Microscopic time-dependent mechanical behavior of shale derived from nanoindentation

Abstract

Understanding the microscopic time-dependent mechanical behavior of shale is critical for assessing macroscopic creep and engineering applications. Grid nanoindentation experiments and nanoindentation creep tests were systematically conducted to investigate microscopic creep behaviors in shale. The indentation creep displacements and creep rates of the shale's soft, intermediate, and hard phases showed the same evolution patterns. The creep deformation was much higher in the soft phase than in the other two phases. However, the difference in the steady-state creep rates between the three mechanical phases was negligible. A linear relationship was observed between the microscopic contact creep modulus and the microscopic Young's modulus, hardness, creep displacement, and creep rate. The primary mechanism of microscopic creep in shale revealed by the creep strain rate sensitivity parameter was the extension and closure of microcracks. The differences in the microscopic creep parameters derived from the experimental data using the deconvolution methods and representative point methods were evaluated, and the applicability of the two methods was described. The performances of commonly used creep models to predict the microscopic creep behaviors were evaluated. The Burgers model provided the best performance in predicting the steady-state creep deformation and creep rate. The ability of the Mori-Tanaka and Voigt-Reuss-Hill models to derive macroscopic parameters from microscopic mechanical parameters was compared. Both methods provided macroscopic Young's modulus values close to the experimental values; however, neither could predict macroscopic creep parameters based on microscopic creep parameters.

Keywords

creep models / homogenization / microscopic creep parameters / nanoindentation creep

References

[1] Chen C, Xie H, Xu J, Peng S, Li C, Li M. Creep behavior of sandstone under the coupling action of stress and pore water pressure using three-dimensional digital image correlation. Int J Damage Mech. 2024; 33(2): 147-173.

[2] Chu Z, Wu Z, Wang Z, Weng L, Liu Q, Fan L. Micro-mechanism of brittle creep in saturated sandstone and its mechanical behavior after creep damage. Int J Rock Mech Min Sci. 2022; 149: 104994.

[3] Du J, Hu L, Meegoda JN, Zhang G. Shale softening: observations, phenomenological behavior, and mechanisms. Appl Clay Sci. 2018; 161: 290-300.

[4] Du J, Luo S, Hu L, Guo B, Guo D, Zhang G. Multiscale mechanical properties of shales: grid nanoindentation and statistical analytics. Acta Geotech. 2022; 17(2): 339-354.

[5] Fan C, Li H, Qin Q, He S, Zhong C. Geological conditions and exploration potential of shale gas reservoir in Wufeng and Longmaxi formation of southeastern Sichuan Basin, China. J Pet Sci Eng. 2020; 191: 107138.

[6] Fischer-Cripps AC. A simple phenomenological approach to nanoindentation creep. Mater Sci Eng A. 2004; 385(1/2): 74-82.

[7] Geng Z, Bonnelye A, Chen M, et al. Time and temperature dependent creep in Tournemire shale. J Geophys Res Solid Earth. 2018; 123(11): 9658-9675.

[8] Goodall R, Clyne TW. A critical appraisal of the extraction of creep parameters from nanoindentation data obtained at room temperature. Acta Mater. 2006; 54(20): 5489-5499.

[9] Guo Q, Yao Y, Hou L, Tang S, Pan S, Yang F. Oil migration, retention, and differential accumulation in “sandwiched” lacustrine shale oil systems from the Chang 7 member of the Upper Triassic Yanchang Formation, Ordos Basin, China. Int J Coal Geol. 2022; 261: 104077.

[10] Gupta N, Mishra B. Influence of stress-induced microcracks on viscoplastic creep deformation in Marcellus shale. Acta Geotech. 2021; 16(5): 1575-1595.

[11] Hill R. The elastic behaviour of a crystalline aggregate. Proc Phys Soc Sect A. 1952; 65(5): 349-354.

[12] Hu J, Xie H, Gao M, Li C, Sun Q. Damage mechanism and heat transfer characteristics of limestone after thermal shock cycle treatments based on geothermal development. Int J Rock Mech Min Sci. 2022; 160: 105269.

[13] Hu J, Xie H, Li C, Liu G. Evolution mechanism of permeability of hot dry rock under coupled effect of thermal fatigue and seawater interaction during coastal geothermal development. Renew Sustain Energy Rev. 2024; 189: 114061.

[14] Hu J, Xie H, Sun Q, Li C, Liu G. Changes in the thermodynamic properties of alkaline granite after cyclic quenching following high temperature action. Int J Min Sci Technol. 2021; 31(5): 843-852.

[15] Hu L, Wang F, Jiang F, Huang G. Study on the influence of mineral composition on the mechanical properties of granite based on FDEM-GBM method. Simul Model Pract Theory. 2023; 129: 102834.

[16] Ishibashi T, Watanabe N, Asanuma H, Tsuchiya N. Linking microearthquakes to fracture permeability change: the role of surface roughness. Geophys Res Lett. 2016; 43(14): 7486-7493.

[17] Jia L, Bai J, Zhang J. Application of nanoindentation creep tests to characterize viscoelasticity behavior of deep Longmaxi shales. IOP Conf Ser Earth Environ Sci. 2021; 861: 062067.

[18] Kong L, Xie H, Li C. Traction-based microplane model for charactering the progressive failure of rock-like material. J Mech Phys Solids. 2025; 194: 105910.

[19] Li B, Yang F, Du P, Liu Z. Study on the triaxial unloading creep mechanical properties and creep model of shale in different water content states. Bull Eng Geol Environ. 2022a; 81(10): 420.

[20] Li C, Chau VT, Xie H, Bažant ZP. Recent advances in mechanics of fracking and new results on 2D simulation of crack branching in anisotropic gas or oil shale. Acta Mech. 2018; 229: 975-992.

[21] Li C, Ostadhassan M, Kong L, Bubach B. Multi-scale assessment of mechanical properties of organic-rich shales: a coupled nanoindentation, deconvolution analysis, and homogenization method. J Petrol Sci Eng. 2019; 174: 80-91.

[22] Li C, Tu J, Xie H, Hu J. Tensile behavior and damage mechanisms of hot dry rock under thermal shock fatigue and seawater dissolution. Adv Geo-Energy Res. 2024; 13(2): 132-145.

[23] Li C, Wang J, Xie H. Anisotropic creep characteristics and mechanism of shale under elevated deviatoric stress. J Petrol Sci Eng. 2020; 185: 106670.

[24] Li Y, Chen JQ, Yang JH, Liu JS, Tong WS. Determination of shale macroscale modulus based on microscale measurement: a case study concerning multiscale mechanical characteristics. Petrol Sci. 2022b; 19(3): 1262-1275.

[25] Liu K, Jin Z, Zeng L, Ostadhassan M, Xu X. Understanding the creep behavior of shale via nano-DMA method. Energy Rep. 2021b; 7: 7478-7487.

[26] Liu K, Ostadhassan M, Bubach B. Application of nanoindentation to characterize creep behavior of oil shales. J Petrol Sci Eng. 2018; 167: 729-736.

[27] Liu K, Ostadhassan M, Zhou J, Gentzis T, Rezaee R. Nanoscale pore structure characterization of the Bakken shale in the USA. Fuel. 2017; 209: 567-578.

[28] Liu Y, Liu S, Kang Y. Probing nanomechanical properties of a shale with nanoindentation: heterogeneity and the effect of water-shale interactions. Energy Fuels. 2021a; 35(15): 11930-11946.

[29] Liu Z, Liu D, Cai Y, Yao Y, Pan Z, Zhou Y. Application of nuclear magnetic resonance (NMR) in coalbed methane and shale reservoirs: a review. Int J Coal Geol. 2020; 218: 103261.

[30] Luo S, Kim D, Wu Y, et al. Big data nanoindentation and analytics reveal the multi-staged, progressively-homogenized, depth-dependent upscaling of rocks' properties. Rock Mech Rock Eng. 2021b; 54: 1501-1532.

[31] Luo S, Wu Y, Li Y, et al. Nanoindentation-enhanced screening of hydraulic fracturing fluid additives. Int J Coal Geol. 2021a; 240: 103744.

[32] Ma Z, Pathegama Gamage R, Zhang C. Application of nanoindentation technology in rocks: a review. Geomech Geophys Geo-Energy Geo-Resour. 2020; 6: 60.

[33] Ma Z, Zhang C, Pathegama Gamage R, Zhang G. Uncovering the creep deformation mechanism of rock-forming minerals using nanoindentation. Int J Min Sci Technol. 2022; 32(2): 283-294.

[34] Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica. 1973; 21(5): 571-574.

[35] Nicksiar M, Martin CD. Evaluation of methods for determining crack initiation in compression tests on low-porosity rocks. Rock Mech Rock Eng. 2012; 45: 607-617.

[36] Oliver WC, Pharr GM. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res. 1992; 7(6): 1564-1583.

[37] Oliver WC, Pharr GM. Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J Mater Res. 2004; 19(1): 3-20.

[38] Räss L, Makhnenko RY, Podladchikov Y, Laloui L. Quantification of viscous creep influence on storage capacity of caprock. Energy Proc. 2017; 114: 3237-3246.

[39] Rassouli FS, Zoback MD. Comparison of short-term and long-term creep experiments in shales and carbonates from unconventional gas reservoirs. Rock Mech Rock Eng. 2018; 51: 1995-2014.

[40] Shi X, Yang X, Yue W, et al. Experimental investigation on the creep behaviors of shale using nanoindentation technique and fractional constitutive models. J Petrol Sci Eng. 2022; 215: 110520.

[41] Slim MI. Creep properties of source rocks using indentation: the role of organic matter on texture and creep rates. Diss. Massachusetts Institute of Earth, Atmospheric, and Planetary Sciences, 2016.

[42] Song J, Xiang D, Hu D, Zhou H, Guo D, Zhang G. Creep characteristics of a fracturing fluid-softened shale investigated by microindentation. Int J Rock Mech Min Sci. 2022; 152: 105067.

[43] Sorelli L, Constantinides G, Ulm FJ, Toutlemonde F. The nano-mechanical signature of ultra high performance concrete by statistical nanoindentation techniques. Cem Concr Res. 2008; 38(12): 1447-1456.

[44] Sun Z, Zhang D, Hou Y, Huangfu N, Li M, Guo F. Support countermeasures for large deformation in a deep tunnel in layered shale with high geostresses. Rock Mech Rock Eng. 2023; 56(6): 4463-4484.

[45] Traore S, Naik Parrikar P, Mokhtari M. Full-field creep mapping in a heterogeneous shale compared to a sandstone. Rock Mech Rock Eng. 2023; 56(1): 89-108.

[46] Ulm FJ, Abousleiman Y. The nanogranular nature of shale. Acta Geotech. 2006; 1: 77-88.

[47] Vandamme M, Tweedie CA, Constantinides G, Ulm FJ, Van Vliet KJ. Quantifying plasticity-independent creep compliance and relaxation of viscoelastoplastic materials under contact loading. J Mater Res. 2012; 27(1): 302-312.

[48] Vandamme M, Ulm FJ. Nanogranular origin of concrete creep. Proc Natl Acad Sci USA. 2009; 106(26): 10552-10557.

[49] Vandamme M, Ulm FJ. Nanoindentation investigation of creep properties of calcium silicate hydrates. Cement Concrete Res. 2013; 52: 38-52.

[50] Wang J, Liu Y, Yang C, et al. Upscaling the creep behavior of clay-rich and quartz-rich shales from nanoindentation measurements: application to the Wufeng-Longmaxi shale, China. Int J Rock Mech Min Sci. 2023; 171: 105580.

[51] Wang Y, Porter DL, Naleway SE, Newell P. Thermo-mechanical characterization of shale using nanoindentation. Sci Rep. 2021; 11(1): 18864.

[52] Xie Y, Hou MZ, Liu H, Li C. Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models. J Rock Mech Geotech Eng. 2024; 16(4): 1262-1279.

[53] Yang C, Xiong Y, Wang J, Li Y, Jiang W. Mechanical characterization of shale matrix minerals using phase-positioned nanoindentation and nano-dynamic mechanical analysis. Int J Coal Geol. 2020; 229: 103571.

[54] Zhang B, Peng C, Chen S, Hu Y, Li X, Zhao J. The mechanical creep property of shale for different loads and temperatures. Int J Rock Mech Min Sci. 2023; 163: 105327.

[55] Zhang Q, Le Roy R, Vandamme M, Zuber B. Long-term creep properties of cementitious materials: comparing microindentation testing with macroscopic uniaxial compressive testing. Cement Concr Res. 2014; 58: 89-98.

[56] Zhou X, Pan X, Berto F. A state-of-the-art review on creep damage mechanics of rocks. Fatigue Fract Eng Mater Struct. 2022; 45(3): 627-652.

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2025 The Author(s). Deep Underground Science and Engineering published by John Wiley & Sons Australia, Ltd on behalf of China University of Mining and Technology.