.1016/S0142-9612(01)00076-X

4. White A.A., Best S.M., Kinloch I.A. Hydroxyapatite–carbon nanotube composites for biomedical applications : a review. International Journal of Applied Ceramic Technology, 2007, vol. 4, no. 1, pp. 1–13. doi: 10.1111/j.1744-7402.2007.02113.x

5. Zhao X., Zheng J., Zhang W., Chen X., Gui Z. Preparation of silicon coated-carbon fiber reinforced HA bio-ceramics for application of load-bearing bone. Ceramics International, 2020, vol. 46, no. 6, pp. 7903–7911. doi: 10.1016/j.ceramint.2019.12.010

6. Khalid P. Suman V.B. Carbon nanotube-hydroxyapatite composite for bone tissue engineering and their interaction with mouse fibroblast L929 In Vitro. Journal of Bionanoscience, 2017, vol. 11, no. 3, pp. 233–240. doi: 10.1166/jbns.2017.1431

7. Ferreira C.R.D., Santiago A.A.G., Vasconcelos R.C., Paiva D.F.F., Pirih F.Q., Araújo A.A., Motta F.V., Bomio M.R.D. Study of microstructural, mechanical, and biomedical properties of zirconia/hydroxyapatite ceramic composites. Ceramics International, 2022, vol. 48, no. 9, pp. 12376–12386. doi: 10.1016/j.ceramint.2022.01.102

8. Lahiri D., Singh V., Keshri A.K., Seal S., Agarwal A. Carbon nanotube toughened hydroxyapatite by spark plasma sintering: microstructural evolution and multiscale tribological properties. Carbon, 2010, vol. 48, no. 11, pp. 3103–3120. doi: 10.1016/j.carbon.2010.04.047

9. Mukherjee S., Kundu B., Chanda A., Sen S. Effect of functionalisation of CNT in the preparation of HAp–CNT biocomposites. Ceramics international, 2015, vol. 41, no. 3, part A, pp. 3766–3774. doi: 10.1016/j.ceramint.2014.11.052

10. Henriques B., Fabris D., Lopes E., Moreira A.C., Mantovani I.F., Fernandes C.P, Fredel M.C. Influence of the addition of Ni-coated carbon nanotubes on the mechanical properties of highly porous zirconia cellular structures. Advanced Engineering Materials, 2022, vol. 24, no. 1, pp. 2100624. doi: 10.1002/adem.202100624

11. Yu L., Jia P., Song Y., Zhao B., Pan Y., Wang J., Cui H., Feng R., Li H., Cui X., Gao Z., Fang X., Zhang L. Effect of carbon nanotubes on the microstructure and properties of plasma electrolytic oxidized ceramic coatings on high silicon aluminum alloy. Journal of Materials Research and Technology, 2022, vol. 18, pp. 3541–3552. doi: 10.1016/j.jmrt.2022.04.035

12. Thirugnanasambantham K.G., Sankaramoorthy T., Karthikeyan R., Kumar K.S. A comprehensive review: Influence of the concentration of carbon nanotubes (CNT) on mechanical characteristics of aluminium metal matrix composites: Part 1. Materials Today: Proceedings, 2021, vol. 45, pp. 2561–2566. doi: 10.1016/j.matpr.2020.11.267

13. Kumar S.P., Selvamani S.T., Vigneshwar M., Hariharan S.J. Tensile, microhardness, and microstructural analysis on Mg-CNT nano composites. Materials Today: Proceedings, 2018, vol. 5, no. 2, part 2. pp. 7882–7888. doi: 10.1016/j.matpr.2017.11.469

14. Veljović Đ., Vuković G.D., Steins I., Palcevskis E., Uskoković P., Petrović R., Janaćković Đ. Improvement of the mechanical properties of spark plasma sintered hap bioceramics by decreasing the grain size and by adding multi-walled carbon nanotubes. Science of Sintering, 2013, vol. 45, no. 2, pp. 233–243. doi: 10.2298/sos1302233v

15. Currey J.D. Mechanical properties of bone tissues with greatly differing functions. Journal of Biomechanics, 1979, vol. 12, no. 4, pp. 313–319. doi: 10.1016/0021-9290(79)90073-3

16. Okamoto M., Dohi Y., Ohgushi H., Shimaoka H., Ikeuchi M., Matsushima A., Yonemasu K., Hosoi H. Influence of the porosity of hydroxyapatite ceramics on in vitro and in vivo bone formation by cultured rat bone marrow stromal cells. Journal of Materials Science: Materials in Medicine, 2006, vol. 17, no. 4, pp. 327–336. doi: 10.1007/s10856-006-8232-z

17. Imbeni V., Kruzic J.J., Marshall G.W., Marshall S.J., Ritchie R.O. The dentin–enamel junction and the fracture of human teeth. Nature Materials, 2005, vol. 4, no. 3, pp. 229–232. doi: 10.1038/nmat1323

18. Nastic A., Merati A., Bielawski M., Bolduc M., Fakolujo O., Nganbe M. Instrumented and Vickers indentation for the characterization of stiffness, hardness and toughness of zirconia toughened Al₂O₃ and SiC armor. Journal of Materials Science and Technology, 2015, vol. 31, no. 8, pp. 773–783. doi: 10.1016/j.jmst.2015.06.005

19. Pashkov D.M., Belyak O.A., Guda A.A., Kolesnikov V.I. Reverse engineering of mechanical and tribological properties of coatings: results of machine learning algorithms. Physical Mesomechanics, 2022, vol. 25, no. 4, pp. 296–305. doi: 10.1134/s1029959922040038

20. Abueidda D.W., Almasri M., Ammourah R., Ravaioli U., Jasiuk I.M., Sobh N.A. Prediction and optimization of mechanical properties of composites using convolutional neural networks. Composite Structures, 2019, vol. 227, pp. 111264. doi: 10.1016/j.compstruct.2019.111264

21. DeVore R., Hanin B., Petrova G. Neural network approximation. Acta Numerica, 2021, vol. 30, pp. 327–444. doi: 10.1017/s0962492921000052

22. Li Y., Li H., Jin C., Shen J. The study of effect of carbon nanotubes on the compressive strength of cement-based materials based on machine learning. Construction and Building Materials, 2022, vol. 358, pp. 129435. doi: 10.1016/j.conbuildmat.2022.129435

23. Akbari P., Zamani M., Mostafaei A. Machine learning prediction of mechanical properties in metal additive manufacturing. Additive Manufacturing, 2024, vol. 91, pp. 104320. doi: 10.1016/j.addma.2024.104320

24. Golkarnarenji G., Naebe M., Badii K., Milani A.S., Jazar R.N., Khayyam H. A machine learning case study with limited data for prediction of carbon fiber mechanical properties. Computers in Industry, 2019, vol. 105, pp. 123–132. doi: 10.1016/j.compind.2018.11.004

25. Krasnov F.V. Identifying data labeling errors using classification models for small datasets. International Journal of Open Information Technologies, 2023, vol. 11, no. 5, pp. 54–62. (in Russian)

26. Xu P., Ji X., Li M., Lu W. Small data machine learning in materials science. npj Computational Materials, 2023, vol. 9, no. 1, pp. 42. doi: 10.1038/s41524-023-01000-z

27. Karamov R., Akhatov I., Sergeichev I.V. Prediction of fracture toughness of pultruded composites based on supervised machine learning. Polymers, 2022, vol. 14, no. 17, pp. 3619. doi: 10.3390/polym14173619

28. Şimşek Türker Y., Kilinçarslan S., Yilmaz Ince E. Performance of ANN, Random Forest and XGBoost methods in predicting the flexural properties of wood beams reinforced with carbon-FRP. Wood Material Science and Engineering, 2025, vol. 20, no. 3, pp. 657–668. doi: 10.1080/17480272.2024.2370942

29. Han T., Huang J., Sant G., Neithalath N., Kumar A. Predicting mechanical properties of ultrahigh temperature ceramics using machine learning. Journal of the American Ceramic Society, 2022, vol. 105, no. 11, pp. 6851–6863. doi: 10.1111/jace.18636

30. Shah V., Zadourian S., Yang C., Zhang Z., Gu, G.X. Data-driven approach for the prediction of mechanical properties of carbon fiber reinforced composites. Materials Advances, 2022, vol. 3, no. 19, pp. 7319–7327. doi: 10.1039/d2ma00698g

31. Carneiro M.V., Salis T.T., Almeida G.M., Braga A.P. Prediction of mechanical properties of steel tubes using a machine learning approach. Journal of Materials Engineering and Performance, 2021, vol. 30, no. 1, pp. 434–443. doi: 10.1007/s11665-020-05345-0

32. Zhang Z., Mansouri Tehrani A., Oliynyk A.O., Day B., Brgoch J. Finding the next superhard material through ensemble learning. Advanced Materials, 2021, vol. 33, no. 5, pp. 2005112. doi: 10.1002/adma.202005112

33. Dovale-Farelo V., Tavadze P., Lang L., Bautista-Hernandez A., Romero A.H. Vickers hardness prediction from machine learning methods. Scientific Reports, 2022, vol. 12, no. 1, pp. 22475. doi: 10.1038/s41598-022-26729-3

34. Qadir A., Ali S., Dusza J., Rafaja D. Predicting hardness of graphene-added Si₃N₄ using machine learning: A data-driven approach. Open Ceramics, 2024, vol. 19, pp. 100634. doi: 10.1016/j.oceram.2024.100634

35. Barabashko M.S., Tkachenko M.V., Neiman A.A., Ponomarev A.N., Rezvanova A.E. Variation of Vickers microhardness and compression strength of the bioceramics based on hydroxyapatite by adding the multi-walled carbon nanotubes. Applied Nanoscience, 2020, vol. 10, no. 8, pp. 2601–2608. doi: 10.1007/s13204-019-01019-z

36. Barabashko M., Ponomarev A., Rezvanova A., Kuznetsov V., Moseenkov S. Young’s modulus and vickers hardness of the hydroxyapatite bioceramics with a small amount of the multi-walled carbon nanotubes. Materials, 2022, vol. 15, no. 15, pp. 5304. doi: 10.3390/ma15155304

37. Shutilov R., Myz A., Kuznetsov V., Karagedov G. Current conductive AL₂O₃ ceramic composites modified by multiwall carbon nanotubes. Perspektivnye Materialy, 2016, no. 8, pp. 64–73. (in Russian)

38. Sidorenko D.A., Zaitsev A.A., Kurbatkina V.V., Levashov E.A., Anreyev V.A., Rupasov S.I., Sevastianov P.I. The effect of carbon nanotube additives on structure and propertiesof metal binders for diamond cutting tools. Powder Metallurgy аnd Functional Coatings, 2012, no. 1, pp. 38–43. (in Russian)