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Relationships in instrumented indentation by Berkovich indenter

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Abstract

The relationships among the ratio of indentation hardness HIT over reduced elastic modulus Er, the ratio of elastic work We over total work Wt, and the ratio of permanent depth hp over the maximum indentation displacement hmax were investigated by instrumented indentation of 25 different materials under Berkovich indenter and various maximum indentation loads. Proportional relationships are found among various indentation variables (e.g. We vs. Wt, HIT vs. Er, and hp vs. hmax). Quadratic polynomial can be used to express the dependence of HIT/Er on We/Wt (or hp/hmax), based on which indentation hardness and reduced elastic modulus can be determined by work-based (or displacement-based) approach without requiring area function of the indenter. HIT and Er obtained by work-based and displacement-based approaches are consistent with those obtained by Oliver and Pharr’s method and those reported in literature.

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Data availability

The raw/processed data required to reproduce these findings are available from the corresponding author M.L. on request (mingliu@fzu.edu.cn or mingliuUK@gmail.com).

References

  1. A. Qiao, T. To, M. Stepniewska, H. Tao, L. Calvez, X. Zhang, M.M. Smedskjaer, Y. Yue, Deformation mechanism of a metal–organic framework glass under indentation. Phys. Chem. Chem. Phys. 23(31), 16923 (2021)

    Article  CAS  Google Scholar 

  2. H. Liu, C. Xu, C. Liu, G. He, T. Yu, Y. Li, Probing the indentation induced nanoscale damage of rhenium. Mater. Des. 186, 108362 (2020)

    Article  CAS  Google Scholar 

  3. R. Yang, T. Zhang, Y. Feng, Theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation for work-hardening materials. J. Mater. Res. 25(11), 2072 (2011)

    Article  Google Scholar 

  4. W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7(6), 1564 (1992)

    Article  CAS  Google Scholar 

  5. J.L. Hempel, M.D. Wells, S. Parkin, Y.T. Cheng, A.J. Huckaba, Unveiling the brittleness of hybrid organic-inorganic 0-D histammonium zinc chlorometallate by nanoindentation. Appl. Phys. Lett. 119(24) (2021).

  6. X. Ding, H. Geng, M. Zhao, Z. Chen, J. Li, Synergistic bond properties of different deformed steel fibers embedded in mortars wet-sieved from self-compacting SFRC. Appl. Sci. Basel 11(21) (2021).

  7. Y. Shelef, B. Bar-On, Interfacial indentations in biological composites. J. Mech. Behav. Biomed. Mater. 114 (2021).

  8. Y. Hwang, K.P. Marimuthu, N. Kim, C. Lee, H. Lee, Extracting plastic properties from in-plane displacement data of spherical indentation. Int. J. Mech. Sci. 197 (2021).

  9. D.Y. Dang, Y.K. Wang, Y.T. Cheng, Communication-fracture behavior of single LiNi0.33Mn0.33Co0.33O2 particles studied by flat punch indentation. J. Electrochem. Soc. 166(13), A2749 (2019).

  10. J.L. Hempel, A. Meyer, R. Hill, Y.T. Cheng, Validating a facile approach to measuring fracture toughness by instrumented indentation without imaging crack-lengths. MRS Commun. 12(2), 279 (2022)

    Article  CAS  Google Scholar 

  11. A. Priyadarshi, M. Khavari, T. Subroto, M. Conte, P. Prentice, K. Pericleous, D. Eskin, J. Durodola, I. Tzanakis, On the governing fragmentation mechanism of primary intermetallics by induced cavitation. Ultrason. Sonochem. 70 (2021).

  12. H. Algamaiah, D.C. Watts, Post-irradiation surface viscoelastic integrity of photo-polymerized resin-based composites. Dent. Mater. 37(12), 1828 (2021)

    Article  CAS  Google Scholar 

  13. A. Meghwal, A. Anupam, V. Luzin, C. Schulz, C. Hall, B. Murty, R.S. Kottada, C.C. Berndt, A.S.M. Ang, Multiscale mechanical performance and corrosion behaviour of plasma sprayed AlCoCrFeNi high-entropy alloy coatings. J. Alloys Compd. 854, 157140 (2021)

    Article  CAS  Google Scholar 

  14. P. Sengupta, S.S. Sahoo, A. Bhattacharjee, S. Basu, I. Manna, Effect of TiC addition on structure and properties of spark plasma sintered ZrB2–SiC–TiC ultrahigh temperature ceramic composite. J. Alloys Compd. 850, 156668 (2021)

    Article  CAS  Google Scholar 

  15. M. Petretta, A. Gambardella, M. Boi, M. Berni, C. Cavallo, G. Marchiori, M.C. Maltarello, D. Bellucci, M. Fini, N. Baldini, Composite scaffolds for bone tissue regeneration based on PCL and Mg-containing bioactive glasses. Biology 10(5), 398 (2021)

    Article  CAS  Google Scholar 

  16. R. Akhter, Z. Zhou, Z. Xie, P. Munroe, TiN versus TiSiN coatings in indentation, scratch and wear setting. Appl. Surf. Sci. 563, 150356 (2021)

    Article  CAS  Google Scholar 

  17. D. Yao, J. Fu, F. Li, Measurement of quasi-static and dynamic mechanical properties of soft materials based on instrumented indentation using a piezoelectric cantilever. Polym. Test. 96, 107056 (2021)

    Article  CAS  Google Scholar 

  18. S.N. Jayanthi, Analysis of micro indentation hardness of thiourea added L-histidine crystals (TLH). Mater. Today 44, 2273 (2021)

    CAS  Google Scholar 

  19. J. Tang, M. Cheng, G.G. Huang, H. Shu, H.T. Xu, Using indentation test to evaluate the properties of metallic material with strain aging, in Applied Mechanics and Materials, vol. 751 (Trans Tech Publ, Bäch, 2015), p.131

    Google Scholar 

  20. L.G. Wang, J.-F. Chen, J.Y. Ooi, A breakage model for particulate solids under impact loading. Powder Technol. 394, 669 (2021)

    Article  CAS  Google Scholar 

  21. M. Pawlikowski, K. Jankowski, K. Skalski, New microscale constitutive model of human trabecular bone based on depth sensing indentation technique. J. Mech. Behav. Biomed. Mater. 85, 162 (2018)

    Article  Google Scholar 

  22. K. Azzez, M. Chaabane, M.-A. Abellan, J.-M. Bergheau, H. Zahouani, A. Dogui, Relevance of indentation test to characterize soft biological tissue: application to human skin. Int. J. Appl. Mech. 10(07), 1850074 (2018)

    Article  Google Scholar 

  23. Y. Liu, W. Wang, Z. Zhao, H. Zhang, The effect of meso-structure and surface topography on the indentation variability of viscoelastic composite materials. Compos. Struct. 220, 81 (2019)

    Article  Google Scholar 

  24. I. Manika, J. Maniks, Effect of substrate hardness and film structure on indentation depth criteria for film hardness testing. J. Phys. D 41(7), 074010 (2008)

    Article  Google Scholar 

  25. Z. Wang, J. Wang, W. Wang, Y. Niu, C. Li, X. Zong, J. Zhang, H. Zhao, Scaling relationships of elastic-perfectly plastic film/coating materials from small scale sharp indentation. Sci. China Technol. Sci. 64(6), 1302 (2021)

    Article  Google Scholar 

  26. O. Alizadeh, G.T. Eshlaghi, S. Mohammadi, Nanoindentation simulation of coated aluminum thin film using quasicontinuum method. Comput. Mater. Sci. 111, 12 (2016)

    Article  CAS  Google Scholar 

  27. L. Ma, X. Wang, J. Wang, J. Zhang, C. Yin, L. Fan, D. Zhang, Graphene oxide–cerium oxide hybrids for enhancement of mechanical properties and corrosion resistance of epoxy coatings. J. Mater. Sci. 56(16), 10108 (2021)

    Article  CAS  Google Scholar 

  28. L. Charleux, S. Gravier, M. Verdier, M. Fivel, J. Blandin, Amorphous and partially crystallized metallic glasses: an indentation study. Mater. Sci. Eng. A 483, 652 (2008)

    Article  Google Scholar 

  29. J. Alkorta, J.M. Martínez–Esnaola, J.G. Sevillano, J. Malzbender, Comments on “Comment on the determination of mechanical properties from the energy dissipated during indentation” by J. Malzbender [J. Mater. Res. 20, 1090 (2005)]. J. Mater. Res. 21(1), 302 (2006).

  30. J. Malzbender, Energy dissipated during spherical indentation. J. Mater. Res. 19(6), 1605 (2011)

    Article  Google Scholar 

  31. J. Malzbender, Comment on the determination of mechanical properties from the energy dissipated during indentation. J. Mater. Res. 20(5), 1090 (2011)

    Article  Google Scholar 

  32. M. Sakai. Energy principle of the indentation-induced inelastic surface deformation and hardness of brittle materials. Acta Metall. Mater. 41(6), 1751 (1993).

  33. I. Gupta, C. Sondergeld, C. Rai, Fracture toughness in shales using nano-indentation. J. Pet. Sci. Eng. 191 (2020).

  34. M. Besterci, L. Pešek, P. Zubko, P. Hvizdoš, Mechanical properties of phases in Al–Al4C3 mechanically alloyed material measured by depth sensing indentation technique. Mater. Lett. 59(16), 1971 (2005)

    Article  CAS  Google Scholar 

  35. X. Wang, X. Peng, Z. Guo, An experimental study of the indentation behaviour of Al foam. Eng. Rev. 34(1), 15 (2014)

    CAS  Google Scholar 

  36. P. Yao, W. Wang, C.Z. Huang, J. Wang, H.T. Zhu, T. Kuriyagawa, Indentation crack initiation and ductile to brittle transition behavior of fused silica, in Advanced Materials Research, vol. 797 (Trans Tech Publ, Bäch, 2013), p.667

    Google Scholar 

  37. B. Huang, M.-H. Zhao, T.-Y. Zhang, Indentation delamination and indentation fracture in ZnO/Si systems. MRS Online Proc. Libr. 687(1), 1 (2001)

    Google Scholar 

  38. S. Guicciardi, T. Shimozono, G. Pezzotti, Nanoindentation characterization of sub-micrometric Y-TZP ceramics. Adv. Eng. Mater. 8(10), 994 (2006)

    Article  CAS  Google Scholar 

  39. C. Schuh, T. Nieh, Y. Kawamura, Rate dependence of serrated flow during nanoindentation of a bulk metallic glass. J. Mater. Res. 17(7), 1651 (2002)

    Article  CAS  Google Scholar 

  40. S.-R. Jian, J.-B. Li, K.-W. Chen, J.S.-C. Jang, J.-Y. Juang, P.-J. Wei, J.-F. Lin, Mechanical responses of Mg-based bulk metallic glasses. Intermetallics 18(10), 1930 (2010)

    Article  CAS  Google Scholar 

  41. J.-I. Jang, G. Pharr, Influence of indenter angle on cracking in Si and Ge during nanoindentation. Acta Mater. 56(16), 4458 (2008)

    Article  CAS  Google Scholar 

  42. T. An, L. Wang, H. Tian, M. Wen, W. Zheng, Deformation and fracture of TiN coating on a Si (1 1 1) substrate during nanoindentation. Appl. Surf. Sci. 257(17), 7475 (2011)

    Article  CAS  Google Scholar 

  43. Y.P. Cao, X.Q. Qian, J. Lu, Z.H. Yao, An energy-based method to extract plastic properties of metal materials from conical indentation tests. J. Mater. Res. 20(5), 1194 (2011)

    Article  Google Scholar 

  44. P. Jiang, T. Zhang, R. Yang, Experimental verification for an instrumented spherical indentation technique in determining mechanical properties of metallic materials. J. Mater. Res. 26(11), 1414 (2011)

    Article  CAS  Google Scholar 

  45. M. Dao, N. Chollacoop, K. Vliet, T.A. Venkatesh, S. Suresh, Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49(19), 3899 (2001)

    Article  CAS  Google Scholar 

  46. D. Torres-Torres, J. Muñoz-Saldaña, L. Gutierrez-Ladron-de Guevara, A. Hurtado-Macías, M. Swain, Geometry and bluntness tip effects on elastic–plastic behaviour during nanoindentation of fused silica: experimental and FE simulation. Modell. Simul. Mater. Sci. Eng. 18(7), 075006 (2010).

  47. C. Gao, M. Liu, Instrumented indentation of fused silica by Berkovich indenter. J Non-Cryst Solids. 475, 151 (2017)

    Article  CAS  Google Scholar 

  48. M. Liu, D. Hou, C. Gao, Berkovich nanoindentation of Zr55Cu30Al10Ni5 bulk metallic glass at a constant loading rate. J Non-Cryst Solids. 561, 120750 (2021)

    Article  CAS  Google Scholar 

  49. C. Gao, L. Yao, M. Liu, Berkovich nanoindentation of borosilicate K9 glass. Opt. Eng. 57(3), 034104 (2018)

    Article  Google Scholar 

  50. J. Gong, H. Miao, Z. Peng, Analysis of the nanoindentation data measured with a Berkovich indenter for brittle materials: effect of the residual contact stress. Acta Mater. 52(3), 785 (2004)

    Article  CAS  Google Scholar 

  51. M. Sakai, Simultaneous estimate of elastic/plastic parameters in depth-sensing indentation tests. Scr. Mater. 51(5), 391 (2004)

    Article  CAS  Google Scholar 

  52. K. Xin, J.C. Lambropoulos, Densification of fused silica: effects on nanoindentation, in Inorganic Optical Materials II, vol. 4102 (International Society for Optics and Photonics, Bellingham, 2000), p.112

    Chapter  Google Scholar 

  53. K. Ikezawa, T. Maruyama, Sharp tip geometry and its effect on hardness in nanoindentation experiments. J. Appl. Phys. 91(12), 9689 (2002)

    Article  CAS  Google Scholar 

  54. M.T. Attaf, Tip bluntness determination using the energy principle and consequent correction to the indentation function. Mater. Lett. 58(6), 1100 (2004)

    Article  CAS  Google Scholar 

  55. J. Nohava, J. Čech, M. Havlíček, R. Consiglio, Indenter wear study and proposal of a simple method for evaluation of indenter blunting. J. Mater. Res. 36(21), 4449 (2021)

    Article  CAS  Google Scholar 

  56. Y. Bao, W. Wang, Y. Zhou, Investigation of the relationship between elastic modulus and hardness based on depth-sensing indentation measurements. Acta Mater. 52(18), 5397 (2004)

    Article  CAS  Google Scholar 

  57. J.L. Bucaille, S. Stauss, E. Felder, J. Michler, Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater. 51(6), 1663 (2003)

    Article  CAS  Google Scholar 

  58. Y.-T. Cheng, C.-M. Cheng, Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. R 44(4), 91 (2004)

    Article  Google Scholar 

  59. J. Woirgard, J. Dargenton, C. Tromas, V. Audurier, A new technology for nanohardness measurements: principle and applications. Surf. Coat. Technol. 100, 103 (1998)

    Article  Google Scholar 

  60. C. Wang, Q. Cao, X. Wang, D. Zhang, S. Qu, J. Jiang, Time-dependent shear transformation zone in thin film metallic glasses revealed by nanoindentation creep. J. Alloys Compd. 696, 239 (2017)

    Article  CAS  Google Scholar 

  61. X. Hao, G. Xiao, T. Jin, B. Su, E. Liu, X. Shu, Effect of indentation size on strain rate sensitivity of zirconia ceramics by nanoindentation. J. Aust. Ceram. Soc. 57(5), 1471 (2021)

    Article  Google Scholar 

  62. W.Y. Huen, H. Lee, V. Vimonsatit, P. Mendis, Relationship of stiffness-based indentation properties using continuous-stiffness-measurement method. Materials 13(1), 97 (2019)

    Article  Google Scholar 

  63. X. Dai, J. Cao, J. Liu, D. Wang, J. Feng, Interfacial reaction behavior and mechanical characterization of ZrO2/TC4 joint brazed by Ag–Cu filler metal. Mater. Sci. Eng. A 646, 182 (2015)

    Article  CAS  Google Scholar 

  64. T. Csanádi, D. Németh, J. Dusza, Z. Lenčéš, P. Šajgalík, Nanoindentation induced deformation anisotropy in β-Si3N4 ceramic crystals. J. Eur. Ceram. Soc. 36(12), 3059 (2016)

    Article  Google Scholar 

  65. Y. Kusano, Z. Barber, J. Evetts, I. Hutchings, Influence of inert gases on ionized magnetron plasma deposition of carbon nitride thin films. Surf. Coat. Technol. 174, 601 (2003)

    Article  Google Scholar 

  66. Y. Kusano, I. Hutchings, Analysis of nano-indentation measurements on carbon nitride films. Surf. Coat. Technol. 169, 739 (2003)

    Article  Google Scholar 

  67. Y.-T. Cheng, C.-M. Cheng, Relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 73(5), 614 (1998)

    Article  CAS  Google Scholar 

  68. J. Chen, S.J. Bull, Investigation of the relationship between work done during indentation and the hardness and Young’s modulus obtained by indentation testing. Int. J. Mater. Res. 99(8), 852 (2008)

    Article  CAS  Google Scholar 

  69. Y.-T. Cheng, Z. Li, C.-M. Cheng, Scaling relationships for indentation measurements. Philos. Mag. A. 82(10), 1821 (2002)

    Article  CAS  Google Scholar 

  70. M. Liu, Q. Zheng, X. Wang, C. Xu, Characterization of distribution of residual stress in shot-peened layer of nickel-based single crystal superalloy DD6 by nanoindentation technique. Mech. Mater. 164, 104143 (2022)

    Article  Google Scholar 

  71. R. Yang, T. Zhang, P. Jiang, Y. Bai. Experimental verification and theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation. Appl. Phys. Lett. 92(23) (2008).

  72. D. Chrobak, M. Dulski, G. Ziółkowski, A. Chrobak, Effect of the indentation load on the raman spectra of the InP crystal. Materials 15(15), 5098 (2022)

    Article  CAS  Google Scholar 

  73. T. Chudoba, P. Schwaller, R. Rabe, J.-M. Breguet, J. Michler, Comparison of nanoindentation results obtained with Berkovich and cube-corner indenters. Philos. Mag. 86(33–35), 5265 (2006)

    Article  CAS  Google Scholar 

  74. K.K. Jha, S. Zhang, N. Suksawang, T.-L. Wang, A. Agarwal, Work-of-indentation as a means to characterize indenter geometry and load–displacement response of a material. J. Phys. D 46(41), 415501 (2013)

    Article  CAS  Google Scholar 

  75. S. Li, W. Yuan, Y. Ding, G. Wang, Indentation load–depth relation for an elastic layer with surface tension. Math. Mech. Solids 24(4), 1147 (2019)

    Article  Google Scholar 

  76. S. Gonzalez, J. Fornell, E. Pellicer, S. Surinach, M.D. Baro, A.L. Greer, F.J. Belzunce, J. Sort, Influence of the shot-peening intensity on the structure and near-surface mechanical properties of Ti40Zr10Cu38Pd12 bulk metallic glass. Appl. Phys. Lett. 103(21) (2013).

  77. V. Matyunin, N. Abusaif, A.Y. Marchenkov, Analysis of the indentation size effect on the hardness measurements of materials, in Journal of Physics: Conference Series, vol. 1399 (IOP Publishing, Bristol, 2019), p.044016

    Google Scholar 

  78. H. Bei, E.P. George, J. Hay, G.M. Pharr, Influence of indenter tip geometry on elastic deformation during nanoindentation. Phys. Rev. Lett. 95(4), 045501 (2005)

    Article  CAS  Google Scholar 

  79. J. Chen, S. Bull, Multi-cycling nanoindentation study on thin optical coatings on glass. J. Phys. D 41(7), 074009 (2008)

    Article  Google Scholar 

  80. G. Lu, J. Liu, H. Qiao, Y. Zhou, T. Jin, J. Zhao, X. Sun, Z. Hu, Surface nano-hardness and microstructure of a single crystal nickel base superalloy after laser shock. Peening. Optic. Laser Technol. 91, 116 (2017)

    Article  CAS  Google Scholar 

  81. L. Wang, L. Wang, Y. Xue, H. Zhang, H. Fu, Nanoindentation response of laser shock peened Ti-based bulk metallic glass. AIP Adv. 5(5), 057156 (2015)

    Article  Google Scholar 

  82. O. Jimenez, M. Audronis, M. Baker, A. Matthews, A. Leyland, Structure and mechanical properties of nitrogen-containing Zr–Cu based thin films deposited by pulsed magnetron sputtering. J. Phys. D 41(15), 155301 (2008)

    Article  Google Scholar 

  83. A. Kawashima, H. Kurishita, H. Kimura, T. Zhang, A. Inoue, Fracture toughness of Zr55Al10Ni5Cu30 bulk metallic glass by 3-point bend testing. Mater. Trans. 46(7), 1725 (2005)

    Article  CAS  Google Scholar 

  84. M. Yamasaki, S. Kagao, Y. Kawamura, Thermal diffusivity and conductivity of Zr55Al10Ni5Cu30 bulk metallic glass. Scr. Mater. 53(1), 63 (2005)

    Article  CAS  Google Scholar 

  85. M.M. Khan, K.M. Deen, W. Haider, Combinatorial development and assessment of a Zr-based metallic glass for prospective biomedical applications. J. Non-Cryst. Solids. 523, 119544 (2019)

    Article  CAS  Google Scholar 

  86. M. Zhang, F. Li, B. Chen, S. Wang, Investigation of micro-indentation characteristics of P/M nickel-base superalloy FGH96 using dislocation-power theory. Mater. Sci. Eng. A 535, 170 (2012)

    Article  CAS  Google Scholar 

  87. R. Jiang, L. Zhang, Y. Zhao, X. Chen, B. Gan, X. Hao, Y. Song, Effects of hot corrosion on fatigue performance of GH4169 alloy. J. Mater. Eng. Perform. 30(3), 2300 (2021)

    Article  CAS  Google Scholar 

  88. S. Wen, R. Zong, F. Zeng, Y. Gao, F. Pan, Evaluating modulus and hardness enhancement in evaporated Cu/W multilayers. Acta Mater. 55(1), 345 (2007)

    Article  CAS  Google Scholar 

  89. S. Krimpalis, K. Mergia, S. Messoloras, A. Dubinko, D. Terentyev, K. Triantou, J. Reiser, G. Pintsuk, Comparative study of the mechanical properties of different tungsten materials for fusion applications. Phys. Scr. 2017(T170), 014068 (2017)

    Article  Google Scholar 

  90. P. Sellappan, A. Sharafat, V. Keryvin, P. Houizot, T. Rouxel, J. Grins, S. Esmaeilzadeh, Elastic properties and surface damage resistance of nitrogen-rich (Ca, Sr)–Si–O–N glasses. J. Non-Cryst. Solids. 356(41–42), 2120 (2010)

    Article  CAS  Google Scholar 

  91. G. Tang, Y.-L. Shen, D. Singh, N. Chawla, Analysis of indentation-derived effective elastic modulus of metal-ceramic multilayers. Int. J. Mech. Mater. Des. 4(4), 391 (2008)

    Article  CAS  Google Scholar 

  92. I. Tanakaa, F. Oba, T. Sekine, E. Ito, A. Kubo, K. Tatsumi, H. Adachi, T. Yamamoto, Hardness of cubic silicon nitride. J. Mater. Res. 17(4), 731 (2002)

    Article  Google Scholar 

  93. M. Liu, Z. Xu, R. Fu, Micromechanical and microstructure characterization of BaO-Sm2O3–5TiO2 ceramic with addition of Al2O3. Ceram. Int. 48(1), 992 (2022)

    Article  CAS  Google Scholar 

  94. M. Turkoz, S. Nezir, O. Ozturk, E. Asikuzun, G. Yildirim, C. Terzioglu, A. Varilci, Experimental and theoretical approaches on mechanical evaluation of Y123 system by Lu addition. J. Mater. Sci. 24(7), 2414 (2013)

    CAS  Google Scholar 

  95. S. Grillo, M. Ducarroir, M. Nadal, E. Tournie, J. Faurie, Nanoindentation of Si, GaP, GaAs and ZnSe single crystals. J. Phys. D 36(1), L5 (2002)

    Article  Google Scholar 

  96. H.M. Wang, B.S. Xu, S.N. Ma, S.Y. Dong, X.Y. Li, Micro mechanical properties of n-Al2O3/Ni composite coating by nanoindentation. Transactions of Nonferrous Metals Society of China (English Edition). 14(SUPPL. 2), 115 (2004)

    CAS  Google Scholar 

  97. T. Kitagaki, T. Hoshino, K. Yano, N. Okamura, H. Ohara, T. Fukasawa and K. Koizumi: Mechanical properties of cubic (U, Zr) O2. J. Nucl. Eng. Radiat. Sci. 4(3) (2018).

  98. H. Fu, L. Cai, Z. Chai, X. Liu, L. Zhang, S. Geng, K. Zhang, H. Liao, X. Wu, X. Wang, Evaluation of bonding properties by flat indentation method for an EBW joint of RAFM steel for fusion application. Nucl. Mater. Energy. 25, 100861 (2020)

    Article  Google Scholar 

  99. L.-C. Chang, Y.-Z. Zheng, Y.-X. Gao, Y.-I. Chen, Mechanical properties and oxidation resistance of sputtered Cr–W–N coatings. Surf. Coat. Technol. 320, 196 (2017)

    Article  CAS  Google Scholar 

  100. F. Chen, X. Tang, H. Huang, J. Liu, H. Li, Y. Qiu, D. Chen, Surface damage and mechanical properties degradation of Cr/W multilayer films irradiated by Xe20+. Appl. Surf. Sci. 357, 1225 (2015)

    Article  CAS  Google Scholar 

  101. A.E. Giannakopoulos, S. Suresh, Determination of elastoplastic properties by instrumented sharp indentation. Scr. Mater. 40(10), 1191 (1999)

    Article  CAS  Google Scholar 

  102. Y.T. Cheng, C.M. Cheng, Scaling approach to conical indentation in elastic-plastic solids with work hardening. J. Appl. Phys. 84(3), 1284 (1998)

    Article  CAS  Google Scholar 

  103. Y.T. Cheng, C.M.C.Z. Zhemin, Scaling relationships in conical indentation of elastic-perfectly plastic solids. Int. J. Solids Struct. 36(8), 1231 (1999)

    Article  Google Scholar 

  104. K.K. Jha, N. Suksawang, D. Lahiri, A. Agarwal, A novel energy-based method to evaluate indentation modulus and hardness of cementitious materials from nanoindentation load–displacement data. Mater. Struct. 48(9), 2915 (2014)

    Article  Google Scholar 

  105. M. Ovsik, M. Stanek, A. Dockal and P. Fluxa: Electron radiation effect on indentation creep of construction polymers. In: 14th International Conference on Local Mechanical Properties (LMP) (Vol. 27, Trans Tech Publ, Zurich) (2019), pp. 116.

  106. C.C. Huang, M.K. Wei, S. Lee, Transient and steady-state nanoindentation creep of polymeric materials. Int. J. Plast 27(7), 1093 (2011)

    Article  CAS  Google Scholar 

  107. O. Smerdova, M. Pecora, M. Gigliotti, Cyclic indentation of polymers: instantaneous elastic modulus from reloading, energy analysis, and cyclic creep. J. Mater. Res. 34(21), 3688 (2019)

    Article  CAS  Google Scholar 

  108. M.Y. N’Jock, F. Roudet, M. Idriss, O. Bartier, D. Chicot, Work-of-indentation coupled to contact stiffness for calculating elastic modulus by instrumented indentation. Mech. Mater. 94, 170 (2016)

    Article  Google Scholar 

  109. M. Dejun, O.C. Wo, J. Liu, H. Jiawen, Determination of Young’s modulus by nanoindentation. Sci. China Ser. E 47(4), 398 (2004)

    Article  Google Scholar 

  110. S. Jayaraman, G. Hahn, W. Oliver, C. Rubin, P. Bastias, Determination of monotonic stress-strain curve of hard materials from ultra-low-load indentation tests. Int. J. Solids Struct. 35(5–6), 365 (1998)

    Article  Google Scholar 

  111. J. Chen, S.J. Bull, Relation between the ratio of elastic work to the total work of indentation and the ratio of hardness to Young’s modulus for a perfect conical tip. J. Mater. Res. 24(3), 590 (2011)

    Article  Google Scholar 

  112. D. Ma, C. Ong, T. Zhang, An instrumented indentation method for Young’s modulus measurement with accuracy estimation. Exper. Mech. 49(5), 719 (2009)

    Article  CAS  Google Scholar 

  113. D. Czekaja, A. Lisińska-Czekaja, J. Plewab, Study of nanomechanical properties of (1-y) BST-yMgO thin films. Ciência Tecnologia dos Mater. 29(1), e71 (2017)

    Article  Google Scholar 

  114. A. Concustell, J. Sort, G. Alcalá, S. Mato, A. Gebert, J. Eckert, M. Baró, Plastic deformation and mechanical softening of Pd40Cu30Ni10P20 bulk metallic glass during nanoindentation. J. Mater. Res. 20(10), 2719 (2005)

    Article  CAS  Google Scholar 

  115. D. Wang, L. Zhang, Y. Chen, H. Wang, Effect of high pressure-high temperature treatment on micro-mechanical properties of TC4 alloy. Heat Treat. Met. 41(2), 143 (2016)

    Google Scholar 

  116. Y.-X. Geng, X. Lin, Y.-X. Wang, J.-B. Qiang, Y.-M. Wang, C. Dong, Mechanical and magnetic properties of new (Fe Co, Ni)–B–Si–Ta bulk glassy alloys. Acta Metall. Sin. (Engl. Lett.) 30(7), 659 (2017)

    Article  CAS  Google Scholar 

  117. D.C. Pender, N.P. Padture, A.E. Giannakopoulos, S. Suresh. Gradients in elastic modulus for improved contact-damage resistance. Part I: The silicon nitride-oxynitride glass system. Acta Mater. 49(16), 3255 (2001)

  118. Y. Choi, H.-S. Lee, D. Kwon, Analysis of sharp-tip-indentation load–depth curve for contact area determination taking into account pile-up and sink-in effects. J. Mater. Res. 19(11), 3307 (2004)

    Article  CAS  Google Scholar 

  119. T.A. Venkatesh, K. Vliet, A.E. Giannakopoulos, S. Suresh, Determination of elasto-plastic properties by instrumented sharp indentation: guidelines for property extraction. Scr. Mater. 42(9), 833 (2000)

    Article  CAS  Google Scholar 

  120. J. Malzbender, G.D. With, Indentation load-displacement curve, plastic deformation, and energy. J. Mater. Res. 17(02), 502 (2002)

    Article  CAS  Google Scholar 

  121. D.J. Ma, C.W. Ong, S.F. Wong, New relationship between Young’s modulus and nonideally sharp indentation parameters. J. Mater. Res. 19(7), 2144 (2004)

    Article  CAS  Google Scholar 

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Acknowledgments

This project is supported by National Key Research and Development Program of China on the International Scientific Innovation Cooperation among Governments (Grant No. 2019YFE0191800), National Natural Science Foundation of China (Grant No. 51705082), and Innovation Programs from Southwest Institute of Physics (Grant Nos. 202101XWCXRZ001 and 202102XWCXYD001).

Funding

Funding was provided by National Key Research and Development Program of China on the International Scientific Innovation Cooperation among Governments (Grant No. 2019YFE0191800), National Natural Science Foundation of China (Grant No. 51705082), and Innovation Programs from Southwest Institute of Physics (Grant Nos. 202101XWCXRZ001 and 202102XWCXYD001).

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Authors and Affiliations

  1. Fujian Provincial Key Laboratory of Terahertz Functional Devices and Intelligent Sensing, School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, 350108, People’s Republic of China

    Ming Liu & Zhibo Cong

  2. Center for Fusion Science, Southwestern Institute of Physics, No. 5, Huangjing Road, Shuangliu County, Chengdu, 610225, People’s Republic of China

    Haiying Fu & Pengyuan Li

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  1. Ming Liu
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Correspondence to Ming Liu or Haiying Fu.

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Liu, M., Cong, Z., Fu, H. et al. Relationships in instrumented indentation by Berkovich indenter. Journal of Materials Research 37, 4084–4102 (2022). https://doi.org/10.1557/s43578-022-00769-x

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