I. V. Chapitre, Caractérisation mécanique des matériaux poreux par indentation instrumentée à l'aide d'un indenteur Knoop IV

, Détermination de la température de frittage

, Application et validation de la méthodologie d'indentation Knoop dans le cas des matériaux céramiques poreux

, Étude des propriétés mécaniques en fonction de la porosité

, Caractérisation mécanique du revêtement étudié par indentation instrumentée

, IV.3.2.2. Application et validation de la méthodologie d'indentation cyclique, vol.134

, Chapitre IV : Caractérisation mécanique des matériaux poreux par IIT à l'aide d'un indenteur Knoop Annexe 2

, Méthodologie d'analyse d'un essai d'indentation instrumentée à l'aide d'un indenteur Knoop : Synoptique d'analyse des résultats d'indentation instrumentée en utilisant un indenteur Knoop

G. Fantozzi, S. L. Gallet, and J. Niepce, Science et technologies céramiques, 2009.

L. Paw?owski, The science and engineering of thermal spray coatings, 2008.

F. Vargas, Élaboration de couches céramiques épaisses à structures micrométriques et nanométriques par projections thermiques pour des applications tribologiques, 2010.

M. F. Ashby, Choix des matériaux en conception mécanique, 2004.

A. C. Fischer-cripps and B. R. Lawn, Stress Analysis of Contact Deformation in QuasiPlastic Ceramics, J. Am. Ceram. Soc, vol.79, pp.2609-2618, 2005.

D. Tabor, A Simple Theory of Static and Dynamic Hardness, Proc. R. Soc. Math. Phys. Eng. Sci, vol.192, pp.247-274, 1948.

I. M. Hutchings, The contributions of David Tabor to the science of indentation hardness, J. Mater. Res, vol.24, pp.581-589, 2009.

I. N. Sneddon, The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile, Int. J. Eng. Sci, vol.3, pp.47-57, 1965.

K. L. Johnson, The correlation of indentation experiments, J. Mech. Phys. Solids, vol.18, pp.115-126, 1970.

A. C. Fischer-cripps, , 2011.

D. Chicot, A. Tricoteaux, J. Lesage, A. Leriche, M. Descamps et al., Mechanical Properties of Porosity-Free Beta Tricalcium Phosphate (?-TCP) Ceramic by Sharp and Spherical Indentations, New J. Glass Ceram, pp.16-28, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00788256

M. Yetna-n'jock, D. Chicot, X. Decoopman, J. Lesage, J. M. Ndjaka et al., Mechanical tensile properties by spherical macroindentation using an indentation strain-hardening exponent, Int. J. Mech. Sci, vol.75, pp.257-264, 2013.

P. Clément, S. Meille, J. Chevalier, and C. Olagnon, Mechanical characterization of highly porous inorganic solids materials by instrumented micro-indentation, Acta Mater, vol.61, pp.6649-6660, 2013.

E. G. Herbert, W. C. Oliver, and G. M. Pharr, On the measurement of yield strength by spherical indentation, Philos. Mag, vol.86, pp.5521-5539, 2006.

H. Hertz, M. Papers, . London, C. Macmillan, and . Ltd, , 1896.

A. Martens and E. Heyn, Handbuch der Materialienkunde für den Maschinenbau, 1912.

J. L. Loubet, M. Bauer, A. Tonck, S. Bec, and B. Gauthier-manuel, Nanoindentation with a surface force apparatus, Mechanical Properties and Deformation Behavior of Materials Having Ultra-Fine Microstructures, pp.429-447, 1993.

M. F. Doerner and W. D. Nix, A method for interpreting the data from depth-sensing indentation instruments, J. Mater. Res, vol.1, pp.601-609, 1986.

W. C. Oliver and G. M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res, vol.7, pp.1564-1583, 1992.
URL : https://hal.archives-ouvertes.fr/hal-01518596

Y. T. Cheng and C. M. Cheng, Relationships between hardness, elastic modulus, and the work of indentation, Appl. Phys. Lett, vol.73, pp.614-616, 1998.

D. Chicot, M. Y. Jock, F. Roudet, X. Decoopman, M. H. Staia et al., Some improvements for determining the hardness of homogeneous materials from the work-of-indentation, Int. J. Mech. Sci, vol.105, pp.279-290, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01249912

Y. W. Bao, W. Wang, and Y. C. Zhou, Investigation of the relationship between elastic modulus and hardness based on depth-sensing indentation measurements, Acta Mater, vol.52, pp.5397-5404, 2004.

A. C. Fischer-cripps, A simple phenomenological approach to nanoindentation creep, Mater. Sci. Eng. A, vol.385, pp.74-82, 2004.

P. Kamta, A. Mejias, F. Roudet, G. Louis, M. Touzin et al., Indentation creep analysis of T22 and T91 chromium based steels, Mater. Sci. Eng. A, vol.652, pp.315-324, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01246127

T. Saraswati, T. Sritharan, S. Mhaisalkar, C. D. Breach, and F. Wulff, Cyclic loading as an extended nanoindentation technique, Mater. Sci. Eng. A, vol.423, pp.14-18, 2006.

D. Chicot, K. Tilkin, K. Jankowski, and A. Wymys?owski, Reliability analysis of solder joints due to creep and fatigue in microelectronic packaging using microindentation technique, Microelectron. Reliab, vol.53, pp.761-766, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00816697

F. Jose, R. Ramaseshan, A. K. Balamurugan, S. Dash, A. K. Tyagi et al., Continuous multi cycle nanoindentation studies on compositionally graded Ti 1?x Al x N multilayer thin films, Mater. Sci. Eng. A, vol.528, pp.6438-6444, 2011.

S. R. Jian, J. Y. Juang, N. C. Chen, J. S. Jang, J. C. Huang et al., Nanoindentation-Induced Structural Deformation in GaN/AlN Multilayers, Nanosci. Nanotechnol. Lett, vol.2, pp.315-321, 2010.

J. Lesage, M. H. Staia, D. Chicot, C. Godoy, and P. E. De-miranda, Effect of thermal treatments on adhesive properties of a NiCr thermal sprayed coating, Thin Solid Films, pp.681-686, 2000.

J. Thurn and R. F. Cook, Simplified Area Function for Sharp Indenter Tips in Depthsensing Indentation, J. Mater. Res, vol.17, pp.1143-1146, 2002.

J. Thurn, D. J. Morris, and R. F. Cook, Depth-sensing indentation at macroscopic dimensions, J. Mater. Res, vol.17, pp.2679-2690, 2002.

M. Sakai and Y. Nakano, Elastoplastic load-depth hysteresis in pyramidal indentation, J. Mater. Res, vol.17, pp.2161-2173, 2002.

B. R. Lawn and V. R. Howes, Elastic recovery at hardness indentations, J. Mater. Sci, vol.16, pp.2745-2752, 1981.

M. Sakai, Energy principle of the indentation-induced inelastic surface deformation and hardness of brittle materials, Acta Metall. Mater, vol.41, pp.1751-1758, 1993.

M. Sakai, S. Shimizu, and T. Ishikawa, The Indentation Load-depth Curve of Ceramics, J. Mater. Res, vol.14, pp.1471-1484, 1999.

M. Sakai, The Meyer hardness: A measure for plasticity?, J. Mater. Res, vol.14, pp.3630-3639, 1999.

, Metallic materials -instrumented indentation test for hardness and materials parameters -Part 1: Test method -Part 2: Verification and calibration of testing machines -Part 3: Calibration of reference blocks, ISO 14577, 2015.

J. C. Hay, A. Bolshakov, and G. M. Pharr, A critical examination of the fundamental relations used in the analysis of nanoindentation data, J. Mater. Res, vol.14, pp.2296-2305, 1999.

R. B. King, Elastic analysis of some punch problems for a layered medium, Int. J. Solids Struct, vol.23, pp.1657-1664, 1987.

M. Dao, N. Chollacoop, K. J. Van-vliet, T. A. Venkatesh, and S. Suresh, Computational modeling of the forward and reverse problems in instrumented sharp indentation, Acta Mater, vol.49, pp.3899-3918, 2001.

J. M. Antunes, L. F. Menezes, and J. V. Fernandes, Three-dimensional numerical simulation of Vickers indentation tests, Int. J. Solids Struct, vol.43, pp.784-806, 2006.

W. C. Oliver and G. M. Pharr, Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology, J. Mater. Res, vol.19, pp.3-20, 2004.

S. I. Bulychev, V. P. Alekhin, M. K. Shorshorov, A. P. Ternovskij, and G. D. Shnyrev, Determination of Young modulus by the hardness indentation diagram, Zavod. Lab, vol.41, pp.1137-1140, 1975.

J. Woirgard, J. C. Dargenton, C. Tromas, and V. Audurier, A new technology for nanohardness measurements: principle and applications, Surf. Coat. Technol, pp.103-109, 1998.

A. E. Giannakopoulos and S. Suresh, Determination of elastoplastic properties by instrumented sharp indentation, Scr. Mater, vol.40, pp.1191-1198, 1999.

I. N. Sneddon, Fourier Transforms, 1951.

M. Troyon and L. Huang, Correction factor for contact area in nanoindentation measurements, J. Mater. Res, vol.20, pp.610-617, 2005.

M. Troyon and L. Huang, Comparison of different analysis methods in nanoindentation and influence on the correction factor for contact area, Surf. Coat. Technol, vol.201, pp.1613-1619, 2006.

M. Troyon and L. Huang, Critical Examination of the Two-slope Method in Nanoindentation, J. Mater. Res, vol.20, pp.2194-2198, 2005.

D. Chicot, F. Roudet, V. Lepingle, and G. Louis, Strain gradient plasticity to study hardness behavior of magnetite (Fe 3 O 4 ) under multicyclic indentation, J. Mater. Res, vol.24, pp.749-759, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00376775

A. C. Fischer-cripps, Critical review of analysis and interpretation of nanoindentation test data, Surf. Coat. Technol, vol.200, pp.4153-4165, 2006.

G. M. Pharr and A. Bolshakov, Understanding nanoindentation unloading curves, J. Mater. Res, vol.17, pp.2660-2671, 2002.

M. Y. , D. Chicot, J. M. Ndjaka, J. Lesage, X. Decoopman et al., A criterion to identify sinking-in and piling-up in indentation of materials, Int. J. Mech. Sci, vol.90, pp.145-150, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01093128

J. M. Antunes, L. F. Menezes, and J. V. Fernandes, Three-dimensional numerical simulation of Vickers indentation tests, Int. J. Solids Struct, vol.43, pp.784-806, 2006.

A. E. Giannakopoulos and T. Zisis, Analysis of Knoop indentation, Int. J. Solids Struct, vol.48, pp.175-190, 2011.

L. A. Berla, A. M. Allen, S. M. Han, and W. D. Nix, A physically based model for indenter tip shape calibration for nanoindentation, J. Mater. Res, vol.25, pp.735-745, 2010.

J. Gong, H. Miao, and Z. Peng, On the contact area for nanoindentation tests with Berkovich indenter: case study on soda-lime glass, Mater. Lett, vol.58, pp.1349-1353, 2004.

A. Krell and S. Schädlich, Nanoindentation hardness of submicrometer alumina ceramics, Mater. Sci. Eng. A, vol.307, pp.172-181, 2001.

K. Herrmann, N. M. Jennett, W. Wegener, J. Meneve, K. Hasche et al., Progress in determination of the area function of indenters used for nanoindentation, Thin Solid Films, vol.377, pp.394-400, 2000.

A. R. Franco, G. Pintaúde, A. Sinatora, C. E. Pinedo, and A. P. Tschiptschin, The use of a Vickers indenter in depth sensing indentation for measuring elastic modulus and Vickers hardness, Mater. Res, vol.7, pp.483-491, 2004.

H. Bei, E. George, J. Hay, and G. Pharr, Influence of Indenter Tip Geometry on Elastic Deformation during Nanoindentation, Phys. Rev. Lett, vol.95, issue.4, 2005.

J. M. Antunes, A. Cavaleiro, L. F. Menezes, M. I. Simões, and J. V. Fernandes, Ultramicrohardness testing procedure with Vickers indenter, Surf. Coat. Technol, vol.149, pp.27-35, 2002.

D. Chicot, M. Yetna-n'jock, E. S. Puchi-cabrera, A. Iost, M. H. Staia et al., A contact area function for Berkovich nanoindentation: Application to hardness determination of a TiHfCN thin film, Thin Solid Films, vol.558, pp.259-266, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00978376

C. Ullner, E. Reimann, H. Kohlhoff, and A. Subaric-leitis, Effect and measurement of the machine compliance in the macro range of instrumented indentation test, Measurement, vol.43, pp.216-222, 2010.

J. B. Pethicai, R. Hutchings, and W. C. Oliver, Hardness measurement at penetration depths as small as 20 nm, Philos. Mag. A, vol.48, pp.593-606, 1983.

N. Gane and J. M. Cox, The micro-hardness of metals at very low loads, Philos. Mag, vol.22, pp.881-0891, 1970.

C. Hays and E. G. Kendall, An analysis of Knoop microhardness, Metallography, vol.6, pp.275-282, 1973.

H. Li and R. C. Bradt, The microhardness indentation load/size effect in rutile and cassiterite single crystals, J. Mater. Sci, vol.28, pp.917-926, 1993.

Q. Ma and D. R. Clarke, Size dependent hardness of silver single crystals, J. Mater. Res, vol.10, pp.853-863, 1995.

W. D. Nix and H. Gao, Indentation size effects in crystalline materials: A law for strain gradient plasticity, J. Mech. Phys. Solids, vol.46, pp.411-425, 1998.

M. L. Weaver, M. E. Stevenson, and R. C. Bradt, Knoop microhardness anisotropy and the indentation size effect on the (100) of single crystal NiAl, Mater. Sci. Eng. A, vol.345, pp.113-117, 2003.

F. G. Yost, On the definition of microhardness, Metall. Trans. A, vol.14, pp.947-952, 1983.

D. Chicot, P. Baets, M. H. Staia, E. S. Puchi-cabrera, G. Louis et al., Influence of tip defect and indenter shape on the mechanical properties determination by indentation of a TiB 2 -60%B 4 C ceramic composite, Int. J. Refract. Met. Hard Mater, vol.38, pp.102-110, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00816692

F. Fröhlich, P. Grau, and W. Grellmann, Performance and analysis of recording microhardness tests, Phys. Status Solidi A, vol.42, pp.79-89, 1977.

J. Gong and Z. Guan, Load dependence of low-load Knoop hardness in ceramics: a modified PSR model, Mater. Lett, vol.47, pp.140-144, 2001.

J. Gong, J. Wu, and Z. Guan, Examination of the indentation size effect in low-load Vickers hardness testing of ceramics, J. Eur. Ceram. Soc, vol.19, pp.2625-2631, 1999.

J. Gong, Z. Zhao, Z. Guan, and H. Miao, Load-dependence of Knoop hardness of Al2O3-TiC composites, J. Eur. Ceram. Soc, vol.20, pp.1895-1900, 2000.

A. K. Mukhopadhyay, S. K. Datta, and D. Chakraborty, On the microhardness of silicon nitride and sialon ceramics, J. Eur. Ceram. Soc, vol.6, pp.303-311, 1990.

M. Atkinson, Further analysis of the size effect in indentation hardness tests of some metals, J. Mater. Res, vol.10, pp.2908-2915, 1995.

D. Chicot, Hardness length-scale factor to model nano-and micro-indentation size effects, Mater. Sci. Eng. A, vol.499, pp.454-461, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00359663

J. Zhang and M. Sakai, Geometrical effect of pyramidal indenters on the elastoplastic contact behaviors of ceramics and metals, Mater. Sci. Eng. A, vol.381, pp.62-70, 2004.

P. Rutkowski, L. Stobierski, D. Zientara, L. Jaworska, P. Klimczyk et al., The influence of the graphene additive on mechanical properties and wear of hotpressed Si 3 N 4 matrix composites, J. Eur. Ceram. Soc, vol.35, pp.87-94, 2015.

A. Iost, Knoop hardness of thin coatings, Scr. Mater, vol.39, pp.231-238, 1998.

B. P. Groth and A. B. Mann, Identifying changes in residual stress using indentation on machined metallic surfaces, Mater. Lett, vol.89, pp.287-290, 2012.

C. Ullner, A. Germak, H. L. Doussal, R. Morrell, T. Reich et al., Hardness testing on advanced technical ceramics, J. Eur. Ceram. Soc, vol.21, pp.439-451, 2001.

L. Riester, P. J. Blau, E. Lara-curzio, and K. Breder, Nanoindentation with a Knoop indenter, vol.377, pp.635-639, 2000.

L. Min, C. Wei-min, L. Nai-gang, and W. Ling-dong, A numerical study of indentation using indenters of different geometry, J. Mater. Res, vol.19, pp.73-78, 2004.

J. Gong, J. Wang, and Z. Guan, A comparison between Knoop and Vickers hardness of silicon nitride ceramics, Mater. Lett, vol.56, pp.941-944, 2002.

D. Chicot, D. Mercier, F. Roudet, K. Silva, M. H. Staia et al., Comparison of instrumented Knoop and Vickers hardness measurements on various soft materials and hard ceramics, J. Eur. Ceram. Soc, vol.27, pp.1905-1911, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00124408

C. Ullner, J. Beckmann, and R. Morrell, Instrumented indentation test for advanced technical ceramics, J. Eur. Ceram. Soc, vol.22, pp.1183-1189, 2002.

G. A. Gogotsi, S. N. Dub, E. E. Lomonova, and B. I. Ozersky, Vickers and knoop indentation behaviour of cubic and partially stabilized zirconia crystals, J. Eur. Ceram. Soc, vol.15, pp.405-4013, 1995.

L. Riester, T. J. Bell, and A. C. Fischer-cripps, Analysis of depth-sensing indentation tests with a Knoop indenter, J. Mater. Res, vol.16, pp.1660-1667, 2001.

A. Nagakubo, H. Ogi, H. Sumiya, and M. Hirao, Elasticity and hardness of nanopolycrystalline boron nitrides: The apparent Hall-Petch effect, Appl. Phys. Lett, vol.105, p.81906, 2014.

D. B. Marshall, T. Noma, and A. G. Evans, A Simple Method for Determining ElasticModulus-to-Hardness Ratios using Knoop Indentation Measurements, J. Am. Ceram. Soc, vol.65, pp.175-176, 1982.

R. S. Lima, A. Kucuk, and C. C. Berndt, Evaluation of microhardness and elastic modulus of thermally sprayed nanostructured zirconia coatings, Surf. Coat. Technol, vol.135, pp.166-172, 2001.

K. L. Johnson, Contact Mechanics

J. C. Conway, Determination of hardness to elastic modulus ratios using Knoop indentation measurements and a model based on loading and reloading half-cycles, J. Mater. Sci, vol.21, pp.2525-2527, 1986.

A. G. Atkins and D. Tabor, Plastic indentation in metals with cones, J. Mech. Phys. Solids, vol.13, pp.149-164, 1965.

B. A. Latella, B. H. Oconnor, N. P. Padture, and B. R. Lawn, Hertzian contact damage in porous alumina ceramics, J. Am. Ceram. Soc, vol.80, pp.1027-1031, 1997.

B. R. Lawn, Indentation of ceramics with spheres: a century after Hertz, J. Am. Ceram. Soc, vol.81, pp.1977-1994, 1998.

A. C. Fischer-cripps and B. R. Lawn, Stress Analysis of Contact Deformation in QuasiPlastic Ceramics, J. Am. Ceram. Soc, vol.79, pp.2609-2618, 1996.

Y. W. Rhee, H. W. Kim, Y. Deng, and B. R. Lawn, Brittle Fracture versus Quasi Plasticity in Ceramics: A Simple Predictive Index, J. Am. Ceram. Soc, vol.84, pp.561-565, 2001.

D. Staub, S. Meille, V. Le-corre, L. Rouleau, and J. Chevalier, Identification of a damage criterion of a highly porous alumina ceramic, Acta Mater, vol.107, pp.261-272, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01398755

G. R. Anstis, P. Chantikul, B. R. Lawn, and D. B. Marshall, A critical evaluation of indentation techniques for measuring fracture toughness: I, direct crack measurements, J. Am. Ceram. Soc, vol.64, pp.533-538, 1981.

S. J. Bull, Analysis methods and size effects in the indentation fracture toughness assessment of very thin oxide coatings on glass, Comptes Rendus Mécanique, vol.339, pp.518-531, 2011.

D. Chicot, G. Duarte, A. Tricoteaux, B. Jorgowski, A. Leriche et al., Vickers Indentation Fracture (VIF) modeling to analyze multi-cracking toughness of titania, alumina and zirconia plasma sprayed coatings, Mater. Sci. Eng. A, vol.527, pp.65-76, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00429771

A. G. Evans and E. A. Charles, Fracture Toughness Determinations by Indentation, J. Am. Ceram. Soc, vol.59, pp.371-372, 1976.

M. M. Lima, C. Godoy, P. J. Modenesi, J. C. Avelar-batista, A. Davison et al., Coating fracture toughness determined by Vickers indentation: an important parameter in cavitation erosion resistance of WC-Co thermally sprayed coatings, Surf. Coat. Technol, vol.177, pp.489-496, 2004.

C. B. Ponton and R. D. Rawlings, Vickers indentation fracture toughness test Part 2 Application and critical evaluation of standardised indentation toughness equations, Mater. Sci. Technol, vol.5, pp.961-976, 1989.

G. D. Quinn and R. C. Bradt, On the Vickers Indentation Fracture Toughness Test, J. Am. Ceram. Soc, vol.90, pp.673-680, 2007.

P. Chantikul, G. R. Anstis, B. R. Lawn, and D. B. Marshall, A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: II, Strength Method, J. Am. Ceram. Soc, vol.64, pp.539-543, 1981.

R. F. Cook and G. M. Pharr, Direct Observation and Analysis of Indentation Cracking in Glasses and Ceramics, J. Am. Ceram. Soc, vol.73, pp.787-817, 1990.

T. Lube, Indentation crack profiles in silicon nitride, J. Eur. Ceram. Soc, vol.21, pp.211-218, 2001.

T. Lube and T. Fett, A threshold stress intensity factor at the onset of stable crack extension of Knoop indentation cracks, Eng. Fract. Mech, vol.71, pp.2263-2269, 2004.

T. , Driving force for indentation cracking in glass: composition, pressure and temperature dependence, Philos. Trans. R. Soc. Math. Phys. Eng. Sci, vol.373, 2015.

Y. Toivola, A. Stein, and R. F. Cook, Depth-sensing indentation response of ordered silica foam, J. Mater. Res, vol.19, pp.260-271, 2004.

J. Luo and R. Stevens, Porosity-dependence of elastic moduli and hardness of 3Y-TZP ceramics, Ceram. Int, vol.25, pp.281-286, 1999.

A. R. Boccaccini and Z. Fan, A new approach for the Young's modulus-porosity correlation of ceramic materials, Ceram. Int, vol.23, pp.239-245, 1997.

W. Pabst, E. Gregorová, and G. Tichá, Elasticity of porous ceramics-A critical study of modulus?porosity relations, J. Eur. Ceram. Soc, vol.26, pp.1085-1097, 2006.

K. R. Janowski and R. C. Rossi, Elastic Behavior of MgO Matrix Composites, J. Am. Ceram. Soc, vol.50, pp.599-603, 1967.

R. W. Rice, Evaluation and extension of physical property-porosity models based on minimum solid area, J. Mater. Sci, vol.31, pp.102-118, 1996.

R. W. Rice, Relation of tensile strength-porosity effects in ceramics to porosity dependence of Young's modulus and fracture energy, porosity character and grain size, Mater. Sci. Eng. A, vol.112, pp.215-224, 1989.

A. S. Wagh, J. P. Singh, and R. B. Poeppel, Dependence of ceramic fracture properties on porosity, J. Mater. Sci, vol.28, pp.3589-3593, 1993.

K. K. Phani and S. K. Niyogi, Elastic modulus-porosity relationship for Si 3 N 4, J. Mater. Sci. Lett, vol.6, pp.511-515, 1987.

K. K. Phani and D. Sanyal, The relations between the shear modulus, the bulk modulus and Young's modulus for porous isotropic ceramic materials, Mater. Sci. Eng. A, vol.490, pp.305-312, 2008.

Z. Hashin, The Elastic Moduli of Heterogeneous Materials, J. Appl. Mech, vol.29, p.143, 1962.

A. Bachar, Thèse de doctorat: Élaboration et caractérisations de bioverres Si-Ca-Na-O et Si-Ca-Na-OF dopés à l'azote

A. Bachar, C. Mercier, A. Tricoteaux, A. Leriche, C. Follet et al., Effects of addition of nitrogen on bioglass properties and structure, J. Non-Cryst. Solids, vol.358, pp.693-701, 2012.

M. Descamps, J. C. Hornez, and A. Leriche, Effects of powder stoichiometry on the sintering of ?-tricalcium phosphate, J. Eur. Ceram. Soc, vol.27, pp.2401-2406, 2007.

A. Tricoteaux, E. Rguiti, D. Chicot, L. Boilet, M. Descamps et al., Influence of porosity on the mechanical properties of microporous ?-TCP bioceramics by usual and instrumented Vickers microindentation, J. Eur. Ceram. Soc, vol.31, pp.1361-1369, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00591036

M. I. Mendelson, Average Grain Size in Polycrystalline Ceramics, J. Am. Ceram. Soc, vol.52, pp.443-446, 1969.

M. Asmani, C. Kermel, A. Leriche, and M. Ourak, Influence of porosity on Young's modulus and Poisson's ratio in alumina ceramics, J. Eur. Ceram. Soc, vol.21, pp.1081-1086, 2001.

C. Bartuli, E. Bemporad, J. M. Tulliani, J. Tirillò, G. Pulci et al., Mechanical properties of cellular ceramics obtained by gel casting: Characterization and modeling, J. Eur. Ceram. Soc, vol.29, pp.2979-2989, 2009.

A. Bandini, D. Chicot, P. Berry, X. Decoopman, A. Pertuz et al., Indentation size effect of cortical bones submitted to different soft tissue removals, J. Mech. Behav. Biomed. Mater, vol.20, pp.338-346, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00816689

L. ?atka, D. Chicot, A. Cattini, L. Paw?owski, and A. Ambroziak, Modeling of elastic modulus and hardness determination by indentation of porous yttria stabilized zirconia coatings, Surf. Coat. Technol, vol.220, pp.131-139, 2013.

D. N. Boccaccini and A. R. Boccaccini, Dependence of ultrasonic velocity on porosity and pore shape in sintered materials, J. Nondestruct. Eval, vol.16, pp.187-192, 1997.

D. Chicot, H. Ageorges, M. Voda, G. Louis, M. A. Ben-dhia et al., Hardness of thermal sprayed coatings: Relevance of the scale of measurement, Surf. Coat. Technol, vol.268, pp.173-179, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01200749

J. Nohava, R. Mu?álek, J. Mat?jí?ek, and M. Vilémová, A contribution to understanding the results of instrumented indentation on thermal spray coatings -Case study on Al 2 O 3 and stainless steel, Surf. Coat. Technol, vol.240, pp.243-249, 2014.

A. Mejias, R. T. Candidato, L. Paw?owski, and D. Chicot, Mechanical properties by instrumented indentation of solution precursor plasma sprayed hydroxyapatite coatings: Analysis of microstructural effect, Surf. Coat. Technol, vol.298, pp.93-102, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01318814

J. Nohava, B. Bonferroni, G. Bolelli, and L. Lusvarghi, Interesting aspects of indentation and scratch methods for characterization of thermally-sprayed coatings, Surf. Coat. Technol, vol.205, pp.1127-1131, 2010.

D. Chicot, F. Roudet, A. Zaoui, G. Louis, and V. Lepingle, Influence of visco-elastoplastic properties of magnetite on the elastic modulus: Multicyclic indentation and theoretical studies, Mater. Chem. Phys, vol.119, pp.75-81, 2010.

T. Y. Tsui, J. Vlassak, and W. D. Nix, Indentation plastic displacement field: Part I. The case of soft films on hard substrates, J. Mater. Res, vol.14, pp.2196-2203, 1999.

K. Hermange, Thèse de doctorat : Revêtements sol-gel composites sur acier pour applications tribologiques, 2016.

F. Ulm, M. Vandamme, C. Bobko, J. Ortega, K. Tai et al., Statistical Indentation Techniques for Hydrated Nanocomposites: Concrete, Bone, and Shale, J. Am. Ceram. Soc, vol.90, pp.2677-2692, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00555551

Y. Xia, M. Bigerelle, S. Bouvier, A. Iost, and P. Mazeran, Quantitative approach to determine the mechanical properties by nanoindentation test: Application on sandblasted materials, Tribol. Int, vol.82, pp.297-304, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01170499

J. Schneider, M. Bigerelle, and A. Iost, Statistical analysis of the Vickers hardness, Mater. Sci. Eng. A, vol.262, pp.256-263, 1999.