Skip to main content
SpringerLink
Log in

An Insight into the Mechanical and Fracture Characterization of Minerals and Mineral Interfaces in Granite Using Nanoindentation and Micro X-Ray Computed Tomography

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

It is extremely important to investigate the mechanical properties and failure characteristics of granite at the mesoscale to understand the mesoscopic evolution mechanism of the time-dependent fracture of deep-buried hard rocks. This study explores the mesoscopic mechanical properties (i.e., hardness, Young’s modulus, and fracture toughness) of the primary granite minerals and their interfaces using nanoindentation. Micro X-ray computed tomography was used to analyze the fracture characteristics of the failed Brazilian disc of granite. Moreover, two homogenization upscaling methods were used to calculate granite’s Young’s modulus and compared with that from uniaxial compression test results. The results demonstrate the following: (1) The mechanical properties of granite minerals are related to the peak load of nanoindentation. Young’s modulus and hardness of quartz, K-feldspar, and plagioclase decrease with an increase in the peak load and tend to be stable when the peak load reaches 5000 μN, whereas Young’s modulus and hardness of biotite at multiple peak loads are in variability and irregularity. (2) Young’s modulus and hardness of quartz–plagioclase and quartz–biotite interfaces are between quartz and plagioclase and quartz and biotite, respectively. Furthermore, a linear formula is proposed to estimate fracture toughness based on Young’s modulus of granite minerals. (3) The generalized means method that predicts granite’s Young’s modulus is more accurate compared to the Mori–Tanaka method. (4) Under Brazilian splitting conditions, ~ 84% of tensile cracks along intragranular cracks primarily occur in feldspar minerals, while ~ 16% along grain boundaries occur at feldspar–biotite interfaces.

Highlights

  • Mesomechanical properties of granite minerals and mineral interfaces.

  • A linear relationship between the fracture toughness and Young’s modulus.

  • Homogenization methods used for upscaling the mesoscopic Young’s modulus of granite.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Data Availability

Datasets related to this article are available from the corresponding author (dpxu@whrsm.ac.cn).

Abbreviations

\(A_{{\text{c}}}\) :

Contact area of the indenter on the sample surface

\(A_{\max }\) :

Maximum contact area of the indenter on the sample surface

\(E\) and \(E_{{\text{r}}}\) :

Young’s modulus and reduced modulus of the sample

\(E_{\hom }\) :

Homogenization Young’s modulus of granite

\(E_{{\text{i}}}\) :

Young’s modulus of the indenter

\(E_{{\text{u}}}\) :

Young’s modulus of the weakest mineral

\(E_{{\text{w}}}\) :

Uniaxial compressive modulus of granite

\(f_{{\text{i}}}\) :

Volume fraction of minerals

\(G_{{\text{c}}}\) :

Critical energy release rate

\(G_{\hom }\) :

Shear modulus of granite

\(H\) :

Hardness of the sample

\(h\) :

Indentation depth of the sample

\(h\), \(h_{{\text{c}}}\), \(h_{{\text{f}}}\), and \(h_{{\text{m}}}\) :

Indentation depth, contact depth, residual depth, and maximum indentation depth

\(J\) :

Scaling parameter

\(K_{\hom }\) :

Bulk modulus of granite

\(K_{{{\text{{\rm I}C}}}}\) :

Tensile (mode I) fracture toughness

\(k_{{\text{s}}}\) and \(k_{{{\text{low}}}}\) :

Bulk moduli of the biotite and biotite porous matrix

\(l\) :

Crack length

\(M\) :

Specific mechanical property

\(P\) :

Applied loading force of the indenter

\(P_{\max }\) :

Peak force of the indenter

\(S\) :

Contact stiffness of the sample

\(U_{{{\text{crack}}}}\), \(U_{{{\text{pp}}}}\), \(U_{{{\text{ir}}}}\), \(U_{{\text{t}}}\), and \(U_{{\text{e}}}\) :

Fracture energy, pure plasticity energy, irreversible energy, total energy, and recoverable elastic energy

\(V\) :

Volume fraction of the weakest mineral

\(\alpha\) and \(\beta\) :

Power law fitting constants

\(\gamma_{{\text{p}}}\) :

Plastic energy

\(\omega\) :

Porosity of the biotite pore matrix

\(\varepsilon\) :

A constant that depends on the indenter tip

\(\mu_{{\text{s}}}\) and \(\mu_{{{\text{low}}}}\) :

Shear moduli of the biotite and biotite porous matrix

\(\nu\) and \(\nu_{{\text{i}}}\) :

Poisson’s ratios of the sample and indenter

\(\sigma_{{\text{f}}}\) :

Critical fracture stress

\(E_{{\text{m}}}\), \(c\) and \(\varphi\) :

Young’s modulus, cohesion, and internal friction angle of minerals and mineral interfaces

References

  • Akono AT, Kabir P, Shi ZF et al (2019) Modeling CO2–induced alterations in Mt. Simon sandstone via nanomechanics. Rock Mech Rock Eng 52:1353–1375

    Google Scholar 

  • Ayatollahi MR, Najafabadi MZ, Koloor SSR et al (2020) Mechanical characterization of heterogeneous polycrystalline rocks using nanoindentation method in combination with generalized means method. J Mech 36:813–823

    Google Scholar 

  • Blake OO, Faulkner DR, Tatham DJ (2019) The role of fractures, effective pressure and loading on the difference between the static and dynamic Poisson’s ratio and Young’s modulus of Westerly granite. Int J Rock Mech Min Sci 116:87–98

    Google Scholar 

  • Chen X, Ogasawara N, Zhao MH et al (2007) On the uniqueness of measuring elastoplastic properties from indentation: the indistinguishable mystical materials. J Mech Phys Solids 55(8):1618–1660

    Google Scholar 

  • Chen Y, Hou YQ, Ji XP et al (2021) Characterization of surface mechanical properties of various aggregates from micro scale using AFM. Constr Build Mater 286:122847

    Google Scholar 

  • Cheng YT, Li ZY, Cheng CM (2002) Scaling relationships for indentation measurements. Philos Mag A 82:1821–1829

    Google Scholar 

  • Constantinides G, Chandran R-KS, Ulm FJ et al (2006) Grid indentation analysis of composite microstructure and mechanics: principles and validation. Mater Sci Eng A 430:189–202

    Google Scholar 

  • Domnich V, Gogotsi Y, Dub S (2000) Effect of phase transformations on the shape of the unloading curve in the nanoindentation of silicon. Appl Phys Lett 76:2214–2216

    Google Scholar 

  • Du JT, Whittle A-J, Hu LM et al (2021) Characterization of meso–scale mechanical properties of Longmaxi shale using grid microindentation experiments. J Rock Mech Geotech Eng 13:555–567

    Google Scholar 

  • Duevel B, Haimson B (1997) Mechanical characterization of pink Lac du Bonnet granite: evidence of nonlinearity and anisotropy. Int J Rock Mech Min Sci 34:543–543

    Google Scholar 

  • Eliyahu M, Emmanuel S, Ruarri J et al (2015) Mechanical properties of organic matter in shales mapped at the nanometer scale. Mar Pet Geol 59:294–304

    Google Scholar 

  • Fujii Y, Takemura T, Takahashi M et al (2007) Surface features of uniaxial tensile fractures and their relation to rock anisotropy in Inada granite. Int J Rock Mech Min Sci 44:98–107

    Google Scholar 

  • Goldsmith W, Sackman J-L, Ewerts C (1976) Static and dynamic fracture strength of Barre granite. Int J Rock Mech Min Sci 13:303–309

    Google Scholar 

  • Guéry AAC, Cormery F, Shao JF, Kondo D (2010) A comparative micromechanical analysis of the effective properties of a geomaterial: effect of mineralogical compositions. Comput Geotech 37(5):585–593

    Google Scholar 

  • Hay J (2009) Introduction to instrumented indentation testing. Exp Tech 33(6):66–72

    Google Scholar 

  • Hu CL, Li ZJ (2015) A review on the mechanical properties of cement–based materials measured by nanoindentation. Constr Build Mater 90:80–90

    Google Scholar 

  • Huang Y, Shen WQ, Shao JF et al (2014) Multi–scale modeling of time-dependent behavior of claystones with a viscoplastic compressible porous matrix. Mech Mater 79:25–34

    Google Scholar 

  • Ji SC, Wang Q, Xia B et al (2004) Mechanical properties of multiphase materials and rocks: a phenomenological approach using generalized means. J Struct Geol 26:1377–1390

    Google Scholar 

  • Jiang Q, Yang B, Yan F et al (2021) Morphological features and fractography analysis for in situ spalling in the China Jinping underground laboratory with a 2400 m burial depth. Tunn Undergr Space Technol 118:104194

    Google Scholar 

  • Juliano T, Gogotsi Y, Domnich V (2003) Effect of indentation unloading conditions on phase transformation induced events in silicon. J Mater Res 18:1192–1201

    Google Scholar 

  • Kuruppu MD, Obara Y, Ayatollahi MR et al (2014) ISRM–suggested method for determining the mode I static fracture toughness using semi–circular bend specimen. Rock Mech Rock Eng 47:267–274

    Google Scholar 

  • Lawn BR, Wilshaw TR (1975) Fracture of brittle solids. Cambridge University Press, London

    Google Scholar 

  • Li Y, Yang JH, Pan ZJ et al (2020) Nanoscale pore structure and mechanical property analysis of coal: an insight combining AFM and SEM images. Fuel 260:116352

    Google Scholar 

  • Li YC, Luo SM, Lu M et al (2021) Cross–scale characterization of sandstones via statistical nanoindentation: evaluation of data analytics and upscaling models. Int J Rock Mech Min Sci 142:104738

    Google Scholar 

  • Liu KQ, Ostadhassan M (2017) Microstructural and geomechanical analysis of Bakken shale at nanoscale. J Pet Sci Eng 153:133–144

    Google Scholar 

  • Liu KQ, Ostadhassan M, Bubach B (2016) Applications of nano–indentation methods to estimate nanoscale mechanical properties of shale reservoir rocks. J Nat Gas Sci Eng 35:1310–1319

    Google Scholar 

  • Liu L, Du GY, Li EB et al (2020) Fracture mechanical behaviors and acoustic emission characteristics of Beishan granite under CCNBD test. Chin J Rock Mech Eng 39(S2):3237–3244

    Google Scholar 

  • Luo SM, Lu YH, Wu YK et al (2020) Cross–scale characterization of the elasticity of shales: statistical nanoindentation and data analytics. J Mech Phys Solids 140:103945

    Google Scholar 

  • Luo SM, Kim DY, Wu YK et al (2021) Big data nanoindentation and analytics reveal the multi-staged, progressively-homogenized, depth-dependent upscaling of rocks’ properties. Rock Mech Rock Eng 54:1501–1532

    Google Scholar 

  • Ma ZY, Gamage RP, Zhang CP (2020) Application of nanoindentation technology in rocks: a review. Geomech Geophys Geo 6(4):1–27

    Google Scholar 

  • Ma ZY, Zhang CP, Gamage RP et al (2021) Uncovering the creep deformation mechanism of rock-forming minerals using nanoindentation. Int J Min Sci Technol 32(2):283–294

    Google Scholar 

  • Mahabadi OK (2012) Investigating the influence of micro–scale heterogeneity and microstructure on the failure and mechanical behaviour of geomaterials. Toronto University, Canada

    Google Scholar 

  • Mahabadi OK, Tatone BSA, Grasselli G (2014) Influence of microscale heterogeneity and microstructure on the tensile behavior of crystalline rocks. J Geophys Res-Solid Earth 119:5324–5341

    Google Scholar 

  • Manjunath GL, Jha B (2019) Nanoscale fracture mechanics of Gondwana coal. Int J Coal Geol 204:102–112

    Google Scholar 

  • Maruvanchery V, Kim E (2020) Mechanical characterization of thermally treated calcite–cemented sandstone using nanoindentation, scanning electron microscopy and automated mineralogy. Int J Rock Mech Min Sci 125:10415

    Google Scholar 

  • Mavko G, Mukerji T, Dvorkin J (2009) The rock physics handbook. Cambridge University Press, London

    Google Scholar 

  • Miller M, Bobko C, Vandamme M, Ulm FJ (2008) Surface roughness criteria for cement paste nanoindentation. Cem Concr Res 38:467–476

    Google Scholar 

  • Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21:571–574

    Google Scholar 

  • Nasseri MHB, Grasselli G, Mohanty B (2010) Fracture toughness and fracture roughness in anisotropic granitic rocks. Rock Mech Rock Eng 43:403–415

    Google Scholar 

  • Nasseri MHB, Rezanezhad F, Young RP (2011) Analysis of fracture damage zone in anisotropic granitic rock using 3D X-ray CT scanning techniques. Int J Fract 168:1–13

    Google Scholar 

  • 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

    Google Scholar 

  • Pöhl F (2019) Pop–in behavior and elastic–to–plastic transition of polycrystalline pure iron during sharp nanoindentation. Sci Rep 9:1564–1583

    Google Scholar 

  • Shen WQ, Kondo D, Dormieux L et al (2013) A closed–form three scale model for ductile rocks with a plastically compressible porous matrix. Mech Mater 59:73–86

    Google Scholar 

  • Shi X, Jiang S, Lu SF et al (2019) Investigation of mechanical properties of bedded shale by nanoindentation tests: a case study on Lower Silurian Longmaxi Formation of Youyang area in southeast Chongqing, China. Petrol Explor Dev 46:163–172

    Google Scholar 

  • Sobhbidari F, Hu QH (2021) Recent advances in the mechanical characterization of shales at nano-to micro-scales: a review. Mech Mater 162:104043

    Google Scholar 

  • Sun CL, Li GC, Gomah M-E et al (2020) Meso–scale mechanical properties of mudstone investigated by nanoindentation. Eng Fract Mech 238:107245

    Google Scholar 

  • Sun CL, Li GC, Xu JH et al (2021) Rheological characteristics of mineral components in sandstone based on nanoindentation. Chin J Rock Mech Eng 40(1):77–87

    Google Scholar 

  • Swan (1978) The mechanical properties of Stripa grantite. Lawrence Berkeley National Laboratory

  • Tabor D (1978) Phase transitions and indentation hardness of Ge and diamond. Nature 273:406–406

    Google Scholar 

  • Tyurin AI, Victorov SD, Kochanov AN et al (2016) Methods of micro- and nanoindentation for characterization of local physical and mechanical properties of multiphase materials. AIP Conf Proc 1783:020227

    Google Scholar 

  • Whittaker BN, Singh RN, Sun G (1992) Rock fracture mechanics: principles, design, and applications. Elsevier

    Google Scholar 

  • Wu YK, Li YC, Luo SM et al (2020) Multiscale elastic anisotropy of a shale characterized by cross-scale big data nanoindentation. Int J Rock Mech Min Sci 134:104458

    Google Scholar 

  • Xie HP, Li CB, Gao MZ et al (2021) Conceptualization and preliminary research on deep in situ rock mechanics. Chin J Rock Mech Eng 40(02):217–232

    Google Scholar 

  • Xu JJ, Tang XH, Wang ZZ et al (2020) Investigating the softening of weak interlayers during landslides using nanoindentation experiments and simulations. Eng Geol 277:105801

    Google Scholar 

  • Yang C, Xiong YQ, Wang J-F et al (2020) Mechanical characterization of shale matrix minerals using phase–positioned nanoindentation and nano–dynamic mechanical analysis. Int J Coal Geol 229:103571

    Google Scholar 

  • Yu (2001) Measuring properties of rock from the site of permanent shiplock in three Gorges project. Test Report, Yangtze River Scientific Research Institute

  • Yuan CC, Xi XK (2011) On the correlation of Young’s modulus and the fracture strength of metallic glasses. J Appl Phys 109:033515

    Google Scholar 

  • Zhang ZX (2002) An empirical relation between mode I fracture toughness and the tensile strength of rock. Int J Rock Mech Min Sci 39:401–406

    Google Scholar 

  • Zhang G, Wei Z, Ferrell RE (2009) Elastic modulus and hardness of muscovite and rectorite determined by nanoindentation. Appl Clay Sci 43:271–281

    Google Scholar 

  • Zhang F, Guo HQ, Zhao JJ et al (2017) Experimental study of micro–mechanical properties of granite. Chin J Rock Mech Eng 36:3864–3872

    Google Scholar 

  • Zhang F, Guo HQ, Hu DW et al (2018) Characterization of the mechanical properties of a claystone by nano–indentation and homogenization. Acta Geotech 13:1395–1404

    Google Scholar 

Download references

Acknowledgements

This research was funded by National Natural Science Foundation of China under Grant Nos. 51979268, 52279117, and 41877256.

Author information

Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, Hubei, China

    Xiu-yang Liu, Ding-ping Xu, Shao-jun Li, Shi-li Qiu & Quan Jiang

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Xiu-yang Liu

Authors
  1. Xiu-yang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ding-ping Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shao-jun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shi-li Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Quan Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ding-ping Xu.

Ethics declarations

Conflict of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Xy., Xu, Dp., Li, Sj. et al. An Insight into the Mechanical and Fracture Characterization of Minerals and Mineral Interfaces in Granite Using Nanoindentation and Micro X-Ray Computed Tomography. Rock Mech Rock Eng 56, 3359–3375 (2023). https://doi.org/10.1007/s00603-023-03221-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-023-03221-6

Keywords

Search

Navigation