Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-19T13:20:54.025Z Has data issue: false hasContentIssue false
  • English
  • Français

Mechanical Characterization of Heterogeneous Polycrystalline Rocks Using Nanoindentation Method in Combination with Generalized Means Method

Published online by Cambridge University Press:  07 May 2020

M.R. Ayatollahi ,
M. Zare Najafabadi ,
S. S. R. Koloor Open the ORCID record for S. S. R. Koloor [Opens in a new window]  and
Michal Petrů
M.R. Ayatollahi
Affiliation:
Fatigue and Fracture Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
M. Zare Najafabadi
Affiliation:
Fatigue and Fracture Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
S. S. R. Koloor*
Affiliation:
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran Institute for Nanomaterials, Advanced Technologies and Innovation, Technical University of Liberec, Liberec, Czech Republic
Michal Petrů
Affiliation:
Institute for Nanomaterials, Advanced Technologies and Innovation, Technical University of Liberec, Liberec, Czech Republic
*
*Corresponding author ([email protected])
Get access

Abstract

The mechanical characterization of rocks is important in engineering design and analysis of rock-related structures. In the current researches, rocks are classified as heterogeneous materials with anisotropic behavior, and advanced methods such as combined experimental-numerical approach are developed to characterize the behavior of rocks. In this study, the nanoindentation experiment in conjunction with the generalized means method is used to determine the Young’s modulus and hardness of eight different polycrystalline granite rocks. In the first step, the Young’s modulus and hardness of granites’ constituents are determined through nanoindentation tests on pure granite minerals. Then, the properties of granites are determined using generalized means method by considering the mechanical properties of minerals, their volume fractions and an empirical constant called the microstructural coefficient. Accurate results with less than 3% error are obtained for 62.5% of the granite samples. The generalized means is introduced as a simple and effective method to characterize the mechanical properties of heterogeneous polycrystalline rocks.

Keywords

NanoindentationGeneralized means methodHeterogeneous polycrystalline materialsGranite rocks
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 6 , December 2020 , pp. 813 - 823
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Soulié, R., Mérillou, S., Terraz, O. and Ghazanfarpour, D., “Modeling and rendering of heterogeneous granular materials: granite application,” in Computer Graphics Forum, 26, no. 1, pp. 66–79: Wiley Online Library (2007).Google Scholar
Debasis, D. and Kumar, V. A., Fundamentals and Applications of Rock Mechanics. PHI Learning, Delhi (2016).Google Scholar
Jeng, F.-S., Wang, T.-T., Li, H. and Huang, T.-H., “Influences of microscopic factors on macroscopic strength and stiffness of inter-layered rocks— revealed by a bonded particle model,” Journal of Mechanics,24, no. 4, pp. 379–389 (2008).Google Scholar
Joshani, M., R. Koloor, S. S., and Abdullah, R., “Damage Mechanics Model for Fracture Process of Steel-concrete Composite Slabs,” in Applied Mechanics and Materials, 165, pp. 339–345: Trans Tech Publ (2012).Google Scholar
Dong, G. and Chen, P., “A comparative experiment investigate of strength parameters for Longmaxi shale at the macro- and mesoscales,” International Journal of Hydrogen Energy, 42, no. 31, pp. 20082–20091, 2017/08/03/ 2017 (2017).CrossRefGoogle Scholar
Han, Q., Chen, P. and Ma, T., “Influencing factor analysis of shale micro-indentation measurement,” Journal of Natural Gas Science and Engineering, 27, pp. 641–650 (2015).CrossRefGoogle Scholar
Ping, C., Qiang, H., Tianshou, M. and Dong, L., “The mechanical properties of shale based on microindentation test,” Petroleum exploration and development, 42, no. 5, pp. 723–732 (2015).Google Scholar
Barla, G., “Rock anisotropy: theory and laboratory testing,” Rock mechanics, pp. 131–169 (1974).Google Scholar
Zeng, Q.-D., Yao, J. and Shao, J., “Numerical study of hydraulic fracture propagation accounting for rock anisotropy,” Journal of Petroleum Science and Engineering, 160, pp. 422–432, 2018/01/01/ 2018 (2018).CrossRefGoogle Scholar
Chen, L., Huang, K. and Chen, Y., “Acoustic emission at wedge indentation fracture in quasi-brittle materials,” Journal of Mechanics, 25, no. 2, pp. 213–223 (2009).CrossRefGoogle Scholar
Tkalich, D., Fourmeau, M., Kane, A., Li, C. C. and Cailletaud, G., “Experimental and numerical study of Kuru granite under confined compression and indentation,” International Journal of Rock Mechanics and Mining Sciences, 87, pp. 55–68, 2016/09/01/ 2016 (2016).CrossRefGoogle Scholar
Shariati, H., Saadati, M., Bouterf, A., Weddfelt, K., Larsson, P.-L. and Hild, F., “On the inelastic mechanical behavior of granite: Study based on quasi-oedometric and indentation tests,” Rock Mechanics and Rock Engineering, 52, no. 3, pp. 645–657 (2019).Google Scholar
Luong, M.-P., and Emami, M., “Characterization of mechanical damage in granite,” Frattura ed Integrità Strutturale: Annals 2014: Fracture and Structural Integrity: Annals 2014, 8 (2014).Google Scholar
Jelagin, D., Saadati, M., Jerjen, I. and Larsson, P.-L., “Mechanical Characterization of Granite Rock Materials: On the Influence from Pre-Existing Defects,” Journal of Testing and Evaluation, 46, no. 2 (2017).CrossRefGoogle Scholar
Dong, G. and Chen, P., “A comparative experimental study of shale indentation fragmentation mechanism at the macroscale and mesoscale,” Advances in Mechanical Engineering, 9, no. 8, p. 1687814017726244 (2017).CrossRefGoogle Scholar
Sesetty, V. and Ghassemi, A., “Effect of rock anisotropy on wellbore stresses and hydraulic fracture propagation,” International Journal of Rock Mechanics and Mining Sciences, 112, pp. 369–384, 2018/12/01/ 2018 (2018).CrossRefGoogle Scholar
Celentano, D. J., Cabezas, E. E., García, C. M. and Monsalve, A. E., “Characterization of the mechanical behaviour of materials in the tensile test: experiments and simulation,” Modelling and Simulation in Materials Science and Engineering, 12, no. 4, pp. S425–S444, 2004/06/12 2004 (2004).CrossRefGoogle Scholar
Sharifi Teshnizi, S. H., R. Koloor, S. S., Sharifishourabi, G., Bin Ayob, A., and Yahya, M. Y., “Mechanical behavior of GFRP laminated composite pipe subjected to uniform radial patch load,” in Advanced Materials Research, 488-489, pp. 542–546 (2012).Google Scholar
Abdi, B., R. Koloor, S. S., Abdullah, M. R., Ayob, A. and Yahya, M. Y. B., “Effect of strain-rate on flexural behavior of composite sandwich panel,” in Applied Mechanics and Materials, 229-231, pp. 766–770 (2012).CrossRefGoogle Scholar
Ng, T. P., R. Koloor, S. S., Djuansjah, J. R. P. and Abdul Kadir, M. R., “Assessment of compressive failure process of cortical bone materials using damage-based model,” Journal of the Mechanical Behavior of Biomedical Materials, 66, pp. 1–11 (2017).CrossRefGoogle Scholar
Sharifi Teshnizi, S. H., R. Koloor, S. S., Sharifishourabi, G., Ayob, A. and Yahya, M. Y., “Effect of ply thickness on displacements and stresses in laminated GFRP cylinder subjected to radial load,” in Advanced Materials Research, 488-489, pp. 367–371 (2012).CrossRefGoogle Scholar
Saksala, T., Gomon, D., Hokka, M. and Kuokkala, V., “Numerical modeling and experimentation of dynamic indentation with single and triple indenters on Kuru granite,” Dynamic Web Programming and HTML5, p. 415 (2012).Google Scholar
Shi, X., Yang, H., Shao, G., Duan, X. and Xiong, Z., “Nanoindentation study of ultrafine WC-10Co cemented carbide,” Materials Characterization, 59, no. 4, pp. 374–379 (2008).CrossRefGoogle Scholar
Zhang, G., Wei, Z. and Ferrell, R. E., “Elastic modulus and hardness of muscovite and rectorite determined by nanoindentation,” Applied Clay Science, 43, no. 2, pp. 271–281 (2009).CrossRefGoogle Scholar
Zhou, X.-P., Zhang, J.-Z., Qian, Q.-H. and Niu, Y., “Experimental investigation of progressive cracking processes in granite under uniaxial loading using digital imaging and AE techniques,” Journal of Structural Geology, 126, pp. 129–145, 2019/09/01/ 2019 (2019).Google Scholar
Karimzadeh, A. and Ayatollahi, M. R., “Mechanical Properties of Biomaterials Determined by Nano-Indentation and Nano-Scratch Tests,” in Nanomechanical Analysis of High Performance Materials, A. Tiwari, Ed. Dordrecht: Springer Netherlands, pp. 189–207 (2014).CrossRefGoogle Scholar
Rahimian Koloor, S. S., Karimzadeh, A., Tamin, M. N., and Abd Shukor, M., “Effects of Sample and Indenter Configurations of Nanoindentation Experiment on the Mechanical Behavior and Properties of Ductile Materials,” Metals, 8, no. 6, p. 421 (2018).CrossRefGoogle Scholar
Perras, M. A. and Diederichs, M. S., “A Review of the Tensile Strength of Rock: Concepts and Testing,” Geotechnical and Geological Engineering, 32, no. 2, pp. 525–546, 2014/04/01 2014 (2014).CrossRefGoogle Scholar
A. C. D.-o. Soil and Rock, Standard Test Method for Compressive Strength and Elastic Moduli of Intact Rock Core Specimens Under Varying States of Stress and Temperatures. ASTM International (2010).Google Scholar
Feng, X. T., Mechanics, Rock and Engineering Volume 2: Laboratory and Testing, Field. Press, CRC (2017).Google Scholar
Ban, H., Karki, P. and Kim, Y.-R., “Nanoindentation test integrated with numerical simulation to characterize mechanical properties of rock materials,” Journal of Testing and Evaluation, 42, no. 3, pp. 787–796 (2014).CrossRefGoogle Scholar
Zhu, W., Hughes, J. J., Bicanic, N. and Pearce, C. J., “Nanoindentation mapping of mechanical properties of cement paste and natural rocks,” Materials characterization, 58, no. 11-12, pp. 1189–1198 (2007).CrossRefGoogle Scholar
Magnenet, V., Auvray, C., Francius, G. and Giraud, A., “Determination of the matrix indentation modulus of Meuse/Haute-Marne argillite,” Applied Clay Science, 52, no. 3, pp. 266–269 (2011).CrossRefGoogle Scholar
Hughes, J. J. and Trtik, P., “Micro-mechanical properties of cement paste measured by depthsensing nanoindentation: a preliminary correlation of physical properties with phase type,” Materials characterization, 53, no. 2-4, pp. 223–231 (2004).Google Scholar
Shukla, P., Kumar, V., Curtis, M., Sondergeld, C. H. and Rai, C. S., “Nanoindentation studies on shales,” in 47th US Rock Mechanics/Geomechanics Symposium, 2013: American Rock Mechanics Association (2013).Google Scholar
Ringstad, C., Lofthus, E. B., Sonstebo, E. F., Fjaer, E., Zausa, F. and Fuh, G.-F. “Prediction of rock parameters from micro-indentation measurements: the effect of sample size,” in SPE/ISRM Rock Mechanics in Petroleum Engineering, 1998: Society of Petroleum Engineers (1998).Google Scholar
R. Koloor, S. S., Abdul-Latif, A., Gong, X. and Tamin, M., “Evolution characteristics of delamination damage in CFRP composites under transverse loading,” in Damage and Fracture of Composite Materials and Structures: Springer, pp. 45–59 (2012).CrossRefGoogle Scholar
Koloor, R., S. S. and Tamin, M. N. “Mode-II interlaminar fracture and crack-jump phenomenon in CFRP composite laminate materials,” Composite Structures, 204, pp. 594–606 (2018).CrossRefGoogle Scholar
R. Koloor, S. S., Rahimian-Koloor, S. M., Karimzadeh, A., Hamdi, M., Petru, M. and Tamin, M., “Nano-level damage characterization of graphene/polymer cohesive interface under tensile separation,” Polymers, 11, no. 9, p. 1435 (2019).CrossRefGoogle Scholar
Karimzadeh, A., Ayatollahi, M. R., R. Koloor, S. S., Bushroa, A. R., Yahya, M. Y. and Tamin, M. N., “Assessment of compressive mechanical behavior of Bis-GMA polymer using hyperelastic models,” Polymers, 11, no. 10, Art. no. 1571 (2019).CrossRefGoogle Scholar
Pouya, A., Zhu, C. and Arson, C., “Self-consistent micromechanical approach for damage accommodation in rock-like polycrystalline materials,” International Journal of Damage Mechanics, 28, no. 1, pp. 134–161 (2019).CrossRefGoogle Scholar
Bennett, K. C., Berla, L. A., Nix, W. D. and Borja, R. I., “Instrumented nanoindentation and 3D mechanistic modeling of a shale at multiple scales,” Acta Geotechnica, 10, no. 1, pp. 1–14 (2015).CrossRefGoogle Scholar
Němeček, J., “Nanoindentation based analysis of heterogeneous structural materials,” Nanoindentation in Materials Science, InTech, Rijeka, pp. 89–108 (2012).Google Scholar
Ji, S., Wang, Q., Xia, B. and Marcotte, D., “Mechanical properties of multiphase materials and rocks: a phenomenological approach using generalized means,” Journal of Structural Geology, 26, no. 8, pp. 1377–1390 (2004).CrossRefGoogle Scholar
Korvin, G., “Axiomatic characterization of the general mixture rule,” Geoexploration, 19, no. 4, pp. 267–276 (1982).CrossRefGoogle Scholar
Spriggs, R., “Expression for effect of porosity on elastic modulus of polycrystalline refractory materials, particularly aluminum oxide,” Journal of the American Ceramic Society, 44, no. 12, pp. 628–629 (1961).Google Scholar
Knudsen, F., “Effect of porosity on Young’s modulus of alumina,” Journal of the American Ceramic Society, 45, no. 2, pp. 94–95 (1962).CrossRefGoogle Scholar
Braem, M., Van Doren, V., Lambrechts, P. and Vanherle, G., “Determination of Young’s modulus of dental composites: a phenomenological model,” Journal of Materials Science, 22, no. 6, pp. 2037–2042 (1987).CrossRefGoogle Scholar
Richard, T. G., “The mechanical behavior of a solid microsphere filled composite,” Journal of Composite Materials, 9, no. 2, pp. 108–113 (1975).CrossRefGoogle Scholar
Smith, J. C., “Experimental values for the elastic constants of a particulate-filled glassy polymer,” J. Res. Natl. Bur. Stand., Sect. A, 80, no. 1, pp. 45–49, (1976).CrossRefGoogle Scholar
Li, H. et al., “Identification of material properties using nanoindentation and surrogate modeling,” International Journal of Solids and Structures, 81, pp. 151–159, 2016/03/01/ 2016 (2016).CrossRefGoogle Scholar
Bor, B., Giuntini, D., Domènech, B., Swain, M. V. and Schneider, G. A., “Nanoindentation-based study of the mechanical behavior of bulk supercrystalline ceramic-organic nanocomposites,” Journal of the European Ceramic Society, 39, no. 10, pp. 3247–3256, 2019/08/01/ 2019 (2019).CrossRefGoogle Scholar
Karimzadeh, A., and Ayatollahi, M. R., “Investigation of mechanical and tribological properties of bone cement by nano-indentation and nano-scratch experiments,” Polymer Testing, 31, no. 6, pp. 828–833, 2012/09/01/ 2012 (2012). CrossRefGoogle Scholar
Karimzadeh, A., Ayatollahi, M. R. and Rahimi, A. “Computer Simulation and Experimental Analysis of Nanoindentation Technique,” in Applied Nanoindentation in Advanced Materials, A. Tiwari and S. Natarajan, Eds.: Wiley, pp. 579–600 (2017).CrossRefGoogle Scholar
Oliver, W. C. and Pharr, G. M., “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments,” Journal of materials research, 7, no. 6, pp. 1564–1583 (1992).CrossRefGoogle Scholar
Oliver, W. C. and Pharr, G. M., “Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology,” Journal of Materials Research, 19, no. 1, pp. 3–20 (2004).CrossRefGoogle Scholar
Angus, H., “The significance of hardness,” Wear, 54, no. 1, pp. 33–78 (1979).CrossRefGoogle Scholar
Goldsmith, W., Sackman, J. and Ewerts, C., “Static and dynamic fracture strength of Barre granite,” in International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 13, no. 11, pp. 303–309: Elsevier (1976).CrossRefGoogle Scholar
Duevel, B. and Haimson, B., “Mechanical characterization of pink Lac du Bonnet granite: Evidence of nonlinearity and anisotropy,” International Journal of Rock Mechanics and Mining Sciences, 34, no. 3-4, pp. 117. e1-117. e18 (1997).Google Scholar
Tugrul, A. and Zarif, I., “Correlation of mineralogical and textural characteristics with engineering properties of selected granitic rocks from Turkey,” Engineering Geology, 51, no. 4, pp. 303–317 (1999).CrossRefGoogle Scholar
Portier, S. and Vuataz, F.-D., “Modelling acid-rock interactions and mineral dissolution during RMA stimulation test performed at the Soultz-sous-Forêts EGS site, France,” in Proceedings World Geothermal Congress, 31, no. 3127, pp. 1–8: International Geothermal Association (2010).Google Scholar
Swan, G., “The mechanical properties of Stripa granite,” Lawrence Berkeley National Lab.(LBNL), Berkeley, CA (United States) (1978).Google Scholar
Vartan, Z., “Table of descriptive mineralogy,” Department of mining engineering, Amirkabir University of Technology, Tehran, Iran (2008).Google Scholar
Jiapeng, S., Cheng, L., Han, J., Ma, A. and Fang, L., “Nanoindentation Induced Deformation and Pop-in Events in a Silicon Crystal: Molecular Dynamics Simulation and Experiment,” (in eng), Scientific reports, 7, no. 1, pp. 10282–10282 (2017).CrossRefGoogle Scholar
Pathak, S., Riesterer, J. L., Kalidindi, S. R. and Michler, J., “Understanding pop-ins in spherical nanoindentation,” Applied Physics Letters, 105, no. 16, p. 161913, 2014/10/20 2014 (2014). CrossRefGoogle Scholar
Karimzadeh, A., R. Koloor, S. S., Ayatollahi, M. R., Bushroa, A. R. and Yahya, M. Y., “Assessment of Nano-Indentation Method in Mechanical Characterization of Heterogeneous Nanocomposite Materials Using Experimental and Computational Approaches,” Scientific Reports, 9, no. 1, p. 15763, 2019/10/31 2019 (2019). Google Scholar
Jee, A.-Y. and Lee, M., “Comparative analysis on the nanoindentation of polymers using atomic force microscopy,” Polymer Testing, 29, no. 1, pp. 95–99, 2010/02/01/ 2010 (2010). Google Scholar
Wang, M. and Pan, N., “Predictions of effective physical properties of complex multiphase materials,” Materials Science and Engineering: R: Reports, 63, no. 1, pp. 1–30 (2008).CrossRefGoogle Scholar
Treagus, S. H., “Modelling the bulk viscosity of two-phase mixtures in terms of clast shape,” Journal of Structural Geology, 24, no. 1, pp. 57–76 (2002).CrossRefGoogle Scholar
Wang, M. and Pan, N., “Elastic property of multiphase composites with random microstructures,” Journal of Computational Physics, 228, no. 16, pp. 5978–5988 (2009).Google Scholar
R. Koloor, S. S., Kashani, J. and Kadir, M. A., “Simulation of Brittle Damage for Fracture Process of Endodontically Treated Tooth,” in 5th Kuala Lumpur International Conference on Biomedical Engineering 2011, pp. 210–214: Springer (2011).Google Scholar
Dwivedi, R., Goel, R., Prasad, V. and Sinha, A., “Thermo-mechanical properties of Indian and other granites,” International Journal of Rock mechanics and mining Sciences, 45, no. 3, pp. 303–315 (2008).Google Scholar
Delgado, N. S., Rodríguez-Rey, A., del Rio, L. S., Sarriá, I. D., Calleja, L. and de Argandona, V. R., “The influence of rock microhardness on the sawability of Pink Porrino granite (Spain),” International Journal of Rock Mechanics and Mining Sciences, 1, no. 42, pp. 161–166 (2005).Google Scholar
Valley, B. and Evans, K. F., “Strength and elastic properties of the Soultz granite,” in Proceedings of the Annual Scientific Meeting of the Soultz Project, Soultz-sous-Forêts, France (2006).Google Scholar