The indentation unloading curve of ceramic materials describes the contact position and thickness between solid film and substrate. Ceramic films are widely used in modern industry, national defense, military and electronic devices. They have the advantages of low density, high specific strength, high temperature resistance and good oxidation resistance. The film thickness is one of the important parameters reflecting the preparation process. It will not only affect the material itself, but also damage the adjacent surface. Therefore, the mechanical properties should be improved by controlling the pressure applied to the substrate interface. Based on the preparation process, this paper introduces the nano indentation unloading curve test of ceramic thin-layer samples by indentation method, studies the changes of material properties and mechanical properties under different thickness and temperature, and describes the microstructure of ceramic thin-film and analyzes its compactness and microstructure by load displacement curve. After a series of experimental tests, the mathematical description of nano indentation unloading curve of ceramic materials and the method of film thickness measurement are summarized.

Long Zhang. Mathematical Description of Nano Indentation Unloading Curve of Ceramic Materials and Test Method of Film Thickness. International Journal of Social Sciences and Economic Management (2021), Vol. 2, Issue 1: 98-113. https://doi.org/10.38007/IJSSEM.2021.020108.

[1] Kermani G ,  Hemmasizadeh A ,  Assari S , et al. Investigation of inhomogeneous and anisotropic material behavior of porcine thoracic aorta using nano-indentation tests. J Mech Behav Biomed Mater, 2017, 69(Complete):50-56. https://doi.org/10.1016/j.jmbbm.2016.12.022

[2] Yu Y ,  Xiao D ,  Liu W , et al. Effect of microstructure on nanoindentation behavior of beryllium materials. Fenmo Yejin Cailiao Kexue yu Gongcheng/Materials Science and Engineering of Powder Metallurgy, 2018, 23(3):306-311.

[3] F Bernachy-Barbe. A data analysis procedure for phase identification in nanoindentation results of cementitious materials. Materials and structures, 2019, 52(5):95.1-95.12. https://doi.org/10.1617/s11527-019-1397-y

[4] Tserpes K ,  Bazios P ,  Pantelakis S , et al. Nanoindentation testing and simulation of nanocrystalline materials. Procedia Structural Integrity, 2020, 28(6):1644-1649. https://doi.org/10.1016/j.prostr.2020.10.136

[5] Borc J ,  Sangwal K ,  Pritula I , et al. Investigation of pop-in events and indentation size effect on the (001) and (100) faces of KDP crystals by nanoindentation deformation. Materials Science and Engineering, 2017, 708(dec.21):1-10. https://doi.org/10.1016/j.msea.2017.09.069

[6] Bamber R ,  Morrell R ,  Waldon C , et al. Design substantiation of ceramic materials on fusion reactor confinement boundaries. Fusion Engineering and Design, 2017, 125(DEC.):283-289.

[7] Mia B ,  Dma B ,  Mv A , et al. Nanoindentation and tribology of ZrB2 based luminescent ceramics - ScienceDirect. Journal of the European Ceramic Society, 2020, 40(14):4901-4908.

[8] Wan Jian, Li Xiang. Study on the Ni-P coatings deposited on the ceramic surface of packaging materials by using electroless plating method. Function material , 2018, 049(008):8108-8111.

[9] Borisenko E ,  Borisenko D ,  Bdikin I , et al. Mechanical characteristics of gallium sulfide crystals measured using micro- and nanoindentation. Materials Science and Engineering, 2019, 757(MAY 29):101-106. https://doi.org/10.1016/j.msea.2019.04.095

[10] Golovin Y I . Nanoindentation and Mechanical Properties of Materials at Submicro- and Nanoscale Levels: Recent Results and Achievements. Physics of the Solid State, 2021, 63(1):1-41.

[11] Roux N ,  Meille S ,  Langlois C , et al. Model Materials for Irradiated Fuels: Study of Local Mechanical Behavior Using Nanoindentation and Microstructural Analysis. Microscopy & Microanalysis, 2018, 20(S3):1832-1833. https://doi.org/10.1017/S1431927614010897

[12] Zhu X ,  Chen Y ,  Yu J , et al. Study on the main factors affecting the breakdown voltage of (Bi0.5Na0.5) TiO3-added (Ba0.659Pb0.341)TiO3 PTCR ceramic materials. Journal of Materials Science: Materials in Electronics, 2019, 30(18):17046-17052.

[13] Eramo G ,  Mangone A . Archaeometry of ceramic materials. Asia Pacific Journal of Risk & Insurance, 2019, 4(11):43-8. https://doi.org/10.1515/psr-2018-0014

[14] Lakhdar Y ,  Tuck C ,  Binner J , et al. Additive manufacturing of advanced ceramic materials. Progress in Materials Science, 2021, 116(2–3):100736.

[15] Mahmoudi S ,  Srasra E ,  Zargouni F . Preparation, qualities and defects of ceramic materials from Tunisian clay minerals. Surface Engineering and Applied Electrochemistry, 2017, 53(3):295-301.

[16] Minota-Yepes I C ,  Lvarez-Roca R ,  Londoo-Badillo F A . Review: Densification process of ceramic materials. Respuestas, 2020, 25(2):199-212. https://doi.org/10.22463/0122820X.2964

[17] Ruscitti A ,  Tapia C ,  Rendtorff N M . A review on additive manufacturing of ceramic materials based on extrusion processes of clay pastes. Cerâmica, 2020, 66(380):354-366.

[18] Sattar N ,  Marza M ,  Talab H . Utilization of diverse cheap materials as pore generating agent to manufacture low-cost porous ceramic. Cerâmica, 2020, 66(378):179-185.

[19] Cha J ,  Liu L ,  Ryu B . Thermal Analysis of Ceramic Materials. Ceramist, 2019, 22(4):393-401. https://doi.org/10.31613/ceramist.2019.22.4.05

[20] Khater G A ,  Safwat E M ,  Kang J , et al. Some Types of Glass-Ceramic Materials and their Applications. International Journal of Research, 2020, 7(3):1-16.

[21] Porozova S E ,  Kul'Met'Eva V B ,  Pozdeeva T Y , et al. Role of nanopowder agglomerates in forming the structure and properties of ceramic materials. Izvestiya vuzov Poroshkovaya metallurgiya i funktsional’nye pokrytiya, 2020(4):4-13.

[22] Jang S ,  Park S ,  Bae C J . Development of ceramic additive manufacturing: process and materials technology. Biomedical Engineering Letters, 2020, 10(4):1-11. https://doi.org/10.1007/s13534-020-00175-4

[23] Zsa B ,  Jza B . Nano-graphene toughened Al 2 O 3 ceramic materials: 3D simulation of the fracture behaviour. Ceramics International, 2020, 46( 18):28569-28577. https://doi.org/10.1016/j.ceramint.2020.08.014