Vickers indentation tests on olivine: size effects

  • Sanae Koizumi
  • Takehiko HiragaEmail author
  • Tohru S. Suzuki
Original Paper


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.


Olivine Hardness Fracture toughness Indentation size effect Grain-size effect 



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Earthquake Research InstituteThe University of TokyoTokyoJapan
  2. 2.National Institute for Materials ScienceTsukubaJapan

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