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Vickers indentation tests on olivine: size effects

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Abstract

We conducted Vickers indentation tests on Fe-free (Mg2SiO4) and Fe-bearing (Mg1.8Fe0.2SiO4) olivine single crystals and high-density polycrystalline material with average grain sizes ranging from 170 to 890 nm. The Vickers microhardness (\(H_{{\text{v}}}\)) of the Fe-free polycrystalline material with the finest grain size is ~ 17 GPa at a load of 0.1 N, while that of the Fe-bearing single crystal is ~ 8 GPa at the largest load applied. Overall, \(H_{{\text{v}}}\) decreases with increasing grain size, load (indentation depth), and the presence of Fe. For each grain size, \(H_{{\text{v}}}\) is well characterized by a power law of the form \(H_{{\text{v}}} /H_{{\text{v}}}^{0} \propto l^{ - x}\), where \(H_{{\text{v}}}^{0}\) is the depth-independent value of \(H_{{\text{v}}}\), \(l\) represents either grain size or indentation depth, and x is 0.09. Despite the small exponent value for each size effect, the nonlinear interaction of the two size effects results in large variations of \(H_{{\text{v}}}\) in our samples. We show that our semi-empirically derived relationship as a function of grain size and indentation depth explains the \(H_{{\text{v}}}\) of both polycrystalline and single-crystal olivine at any indentation conditions. Indentation fracture toughness of the finest-grained material is 0.8 \({\text{MPa}}\;{\text{m}}^{1/2}\), which increases slightly to 1.1 \({\text{MPa}}\;{\text{m}}^{1/2}\) with increasing grain size, while the toughness of the single crystals varies from 0.5 to 0.8 \({\text{MPa}}\;{\text{m}}^{1/2}\) depending on the crystallographic orientation of the fracture planes.

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References

  1. Al-Rub RKA (2007) Prediction of micro and nanoindentation size effect from conical or pyramidal indentation. Mech Mater 39(8):787–802

  2. 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(9):533–538

  3. Atkinson BK (1984) Subcritical crack growth in geological materials. J Geophys Res Solid Earth 89(B6):4077–4114

  4. Becher PF (1974) Surface hardening of sapphire and rutile associated with machining. J Am Ceram Soc 57(2):107–108

  5. Cook RF, Pharr GM (1990) Direct observation and analysis of indentation cracking in glasses and ceramics. J Am Ceram Soc 73(4):787–817

  6. Cooper RF (1990) Differential stress-induced melt migration: an experimental approach. J Geophys Res Solid Earth 95(B5):6979–6992

  7. Darot M, Gueguen Y, Benchemam Z, Gaboriaud R (1985) Ductile-brittle transition investigated by micro-indentation: results for quartz and olivine. Phys Earth Planet Int 40(3):180–186

  8. De Guzman MS, Neubauer G, Flinn P, Nix WD (1993) The role of indentation depth on the measured hardness of materials. MRS Online Proc Libr Arch 308:613–618

  9. deMartin B, Hirth G, Evans B (2004) Experimental constraints on thermal cracking of peridotite at oceanic spreading centers. Wash DC Am Geophys Union Geophys Monogr Ser 148:167–185

  10. 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(3–4):199–211

  11. Dunstan DJ, Bushby AJ (2014) Grain size dependence of the strength of metals: the Hall–Petch effect does not scale as the inverse square root of grain size. Int J Plast 53:56–65

  12. Elmustafa AA, Stone DS (2002) Indentation size effect in polycrystalline FCC metals. Acta Mater 50(14):3641–3650

  13. Evans AG (1978) Microfracture from thermal expansion anisotropy I single phase systems. Acta Metall 26(12):1845–1853

  14. Evans AG, Charles EA (1976) Fracture toughness determinations by indentation. J Am Ceram Soc 59(7–8):371–372

  15. 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(B10):5505–5524

  16. Fathi MH, Kharaziha M (2009) Two-step sintering of dense, nanostructural forsterite. Mater Lett 63(17):1455–1458

  17. Fei H, Koizumi S, Sakamoto N, Hashiguchi M, Yurimoto H, Marquardt K, Miyajima N, Yamazaki D, Katsura T (2016) New constraints on upper mantle creep mechanism inferred from silicon grain-boundary diffusion rates. Earth Planet Sci Lett 433:350–359

  18. Guignard J, Bystricky M, Béjina F (2011) Dense fine-grained aggregates prepared by spark plasma sintering (SPS), an original technique in experimental petrology. Eur J Mineral 23(3):323–331

  19. Hall EO (1951) The deformation and ageing of mild steel: III discussion of results. Proc Phys Soc Sect B 64(9):747

  20. Hansen LN, Kumamoto KM, Thom CA, Wallis D, Durham 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

  21. Hassanzadeh-Tabrizi SA (2017) Spark plasma sintering of forsterite nanopowder and mechanical properties of sintered materials. Ceram Int 43(17):15714–15718

  22. Jung BB, Lee HK, Park HC (2013) Effect of grain size on the indentation hardness for polycrystalline materials by the modified strain gradient theory. Int J Solids Struct 50(18):2719–2724

  23. Kharaziha M, Fathi MH (2010) Improvement of mechanical properties and biocompatibility of forsterite bioceramic addressed to bone tissue engineering materials. J Mech Behav Biomed Mater 3(7):530–537

  24. Koizumi S, Hiraga T, Tachibana C, Tasaka M, Miyazaki T, Kobayashi T, Takamasa A, Ohashi N, Sano S (2010) Synthesis of highly dense and fine-grained aggregates of mantle composites by vacuum sintering of nano-sized mineral powders. Phys Chem Miner 37(8):505–518

  25. Koizumi S, Suzuki TS, Sakka Y, Yabe K, Hiraga T (2016) Synthesis of crystallographically oriented olivine aggregates using colloidal processing in a strong magnetic field. Phys Chem Miner 43(10):689–706

  26. Kranjc K, Rouse Z, Flores KM, Skemer P (2016) Low-temperature plastic rheology of olivine determined by nanoindentation. Geophys Res Lett 43(1):176–184

  27. Krell A (1998) A new look at the influences of load, grain size and grain boundaries on the room temperature hardness of ceramics. Int J Refract Metal Hard Mater 16(4–6):331–335

  28. Kumamoto KM, Thom CA, Wallis D, Hansen LN, Armstrong DE, 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(9):e1701338

  29. Kumazawa M, Anderson OL (1969) Elastic moduli, pressure derivatives, and temperature derivatives of single-crystal olivine and single-crystal forsterite. J Geophys Res 74(25):5961–5972

  30. Li Z, Ghosh A, Kobayashi AS, Bradt RC (1989) Indentation fracture toughness of sintered silicon carbide in the Palmqvist crack regime. J Am Ceram Soc 72(6):904–911

  31. 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(5):1028–1032

  32. Li Y, Bushby AJ, Dunstan DJ (2016) The Hall–Petch effect as a manifestation of the general size effect. Proc R Soc A Math Phys Eng Sci 472(2190):20150890

  33. Manika I, Maniks J (2006) Size effects in micro-and nanoscale indentation. Acta Mater 54(8):2049–2056

  34. Maruyama G, Hiraga T (2017) Grain-to multiple-grain-scale deformation processes during diffusion creep of forsterite + diopside aggregate: 1. Direct observations. J Geophys Res Solid Earth 122(8):5890–5915

  35. McElhaney KW, Vlassak JJ, Nix WD (1998) Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. J Mater Res 13(5):1300–1306

  36. Miyoshi T, Sagawa N, Sasa T (1985) Study of evaluation for fracture toughness of structural ceramics. J Jpn Soc Mech Eng A 51:2489–2497 (in Japanese)

  37. Niihara K (1983) A fracture mechanics analysis of indentation-induced Palmqvist crack in ceramics. J Mater Sci Lett 2(5):221–223

  38. Niihara K, Morena R, Hasselman DPH (1982) Evaluation of K IC of brittle solids by the indentation method with low crack-to-indent ratios. J Mater Sci Lett 1(1):13–16

  39. Nix WD, Gao H (1998) Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids 46(3):411–425

  40. Petch NJ (1953) The cleavage strength of polycrystals. J Iron Steel Inst 174:25–28

  41. 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

  42. Ponton CB, Rawlings RD (1989) Vickers indentation fracture toughness test Part 1 Review of literature and formulation of standardised indentation toughness equations. Mater Sci Technol 5(9):865–872

  43. Swain MV, Atkinson BK (1978) Fracture surface energy of olivine. Pure Appl Geophys 116(4–5):866–872

  44. Townsend D, Field JE (1990) Fracture toughness and hardness of zinc sulphide as a function of grain size. J Mater Sci 25(2):1347–1352

  45. Watson GW, Oliver PM, Parker SC (1997) Computer simulation of the structure and stability of forsterite surfaces. Phys Chem Miner 25(1):70–78

  46. Watts AB, Zhong S (2000) Observations of flexure and the rheology of oceanic lithosphere. Geophys J Int 142(3):855–875

  47. Webb SL (1989) The elasticity of the upper mantle orthosilicates olivine and garnet to 3 GPa. Phys Chem Miner 16(7):684–692

  48. White SH, Burrows SE, Carreras J, Shaw ND, Humphreys FJ (1980) On mylonites in ductile shear zones. J Struct Geol 2(1–2):175–187

  49. Whitney DL, Broz M, Cook RF (2007) Hardness, toughness, and modulus of some common metamorphic minerals. Am Miner 92(2–3):281–288

  50. Yang B, Vehoff H (2007) Dependence of nanohardness upon indentation size and grain size–a local examination of the interaction between dislocations and grain boundaries. Acta Mater 55(3):849–856

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Acknowledgements

We thank S. Ohtsuka, M. Uchida, N. Hokanishi, A. Takeuchi, and A. Yasuda for their technical assistance. The manuscript was significantly improved by insightful comments from C.A. Thom and an anonymous reviewer. A portion of this work was conducted at the Center for Nano Lithography & Analysis of the University of Tokyo, supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. This study was supported by the JSPS through Grant-in-Aid for Scientific Research 18H03734, 15H05827, Earthquake Research Institute's cooperative research program to T. H. and by the Sasakawa Scientific Research Grant 29-602 and by the JSPS through Grant-in-Aid for Scientific Research 18K03799 to S. K.

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Correspondence to Takehiko Hiraga.

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Koizumi, S., Hiraga, T. & Suzuki, T.S. Vickers indentation tests on olivine: size effects. Phys Chem Minerals 47, 8 (2020). https://doi.org/10.1007/s00269-019-01075-5

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Keywords

  • Olivine
  • Hardness
  • Fracture toughness
  • Indentation size effect
  • Grain-size effect