Abstract
Understanding the dynamics of the lithosphere relies heavily on the scale-dependent rheology of minerals. While quartz, feldspar, and phyllosilicates are the key phases to govern the rheology of the crust and tectonic margins, olivine and other mafic phases control the same in the upper mantle. Phase transition, solid-state substitution, polymorphism, etc. also affect mineral phase rheology. High pressure–temperature deformation tests with natural, synthetic and analog materials have improved our interpretation of the geodynamic state of the lithosphere. However, deforming and studying a single crystal is not easy, because of the scarcity of specimens and laborious sample preparations. Experimental micro- to nanoindentation at room and/or elevated temperatures has proven to be a convenient method over mesoscale compressive testing. Micro- to nanoindentation technique enables higher precision, faster data acquisition and ultra-high resolution (nanoscale) load and displacement. Hardness, elastic moduli, yield stress, fracture toughness, fracture surface energy and rate-dependent creep of mono- or polycrystalline minerals are evaluated using this technique. Here, we present a comprehensive assessment of micro- to nano-mechanics of minerals. We first cover the fundamental theories of instrumented indentation, experimental procedures, pre- and post-indentation interpretations using various existing models followed by a detailed discussion on the application of nanoindentation in understanding the rheology and deformation mechanisms of various minerals commonly occur in the crust and upper mantle. We also address some of the major limitations of indentation tests (e.g., indentation size effect). Finally, we suggest potential future research areas in mineral rheology using instrumented indentation.
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References
Acharya A, Bassani JL (2000) Lattice incompatibility and a gradient theory of crystal plasticity. J Mech Phys Solids 48:1565–1595. https://doi.org/10.1016/S0022-5096(99)00075-7
Alao A-R, Yin L (2014) Loading rate effect on the mechanical behavior of zirconia in nanoindentation. Mater Sci Eng A 619:247–255. https://doi.org/10.1016/j.msea.2014.09.101
Alekhin VP, Berlin GS, Shorshor MK, Shnyrev G, Ternovsk AP, Skvortso VN, Krushcho MM, Merkulov V, Kalei G, Isaev A (1971) Instrument for micromechanical tests of solid materials. Instrum Exp Tech USSR 14:1265
Anstis GR, Chantikul P, Lawn BR, Marshall DB (1981) A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements. J Am Ceram Soc 64:533–538. https://doi.org/10.1111/j.1151-2916.1981.tb10320.x
Ashraf W, Tian N (2016) Nanoindentation assisted investigation on the viscoelastic behavior of carbonated cementitious matrix: influence of loading function. Constr Build Mater 127:904–917. https://doi.org/10.1016/j.conbuildmat.2016.10.021
Aslin J, Mariani E, Dawson K, Barsoum MW (2019) Ripplocations provide a new mechanism for the deformation of phyllosilicates in the lithosphere. Nat Commun 10:686. https://doi.org/10.1038/s41467-019-08587-2
Atkinson BK (1979) A fracture mechanics study of subcritical tensile cracking of quartz in wet environments. Pure Appl Geophys 117:1011–1024. https://doi.org/10.1007/BF00876082
Atkinson BK, Avdis V (1980) Fracture mechanics parameters of some rock-forming minerals determined using an indentation technique. Int J Rock Mech Min Sci Geomech Abstr 17:383–386. https://doi.org/10.1016/0148-9062(80)90523-9
Ayatollahi MR, Najafabadi MZ, Koloor SSR, Petrů M (2020) Mechanical characterization of heterogeneous polycrystalline rocks using nanoindentation method in combination with generalized means method. J Mech 36:813–823. https://doi.org/10.1017/jmech.2020.18
Basu S, Moseson A, Barsoum MW (2006) On the determination of spherical nanoindentation stress–strain curves. J Mater Res 21:2628–2637. https://doi.org/10.1557/jmr.2006.0324
Basu S, Zhou A, Barsoum MW (2009) On spherical nanoindentations, kinking nonlinear elasticity of mica single crystals and their geological implications. J Struct Geol 31:791–801. https://doi.org/10.1016/j.jsg.2009.05.008
Bishop RF, Hill R, Mott NF (1945) The theory of indentation and hardness tests. Proc Phys Soc 57:147–159. https://doi.org/10.1088/0959-5309/57/3/301
Blacic JD, Christie JM (1984) Plasticity and hydrolytic weakening of quartz single crystals. J Geophys Res Solid Earth 89:4223–4239. https://doi.org/10.1029/JB089iB06p04223
Bloss FD, Shekarchi E, Shell HR (1959) Hardness of synthetic and natural micas1. Am Mineral 44:33–48
Bower AF, Fleck NA, Needleman A, Ogbonna N, Enderby JE (1993) Indentation of a power law creeping solid. Proc R Soc Lond Ser Math Phys Sci 441:97–124. https://doi.org/10.1098/rspa.1993.0050
Brace WF (1963) Behavior of Quartz during Indentation. J Geol 71:581–595. https://doi.org/10.1086/626934
Breault RW, Bayham SC, Monazam ER (2016) Applications of tribology and fracture mechanics to determine wear and impact attrition of particulate solids in CFB systems. In: Berruti F, Bi X, Cocco R, Chaouki J, Fluidization XV (eds) ECI Symposium Series. https://dc.engconfintl.org/fluidization_xv/154
Brinell JA (1900) Way of determining the hardness of bodies and some applications of the same. Tek Tidskr 5:69
Broitman E (2017) Indentation hardness measurements at macro-, micro-, and nanoscale: a critical overview. Tribol Lett 65:1–18. https://doi.org/10.1007/s11249-016-0805-5
Brookes CA, O’neill JB, Redfern BAW (1971) Anisotropy in the hardness of single crystals. Proc R Soc Lond Math Phys Sci A 322(1548):18
Broz ME, Cook RF, Whitney DL (2006) Microhardness, toughness, and modulus of Mohs scale minerals. Am Mineral 91:135–142. https://doi.org/10.2138/am.2006.1844
Bückle H (1965) Mikrohärteprüfung und ihre Anwendung. Berliner Union, Stuttgart
Bull SJ (2003) On the origins and mechanisms of the indentation size effect. Int J Mater Res 94:787–792. https://doi.org/10.3139/ijmr-2003-0138
Bull SJ, Page TF, Yoffe EH (1989) An explanation of the indentation size effect in ceramics. Philos Mag Lett 59:281–288. https://doi.org/10.1080/09500838908206356
Carlton CE, Ferreira PJ (2012) In situ TEM nanoindentation of nanoparticles. Micron 43:1134–1139. https://doi.org/10.1016/j.micron.2012.03.002
Ceccato A, Menegon L, Hansen LN (2022) Strength of dry and wet quartz in the low-temperature plasticity regime: insights from nanoindentation. Geophys Res Lett 49:e2021GL094633. https://doi.org/10.1029/2021GL094633
Chakoumakos BC, Oliver WC, Lumpkin GR, Ewing RC (1991) Hardness and elastic modulus of zircon as a function of heavy-particle irradiation dose: I. In situ α-decay event damage. Radiat Eff Defects Solids 118:393–403. https://doi.org/10.1080/10420159108220764
Chen Z, Sucech S, Faber KT (2010) A hierarchical study of the mechanical properties of gypsum. J Mater Sci 45:4444–4453. https://doi.org/10.1007/s10853-010-4527-z
Cheng Y-T, Li Z, Cheng C-M (2002) Scaling relationships for indentation measurements. Philos Mag A 82:1821–1829. https://doi.org/10.1080/01418610208235693
Darot M, Gueguen Y, Benchemam Z, Gaboriaud R (1985) Ductile-brittle transition investigated by micro-indentation: results for quartz and olivine. Phys Earth Planet Inter 40:180–186. https://doi.org/10.1016/0031-9201(85)90128-1
Dorner D (2002) Indentation methods in experimental rock deformation. Doctoral Dissertation, Ruhr-Universität Bochum, Bochum, Germany
Dorner D, Stöckhert B (2004) Plastic flow strength of jadeite and diopside investigated by microindentation hardness tests. Tectonophysics 379:227–238. https://doi.org/10.1016/j.tecto.2003.11.008
Druiventak A, Trepmann CA, Renner J, Hanke K (2011) Low-temperature plasticity of olivine during high stress deformation of peridotite at lithospheric conditions—an experimental study. Earth Planet Sci Lett 311:199–211. https://doi.org/10.1016/j.epsl.2011.09.022
Dukino RD, Swain MV (1992) Comparative measurement of indentation fracture toughness with Berkovich and Vickers indenters. J Am Ceram Soc 75:3299–3304. https://doi.org/10.1111/j.1151-2916.1992.tb04425.x
Eliyahu M, Emmanuel S, Day-Stirrat RJ, Macaulay CI (2015) Mechanical properties of organic matter in shales mapped at the nanometer scale. Mar Pet Geol 59:294–304. https://doi.org/10.1016/j.marpetgeo.2014.09.007
Emmanuel S, Eliyahu M, Day-Stirrat RJ, Hofmann R, Macaulay CI (2016) Impact of thermal maturation on nano-scale elastic properties of organic matter in shales. Mar Pet Geol 70:175–184. https://doi.org/10.1016/j.marpetgeo.2015.12.001
Evans B (1984) The effect of temperature and impurity content on indentation hardness of quartz. J Geophys Res Solid Earth 89:4213–4222. https://doi.org/10.1029/JB089iB06p04213
Evans B, Goetze C (1979) The temperature variation of hardness of olivine and its implication for polycrystalline yield stress. J Geophys Res Solid Earth 84:5505–5524. https://doi.org/10.1029/JB084iB10p05505
Faul UH, Fitz Gerald JD, Farla RJM, Ahlefeldt R, Jackson I (2011) Dislocation creep of fine-grained olivine. J Geophys Res Solid Earth. https://doi.org/10.1029/2009JB007174
Feng G, Ngan AHW (2002) Effects of creep and thermal drift on modulus measurement using depth-sensing indentation. J Mater Res 17:660–668. https://doi.org/10.1557/JMR.2002.0094
Ferguson CC, Lloyd GE, Knipe RJ (1987) Fracture mechanics and deformation processes in natural quartz: a combined Vickers indentation, SEM, and TEM study. Can J Earth Sci 24:544–555. https://doi.org/10.1139/e87-053
Field JS, Swain MV (1993) A simple predictive model for spherical indentation. J Mater Res 8:297–306. https://doi.org/10.1557/JMR.1993.0297
Fischer-Cripps AC (2004) A simple phenomenological approach to nanoindentation creep. Mater Sci Eng A 385:74–82. https://doi.org/10.1016/j.msea.2004.04.070
Fischer-Cripps AC (2006) Critical review of analysis and interpretation of nanoindentation test data. Surf Coat Technol 200:4153–4165. https://doi.org/10.1016/j.surfcoat.2005.03.018
Fischer-Cripps AC (2011) Nanoindentation, mechanical engineering series. Springer, New York. https://doi.org/10.1007/978-1-4419-9872-9
Frost HJ, Ashby MF (1982) Deformation mechanism maps: the plasticity and creep of metals and ceramics. Pergamon Press, Oxford
Gaboriaud RJ, Darot M, Gueguen Y, Woirgard J (1981) Dislocations in olivine indented at low temperatures. Phys Chem Miner 7:100–104. https://doi.org/10.1007/BF00309460
Ginder RS, Nix WD, Pharr GM (2018) A simple model for indentation creep. J Mech Phys Solids 112:552–562. https://doi.org/10.1016/j.jmps.2018.01.001
Goldsby DL, Rar A, Pharr GM, Tullis TE (2004) Nanoindentation creep of quartz, with implications for rate- and state-variable friction laws relevant to earthquake mechanics. J Mater Res 19:9
Gouldstone A, Chollacoop N, Dao M, Li J, Minor AM, Shen Y-L (2007) Indentation across size scales and disciplines: recent developments in experimentation and modeling. Acta Mater 55:4015–4039. https://doi.org/10.1016/j.actamat.2006.08.044
Graham EK Jr, Barsch GR (1969) Elastic constants of single-crystal forsterite as a function of temperature and pressure. J Geophys Res 1896–1977(74):5949–5960. https://doi.org/10.1029/JB074i025p05949
Griggs D (1967) Hydrolytic weakening of quartz and other silicates*. Geophys J Int 14:19–31. https://doi.org/10.1111/j.1365-246X.1967.tb06218.x
Griggs DT, Blacic JD (1965) Quartz: anomalous weakness of synthetic crystals. Science 147:292–295. https://doi.org/10.1126/science.147.3655.292
Grodzinski P (1953) Hardness testing of plastics. Plastics 18:312–314
Hackney SA, Aifantis KE, Tangtrakarn A, Shrivastava S (2012) Using the Kelvin-Voigt model for nanoindentation creep in Sn-C/PVDF nanocomposites. Mater Sci Technol 28:1161–1166. https://doi.org/10.1179/1743284712Y.0000000063
Hansen LN, Kumamoto KM, Thom CA, Wallis D, Durham WB, Goldsby DL, Breithaupt T, Meyers CD, Kohlstedt DL (2019) Low-temperature plasticity in olivine: grain size, strain hardening, and the strength of the lithosphere. J Geophys Res Solid Earth 124:5427–5449. https://doi.org/10.1029/2018JB016736
Hansen LN, David EC, Brantut N, Wallis D (2020) Insight into the microphysics of antigorite deformation from spherical nanoindentation. Philos Trans R Soc Math Phys Eng Sci 378:20190197. https://doi.org/10.1098/rsta.2019.0197
Hays C, Kendall EG (1973) An analysis of Knoop microhardness. Metallography 6:275–282. https://doi.org/10.1016/0026-0800(73)90053-0
Hemley RJ, Prewitt CT, Kingma KJ (1994) High-pressure behavior of silica. Rev Mineral Geochem 29:41–81
Hill R, Lee EH, Tupper SJ (1947) The theory of wedge indentation of ductile materials. Proc R Soc Lond Ser Math Phys Sci. https://doi.org/10.1098/rspa.1947.0009
Hirth G, Teyssier C, Dunlap JW (2001) An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks. Int J Earth Sci 90:77–87. https://doi.org/10.1007/s005310000152
Hobbs BE, McLaren AC, Paterson MS (1972) Plasticity of single crystals of synthetic quartz. Wash DC Am Geophys Union Geophys Monogr Ser 16:29–53. https://doi.org/10.1029/GM016p0029
Hogan JD, Boonsue S, Spray JG, Rogers RJ (2012) Micro-scale deformation of gypsum during micro-indentation loading. Int J Rock Mech Min Sci 54:140–149. https://doi.org/10.1016/j.ijrmms.2012.05.028
Huang Y, Gao H, Nix WD, Hutchinson JW (2000) Mechanism-based strain gradient plasticity—II. Analysis. J Mech Phys Solids 48:99–128. https://doi.org/10.1016/S0022-5096(99)00022-8
ISO, B. 2002. 14577–1, 2002. Metallic materials-Instrumented indentation test for hardness and materials parameters-Part, 1.
Jaya BN, Jayaram V (2014) Crack stability in edge-notched clamped beam specimens: modeling and experiments. Int J Fract 188:213–228. https://doi.org/10.1007/s10704-014-9956-2
Johnson KL (1970) The correlation of indentation experiments. J Mech Phys Solids 18:115–126. https://doi.org/10.1016/0022-5096(70)90029-3
Kalidindi SR, Pathak S (2008) Determination of the effective zero-point and the extraction of spherical nanoindentation stress–strain curves. Acta Mater 56:3523–3532. https://doi.org/10.1016/j.actamat.2008.03.036
Karato S (2008) Deformation of earth materials: an introduction to the rheology of solid earth. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511804892
Kawazoe T, Karato S, Otsuka K, Jing Z, Mookherjee M (2009) Shear deformation of dry polycrystalline olivine under deep upper mantle conditions using a rotational Drickamer apparatus (RDA). Phys Earth Planet Inter 174:128–137. https://doi.org/10.1016/j.pepi.2008.06.027
Kekulawala KRSS, Paterson MS, Boland JN (1978) Hydrolytic weakening in quartz. Tectonophysics 46:T1–T6. https://doi.org/10.1016/0040-1951(78)90101-4
Kekulawala KRSS, Paterson MS, Boland JN (1981) An experimental study of the role of water in quartz deformation. Wash DC Am Geophys Union Geophys Monogr Ser 24:49–60. https://doi.org/10.1029/GM024p0049
Kiener D, Minor AM (2011) Source truncation and exhaustion: insights from quantitative in situ TEM tensile testing. Nano Lett 11:3816–3820. https://doi.org/10.1021/nl201890s
Kingma KJ, Meade C, Hemley RJ, Mao H, Veblen DR (1993) Microstructural observations of α-quartz amorphization. Science 259:666–669. https://doi.org/10.1126/science.259.5095.666
Kinosita K (1972) Recent developments in the study of mechanical properties of thin films. Thin Solid Films 12:17–28. https://doi.org/10.1016/0040-6090(72)90387-2
Kocks UF, Argon AS, Ashby MF (1975) Thermodynamics and kinetics of slip. In: Chalmers B, Christian JW, Massalski TB (eds) Progress in materials science, volume 19, Pergamon Press Ltd. Headington Hill Hall, Oxford, England. ISBN 9780080179643
Koizumi S, Hiraga T, Suzuki TS (2020) Vickers indentation tests on olivine: size effects. Phys Chem Miner 47:8. https://doi.org/10.1007/s00269-019-01075-5
Kollenberg W (1986) Microhardness measurement on haematite crystals at temperatures up to 900°C. J Mater Sci 21:4310–4314. https://doi.org/10.1007/BF01106547
Kollenberg W (1988) Plastic deformation of Al2O3 single crystals by indentation at temperatures up to 750°C. J Mater Sci 23:3321–3325. https://doi.org/10.1007/BF00551312
Kranjc K, Rouse Z, Flores KM, Skemer P (2016) Low-temperature plastic rheology of olivine determined by nanoindentation. Geophys Res Lett 43:176–184. https://doi.org/10.1002/2015GL065837
Kumamoto KM, Thom CA, Wallis D, Hansen LN, Armstrong DEJ, Warren JM, Goldsby DL, Wilkinson AJ (2017) Size effects resolve discrepancies in 40 years of work on low-temperature plasticity in olivine. Sci Adv 3:e1701338. https://doi.org/10.1126/sciadv.1701338
Lanin ES, Sone H, Yu Z, Liu Q, Wang B (2021) Comparison of biotite elastic properties recovered by spherical nanoindentations and atomistic simulations—influence of nano-scale defects in phyllosilicates. J Geophys Res Solid Earth 126:e2021JB021902. https://doi.org/10.1029/2021JB021902
Laugier MT (1987) New formula for indentation toughness in ceramics. J Mater Sci Lett 6:355–356. https://doi.org/10.1007/BF01729352
Lawn BR, Swain MV (1975) Microfracture beneath point indentations in brittle solids. J Mater Sci 10:113–122. https://doi.org/10.1007/BF00541038
Lawn B, Wilshaw R (1975) Indentation fracture: principles and applications. J Mater Sci 10:1049–1081. https://doi.org/10.1007/BF00823224
Lawn BR, Evans AG, Marshall DB (1980) Elastic/plastic indentation damage in ceramics: the median/radial crack system. J Am Ceram Soc 63:574–581. https://doi.org/10.1111/j.1151-2916.1980.tb10768.x
Lawn B, Marshall D, Raj R, Hirth G, Page T, Yeomans J (2021) Precipitous weakening of quartz at the α–β phase inversion. J Am Ceram Soc 104:23–26. https://doi.org/10.1111/jace.17470
Lei M, Dang F-N, Xue H-B, Yu Z, He M-M (2021) Study on mechanical properties of granite minerals based on nanoindentation test technology. Therm Sci 25:4457–4463
Lepienski CM, Foerster CE (2004) Nanomechanical properties by nanoindentation. In: Nalwa HS (ed) Encyclopedia of nanoscience and nanotechnology. American Scientific Publishers, California. Volume 7, pp. 1–20. ISBN 9781588830012
Li X, Bhushan B (2002) A review of nanoindentation continuous stiffness measurement technique and its applications. Mater Charact 48:11–36. https://doi.org/10.1016/S1044-5803(02)00192-4
Li H, Bradt RC (1991) Knoop microhardness anisotropy of single-crystal LaB6. Mater Sci Eng A 142:51–61. https://doi.org/10.1016/0921-5093(91)90753-A
Li H, Bradt RC (1993) The microhardness indentation load/size effect in rutile and cassiterite single crystals. J Mater Sci 28:917–926. https://doi.org/10.1007/BF00400874
Li H, Ghosh A, Han YH, Bradt RC (1993) The frictional component of the indentation size effect in low load microhardness testing. J Mater Res 8:1028–1032. https://doi.org/10.1557/JMR.1993.1028
Li C, Ostadhassan M, Guo S, Gentzis T, Kong L (2018) Application of PeakForce tapping mode of atomic force microscope to characterize nanomechanical properties of organic matter of the Bakken Shale. Fuel 233:894–910. https://doi.org/10.1016/j.fuel.2018.06.021
Li Y, Luo S, Lu M, Wu Y, Zhou N, Wang D, Lu Y, Zhang G (2021) Cross-scale characterization of sandstones via statistical nanoindentation: evaluation of data analytics and upscaling models. Int J Rock Mech Min Sci 142:104738. https://doi.org/10.1016/j.ijrmms.2021.104738
Li X, Zhang W, Han M, Xie F, Li D, Zhang J, Long B (2023) Indentation size effect: an improved mechanistic model incorporating surface undulation and indenter tip irregularity. J Mater Res Technol 23:143–153. https://doi.org/10.1016/j.jmrt.2023.01.001
Linker MF, Kirby SH (1981) Anisotropy in the rheology of hydrolytically weakened synthetic quartz crystals. Wash DC Am Geophys Union Geophys Monogr Ser 24:29–48. https://doi.org/10.1029/GM024p0029
Lips EMH, Sack J (1936) A hardness tester for microscopical objects. Nature 138:328–329. https://doi.org/10.1038/138328a0
Liu S, Wheeler JM, Howie PR, Zeng XT, Michler J, Clegg WJ (2013) Measuring the fracture resistance of hard coatings. Appl Phys Lett 102:171907. https://doi.org/10.1063/1.4803928
Liu K, Ostadhassan M, Bubach B (2018) Application of nanoindentation to characterize creep behavior of oil shales. J Pet Sci Eng 167:729–736. https://doi.org/10.1016/j.petrol.2018.04.055
Liu E, Kong L, Xiao G, Lin J, Zhao G, Li H (2021) Creep correction of elastic modulus and hardness for viscoelastic materials during microindentation. Polym Adv Technol 32:955–963. https://doi.org/10.1002/pat.5142
Long H, Weidner DJ, Li L, Chen J, Wang L (2011) Deformation of olivine at subduction zone conditions determined from in situ measurements with synchrotron radiation. Phys Earth Planet Inter 186:23–35. https://doi.org/10.1016/j.pepi.2011.02.006
Lucca DA, Herrmann K, Klopfstein MJ (2010) Nanoindentation: measuring methods and applications. CIRP Ann 59:803–819. https://doi.org/10.1016/j.cirp.2010.05.009
Ludwik P (1908) Die kegelprobe. Springer Berlin Heidelberg, Berlin, pp 3–17. https://doi.org/10.1007/978-3-662-33196-5_1
Ma Q, Clarke DR (1995) Size dependent hardness of silver single crystals. J Mater Res 10:853–863. https://doi.org/10.1557/JMR.1995.0853
Ma Z, Pathegama Gamage R, Zhang C (2020) Application of nanoindentation technology in rocks: a review. Geomech Geophys Geo-Energy Geo-Resour 6:60. https://doi.org/10.1007/s40948-020-00178-6
Ma Z, Gamage RP, Zhang C (2021a) Mechanical properties of α-quartz using nanoindentation tests and molecular dynamics simulations. Int J Rock Mech Min Sci 147:104878. https://doi.org/10.1016/j.ijrmms.2021.104878
Ma Z, Pathegama Gamage R, Zhang C (2021b) Effects of temperature and grain size on the mechanical properties of polycrystalline quartz. Comput Mater Sci 188:110138. https://doi.org/10.1016/j.commatsci.2020.110138
Ma Z, Zhang C, Pathegama Gamage R, Zhang G (2022) Uncovering the creep deformation mechanism of rock-forming minerals using nanoindentation. Int J Min Sci Technol 32:283–294. https://doi.org/10.1016/j.ijmst.2021.11.010
Maio DD, Roberts SG (2005) Measuring fracture toughness of coatings using focused-ion-beam-machined microbeams. J Mater Res 20:299–302. https://doi.org/10.1557/JMR.2005.0048
Manjunath GL, Jha B (2019) Nanoscale fracture mechanics of Gondwana coal. Int J Coal Geol 204:102–112. https://doi.org/10.1016/j.coal.2019.02.007
Marrow TJ, Šulak I, Li B-S, Vukšić M, Williamson M, Armstrong DEJ (2022) High temperature spherical nano-indentation of graphite crystals. Carbon 191:236–242. https://doi.org/10.1016/j.carbon.2022.01.067
Masuda T, Hiraga T, Ikei H, Kanda H, Kugimiya Y, Akizuki M (2000) Plastic deformation of quartz at room temperature: A Vickers nano-indentation test. Geophys Res Lett 27:2773–2776. https://doi.org/10.1029/1999GL008460
Mata M, Alcalá J (2003) Mechanical property evaluation through sharp indentations in elastoplastic and fully plastic contact regimes. J Mater Res 18:1705–1709. https://doi.org/10.1557/JMR.2003.0234
Mata M, Anglada M, Alcalá J (2002) Contact deformation regimes around sharp indentations and the concept of the characteristic strain. J Mater Res 17:964–976. https://doi.org/10.1557/JMR.2002.0144
Mei S, Suzuki AM, Kohlstedt DL, Dixon NA, Durham WB (2010) Experimental constraints on the strength of the lithospheric mantle. J Geophys Res Solid Earth. https://doi.org/10.1029/2009JB006873
Menčík J, He LH, Swain MV (2009) Determination of viscoelastic–plastic material parameters of biomaterials by instrumented indentation. J Mech Behav Biomed Mater 2:318–325. https://doi.org/10.1016/j.jmbbm.2008.09.002
Mikowski A, Soares P, Wypych F, Lepienski CM (2008) Fracture toughness, hardness, and elastic modulus of kyanite investigated by a depth-sensing indentation technique. Am Mineral 93:844–852. https://doi.org/10.2138/am.2008.2694
Minor AM, Lilleodden ET, Stach EA, Morris JW (2002) In-situ transmission electron microscopy study of the nanoindentation behavior of Al. J Electron Mater 31:958–964. https://doi.org/10.1007/s11664-002-0028-4
Minor AM, Lilleodden ET, Stach EA, Morris JW (2004) Direct observations of incipient plasticity during nanoindentation of Al. J Mater Res 19:176–182. https://doi.org/10.1557/jmr.2004.19.1.176
Moser B, Kuebler J, Meinhard H, Muster W, Michler J (2005) Observation of instabilities during plastic deformation by in-situ SEM indentation experiments. Adv Eng Mater 7:388–392. https://doi.org/10.1002/adem.200500049
Moser B, Löffler JF, Michler J (2006) Discrete deformation in amorphous metals: an in situ SEM indentation study. Philos Mag 86:5715–5728. https://doi.org/10.1080/14786430600627301
Mott BW (1956) Micro-indentation hardness testing. Butterworths Scientific Publications, London p. 272
Mukherjee AL (1964) Mineragraphic studies of disseminated bodies of magnetite in granite-pegmatite at Nawadiha in Hazaribagh district. Bihar Proc Indian Acad Sci 60:341–346. https://doi.org/10.1007/BF03053891
Mukhopadhyay NK (2005) Analysis of microhardness data using the normalized power law equation and energy balance model. J Mater Sci 40:241–244
Mukhopadhyay NK, Paufler P (2006) Micro- and nanoindentation techniques for mechanical characterisation of materials. Int Mater Rev 51:209–245. https://doi.org/10.1179/174328006X102475
Nadeau JS (1970) Influence of hydrogen and alkali impurities on the high-temperature indentation hardness of natural quartz crystals. J Am Ceram Soc 53:568–570. https://doi.org/10.1111/j.1151-2916.1970.tb15968.x
Newey D, Wilkins MA, Pollock HM (1982) An ultra-low-load penetration hardness tester. J Phys E 15:119. https://doi.org/10.1088/0022-3735/15/1/023
Nili H, Kalantar-zadeh K, Bhaskaran M, Sriram S (2013) In situ nanoindentation: probing nanoscale multifunctionality. Prog Mater Sci 58:1–29. https://doi.org/10.1016/j.pmatsci.2012.08.001
Nix WD, Gao H (1998) Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids 46:411–425. https://doi.org/10.1016/S0022-5096(97)00086-0
Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–1583. https://doi.org/10.1557/JMR.1992.1564
Oliver WC, Pharr GM (2004) Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J Mater Res 19:3–20. https://doi.org/10.1557/jmr.2004.19.1.3
Orowan E (1940) Problems of plastic gliding. Proc Phys Soc 52:8–22. https://doi.org/10.1088/0959-5309/52/1/303
Orzol, J., Stoeckhert, B., Rummel, F., 2002. An Experimental Study of the Rheology of Jadeite 2002, MR51A-11.
Ouchterlony F (1976) Stress intensity factors for the expansion loaded star crack. Eng Fract Mech 8:447–448
Parks GA (1984) Surface and interfacial free energies of quartz. J Geophys Res Solid Earth 89:3997–4008. https://doi.org/10.1029/JB089iB06p03997
Pathak S, Kalidindi SR (2015) Spherical nanoindentation stress–strain curves. Mater Sci Eng R Rep 91:1–36. https://doi.org/10.1016/j.mser.2015.02.001
Pethica, J.B., Oliver, W.C., 1988. Mechanical Properties of Nanometre Volumes of Material: use of the Elastic Response of Small Area Indentations. MRS Online Proc. Libr. OPL 130. https://doi.org/10.1557/PROC-130-13
Pethica JB, Tabor D (1979) Contact of characterised metal surfaces at very low loads: deformation and adhesion. Surf Sci 89:182–190. https://doi.org/10.1016/0039-6028(79)90606-X
Pethicai JB, Hutchings R, Oliver WC (1983) Hardness measurement at penetration depths as small as 20 nm. Philos Mag A. https://doi.org/10.1080/01418618308234914
Pharr GM, Herbert EG, Gao Y (2010) The indentation size effect: a critical examination of experimental observations and mechanistic interpretations. Annu Rev Mater Res 40:271–292. https://doi.org/10.1146/annurev-matsci-070909-104456
Prandtl, L., 1920. Goettinger Nachr. Math. Phys Kl 74.
Quinn JB, Quinn GD (1997) Indentation brittleness of ceramics: a fresh approach. J Mater Sci 32:4331–4346. https://doi.org/10.1023/A:1018671823059
Rabe R, Breguet J-M, Schwaller P, Stauss S, Haug F-J, Patscheider J, Michler J (2004) Observation of fracture and plastic deformation during indentation and scratching inside the scanning electron microscope. Thin Solid Films 469–470:206–213. https://doi.org/10.1016/j.tsf.2004.08.096
Raterron P, Wu Y, Weidner DJ, Chen J (2004) Low-temperature olivine rheology at high pressure. Phys Earth Planet Inter 145:149–159. https://doi.org/10.1016/j.pepi.2004.03.007
Rockwell SP (1922) The testing of metals for hardness. Trans Am Soc Steel Treat 2:1013–1033
Rzepiejewska-Malyska KA, Buerki G, Michler J, Major RC, Cyrankowski E, Asif SAS, Warren OL (2008) In situ mechanical observations during nanoindentation inside a high-resolution scanning electron microscope. J Mater Res 23:1973–1979. https://doi.org/10.1557/JMR.2008.0240
Rzepiejewska-Malyska K, Parlinska-Wojtan M, Wasmer K, Hejduk K, Michler J (2009) In-situ SEM indentation studies of the deformation mechanisms in TiN, CrN and TiN/CrN. Micron 40:22–27. https://doi.org/10.1016/j.micron.2008.02.013
Sakai M, Muto H (1998) A novel deformation process in an aggregate: a candidate for superplastic deformation. Scr Mater 38:909–915. https://doi.org/10.1016/S1359-6462(97)00568-X
Sangwal K (2000) On the reverse indentation size effect and microhardness measurement of solids. Mater Chem Phys 63:145–152. https://doi.org/10.1016/S0254-0584(99)00216-3
Sangwal K (2009) Review: Indentation size effect, indentation cracks and microhardness measurement of brittle crystalline solids – some basic concepts and trends. Cryst Res Technol 44:1019–1037. https://doi.org/10.1002/crat.200900385
Sebastiani M, Johanns KE, Herbert EG, Carassiti F, Pharr GM (2015a) A novel pillar indentation splitting test for measuring fracture toughness of thin ceramic coatings. Philos Mag 95:1928–1944. https://doi.org/10.1080/14786435.2014.913110
Sebastiani M, Johanns KE, Herbert EG, Pharr GM (2015b) Measurement of fracture toughness by nanoindentation methods: Recent advances and future challenges. Curr. Opin. Solid State Mater. Sci Recent Adv Nanoindentation 19:324–333. https://doi.org/10.1016/j.cossms.2015.04.003
Sharma P, Prakash R, Abedi S (2019) Effect of temperature on nano- and microscale creep properties of organic-rich shales. J Pet Sci Eng 175:375–388. https://doi.org/10.1016/j.petrol.2018.12.039
Shaw MC, DeSalvo GJ (2012) The role of elasticity in hardness testing. Metallogr Microstruct Anal 1:310–317. https://doi.org/10.1007/s13632-012-0047-3
Shi X, He Z, Long S, Peng Y, Li D, Jiang S (2019) Loading rate effect on the mechanical behavior of brittle longmaxi shale in nanoindentation. Int J Hydrog Energy 44:6481–6490. https://doi.org/10.1016/j.ijhydene.2019.01.028
Shi X, Jiang S, Yang L, Tang M, Xiao D (2020) Modeling the viscoelasticity of shale by nanoindentation creep tests. Int J Rock Mech Min Sci 127:104210. https://doi.org/10.1016/j.ijrmms.2020.104210
Shubnikov AV, Tsinzerling EV (1932) Impact and pressure figures, and mechanical twins in quartz. Z Krist Krist Krist Krist 83:243–264
Shuman DJ, Costa ALM, Andrade MS (2007) Calculating the elastic modulus from nanoindentation and microindentation reload curves. Mater Charact 58:380–389. https://doi.org/10.1016/j.matchar.2006.06.005
Sly MK, Thind AS, Mishra R, Flores KM, Skemer P (2020) Low-temperature rheology of calcite. Geophys J Int 221:129–141. https://doi.org/10.1093/gji/ggz577
Smith RL, Sandland GE (1925) Some notes on the use of a diamond pyramid for hardness testing. J Iron Steel Inst 111:285–304
Sobhbidari F, Hu Q (2021) Recent advances in the mechanical characterization of shales at nano-to micro-scales: a review. Mech Mater 162:104043. https://doi.org/10.1016/j.mechmat.2021.104043
Stöckhert B, Renner J (1998) Rheology of crustal rocks at ultrahigh pressure. In: Hacker BR, Liou JG (eds) When continents collide: geodynamics and geochemistry of ultrahigh-pressure rocks, petrology and structural geology. Springer Netherlands, Dordrecht, pp 57–95. https://doi.org/10.1007/978-94-015-9050-1_3
Strozewski B, Sly MK, Flores KM, Skemer P (2021) Viscoplastic rheology of α-Quartz investigated by nanoindentation. J Geophys Res Solid Earth. https://doi.org/10.1029/2021JB022229
Su C, Herbert EG, Sohn S, LaManna JA, Oliver WC, Pharr GM (2013) Measurement of power-law creep parameters by instrumented indentation methods. J Mech Phys Solids 61:517–536. https://doi.org/10.1016/j.jmps.2012.09.009
Sun C, Li G, Gomah ME, Xu J, Rong H (2021) Experimental investigation on the nanoindentation viscoelastic constitutive model of quartz and kaolinite in mudstone. Int J Coal Sci Technol 8:925–937. https://doi.org/10.1007/s40789-020-00393-2
Swain MV, Atkinson BK (1978) Fracture surface energy of olivine. Pure Appl Geophys 116:866–872. https://doi.org/10.1007/BF00876542
Swain MV, Hagan JT (1976) Indentation plasticity and the ensuing fracture of glass. J Phys Appl Phys 9:2201–2214. https://doi.org/10.1088/0022-3727/9/15/011
Swain MV, Lawn BR (1976) Indentation fracture in brittle rocks and glasses. Int J Rock Mech Min Sci Geomech Abstr 13:311–319. https://doi.org/10.1016/0148-9062(76)91830-1
Syed Asif SA, Pethica JB (1997) Nanoindentation creep of single-crystal tungsten and gallium arsenide. Philos Mag A 76:1105–1118. https://doi.org/10.1080/01418619708214217
Tabor D (1970) The hardness of solids. Rev Phys Technol 1:145–179. https://doi.org/10.1088/0034-6683/1/3/I01
Ternovskij AP, Alechin VP, Shorshorov MC, Khrushchov MM, Skvorcov VN (1973) O Mikromechaniceskich Ispytanijach Materialov Putjom Vdavlivanija [About Micromechanical Material Tests by Indentation]. Zavod Lab 39:1242–1247
Thom C, Goldsby D (2019) Nanoindentation studies of plasticity and dislocation creep in halite. Geosciences 9:79. https://doi.org/10.3390/geosciences9020079
Thom CA, Carpick RW, Goldsby DL (2018) Constraints on the physical mechanism of frictional aging from nanoindentation. Geophys Res Lett 45:13306–13311. https://doi.org/10.1029/2018GL080561
Tsenn MC, Carter NL (1987) Upper limits of power law creep of rocks. Tectonophysics 136:1–26. https://doi.org/10.1016/0040-1951(87)90332-5
Turley DM, Samuels LE (1981) The nature of mechanically polished surfaces of copper. Metallography 14:275–294. https://doi.org/10.1016/0026-0800(81)90001-X
Vaidya A, Pathak K (2019) 17–Mechanical stability of dental materials. In: Asiri AM, Inamuddin MA (eds) Applications of nanocomposite materials in dentistry. Elsevier, Amsterdam, pp 285–305. https://doi.org/10.1016/B978-0-12-813742-0.00017-1. ISBN 9780128137420
Vernik L, Liu X (1997) Velocity anisotropy in shales: a petrophysical study. Geophysics 62:521–532. https://doi.org/10.1190/1.1444162
Viktorov SD, Golovin YuI, Kochanov AN, Tyurin AI, Shuklinov AV, Shuvarin IA, Pirozhkova TS (2014) Micro- and nano-indentation approach to strength and deformation characteristics of minerals. J Min Sci 50:652–659. https://doi.org/10.1134/S1062739114040048
Wallis D, Hansen LN, Kumamoto KM, Thom CA, Plümper O, Ohl M, Durham WB, Goldsby DL, Armstrong DEJ, Meyers CD, Goddard RM, Warren JM, Breithaupt T, Drury MR, Wilkinson AJ (2020) Dislocation interactions during low-temperature plasticity of olivine and their impact on the evolution of lithospheric strength. Earth Planet Sci Lett 543:116349. https://doi.org/10.1016/j.epsl.2020.116349
Wang Z, Wang H, Cates ME (2001) Effective elastic properties of solid clays. Geophysics 66:428–440. https://doi.org/10.1190/1.1444934
Wang J, Liu Y, Yang C, Jiang W, Li Y, Xiong Y (2022) Modeling the viscoelastic behavior of Quartz and clay minerals in shale by nanoindentation creep tests. Geofluids 2022:1–16. https://doi.org/10.1155/2022/2860077
Weaver JS, Khosravani A, Castillo A, Kalidindi SR (2016) High throughput exploration of process-property linkages in Al-6061 using instrumented spherical microindentation and microstructurally graded samples. Integr Mater Manuf Innov 5:192–211. https://doi.org/10.1186/s40192-016-0054-3
Westbrook JH (1958) Temperature dependence of strength and brittleness of some Quartz structures. J Am Ceram Soc 41:433–440. https://doi.org/10.1111/j.1151-2916.1958.tb12891.x
Whitney DL, Broz M, Cook RF (2007) Hardness, toughness, and modulus of some common metamorphic minerals. Am Mineral 92:281–288. https://doi.org/10.2138/am.2007.2212
Wu Y, Luo S, Wang D, Burns SJ, Li E, DeGroot DJ, Yu Y, Zhang G (2021) Origin, growth, and characteristics of calcareous concretions in the varved sediments of a Glacial Lake. Eng Geol 287:106112. https://doi.org/10.1016/j.enggeo.2021.106112
Yang J, Hatcherian J, Hackley PC, Pomerantz AE (2017) Nanoscale geochemical and geomechanical characterization of organic matter in shale. Nat Commun 8:2179. https://doi.org/10.1038/s41467-017-02254-0
Yin H, Zhang G (2011) Nanoindentation behavior of muscovite subjected to repeated loading. J Nanomech Micromech 1:72–83. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000033
Zelin MG, Mukherjee AK (1996) Geometrical aspects of superplastic flow. Mater Sci Eng A 208:210–225. https://doi.org/10.1016/0921-5093(95)10080-6
Zhang G, Wei Z, Ferrell R (2009) Elastic modulus and hardness of muscovite and rectorite determined by nanoindentation. Appl Clay Sci 43:271–281. https://doi.org/10.1016/j.clay.2008.08.010
Zhang G, Wei Z, Ferrell RE, Guggenheim S, Cygan RT, Luo J (2010) Evaluation of the elasticity normal to the basal plane of non-expandable 2:1 phyllosilicate minerals by nanoindentation. Am Mineral 95:863–869. https://doi.org/10.2138/am.2010.3398
Zhang J, Hu L, Pant R, Yu Y, Wei Z, Zhang G (2013) Effects of interlayer interactions on the nanoindentation behavior and hardness of 2:1 phyllosilicates. Appl Clay Sci 80–81:267–280. https://doi.org/10.1016/j.clay.2013.04.013
Acknowledgements
This manuscript benefited greatly from the editorial guardianship of Larissa Dobrzhinetskaya and enriching reviews from two anonymous reviewers. RM acknowledges a junior research fellowship from IIT Kanpur and a Prime Minister’s Research Fellowship from the Ministry of Education, Government of India. This work is a part of a Swarnajayanti Fellowship (DST/SJF/E&ASA-01/2015-16) awarded to SM by the Department of Science and Technology, Government of India.
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This work is a part of a Swarnajayanti Fellowship (DST/SJF/E&ASA-01/2015–16) awarded to SM.
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Mukherjee, R., Misra, S. Nanomechanics of minerals: understandings and developments through instrumented nanoindentation techniques. Phys Chem Minerals 50, 10 (2023). https://doi.org/10.1007/s00269-023-01235-8
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DOI: https://doi.org/10.1007/s00269-023-01235-8