Coalescence of Two Coplanar Internal Penny-Shaped Cracks in Brittle Solid under Uniaxial Tension Based on 3D-ILC
Publication: International Journal of Geomechanics
Volume 23, Issue 4
Abstract
Crack coalescence is an important topic in the research of brittle fracture mechanics. Most of the previous studies have focused on surface or penetrating cracks, while few experimental studies have been performed on internal cracks coalescence. This study fills in the missing data. First, the 3D internal laser-engraved crack (3D-ILC) method was introduced to make internal cracks in glass without causing any damage to the surfaces of the glass. Next, uniaxial tensile tests were performed on the samples with two coplanar internal penny-shaped cracks. A new grid reconstruction algorithm is also proposed to simulate the coalescence and the growth path of two coplanar internal cracks. The crack coalescence process and fracture characteristics were analyzed in detail. The results indicate that the fracture in the test is static fracture, while the fracture is Mode I, based on the characteristics of the fracture morphology. In addition, the Wallner lines were observed after the coalescence of cracks, which were overall elliptical in shape. Before coalescence, the stress intensity factor I (KI) at the center was higher than that at the outside, indicating the attraction of the twin cracks. Then, after coalescence, the KI increased significantly at that coalescence site, which indicated that the new crack had rapidly become “elliptical” in shape following the coalescence. The normalized KII/|KImax| and KIII/|KImax| of the coplanar cracks were approximately equal to 0 in the simulation, and it was confirmed that the fracture in the test was Mode I.
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Acknowledgments
This research was supported by the National Natural Science Foundation of China (Nos. 51409170, U1765204, 52104125), the open fund of State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Beijing (No. SKLGDUEK2133), the open fund of Badong National Observation and Research Station of Geohazards (No. BNORSG202205), and the Young Elite Scientists Sponsorship Program by CAST (No. 2021QNRC001). The authors would also like to express their sincere gratitude to the editor and reviewers for their valuable comments.
References
Ai, C., X. X. Li, J. Zhang, D. Jia, and W. J. Tan. 2018. “Experimental investigation of propagation mechanisms and fracture morphology for coalbed methane reservoirs.” Pet. Sci. 15 (04): 137–151.
Briñez, J. C., A. Restrepo Martínez, and J. W. Branch. 2018. “Computational hybrid phase shifting technique applied to digital photoelasticity.” Optik 157: 287–297. https://doi.org/10.1016/j.ijleo.2017.11.060.
Cao, P., T. Liu, C. Pu, and H. Lin. 2015. “Crack propagation and coalescence of brittle rock-like specimens with pre-existing cracks in compression.” Eng. Geol. 187: 113–121. https://doi.org/10.1016/j.enggeo.2014.12.010.
Chen, S., Z. Xia, F. Feng, and D. Yin. 2020. “Numerical study on strength and failure characteristics of rock samples with different hole defects.” Bull. Eng. Geol. Environ. 7: 1–18.
Dyskin, A. V., R. J. Jewell, H. Joer, E. Sahouryeh, and K. B. Ustinov. 1994. “Experiments on 3D crack growth in uniaxial compression.” Int. J. Fract. 65 (4): R77–R83. https://doi.org/10.1007/BF00012382.
Fu, J.-W., K. Chen, W.-s. Zhu, X.-z. Zhang, and X.-j. Li. 2016. “Progressive failure of new modelling material with a single internal crack under biaxial compression and the 3-D numerical simulation.” Eng. Fract. Mech. 165: 140–152. https://doi.org/10.1016/j.engfracmech.2016.08.002.
Fu, J. W., W. S. Zhu, L. G. Wang, and X. G. Wang. 2011. “Numerical simulation of the crack propagation processes in rocks with double joints.” Appl. Mech. Mater. 90–93: 559–564.
Griffith, A. A. 1921. “The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London.” Series A, Containing Papers of a Mathematical or Physical Character 221 (582–593): 163–198.
He, M., Q. Sui, M. Li, Z. Wang, and Z. Tao. 2022. “Compensation excavation method control for large deformation disaster of mountain soft rock tunnel.” Int. J. Min. Sci. Technol. 32 (5): 951–963. https://doi.org/10.1016/j.ijmst.2022.08.004.
Huang, Y.-H., S.-Q. Yang, and W.-L. Tian. 2019. “Crack coalescence behavior of sandstone specimen containing two pre-existing flaws under different confining pressures.” Theor. Appl. Fract. Mech. 99: 118–130. https://doi.org/10.1016/j.tafmec.2018.11.013.
Ju, Y., C. Wan, Z. Ren, L. Mao, G. Fu, and F.-p. Chiang. 2020. “Quantification of continuous evolution of full-field stress associated with shear deformation of faults using three-dimensional printing and phase-shifting methods.” Int. J. Rock Mech. Min. Sci. 126: 104187. https://doi.org/10.1016/j.ijrmms.2019.104187.
Lawn, B. 1993. “Fracture of brittle solids.” In Cambridge solid state science series. 2nd ed., edited by E. A. Davis and I. M. Ward FRS, 7. Cambridge: Cambridge University Press.
Li, L. C., C. A. Tang, G. Li, S. Y. Wang, Z. Z. Liang, and Y. B. Zhang. 2012. “Numerical simulation of 3D hydraulic fracturing based on an improved flow-stress-damage model and a parallel FEM technique.” Rock Mech. Rock Eng. 45 (5): 801–818.
Liu, J., H. Su, H. Jing, C. Hu, and Q. Yin. 2020. “Experimental study on the fracture evolution process of rock-like specimens containing a closed rough joint based on 3D-printing technology.” Adv. Civ. Eng. 1: 1–16.
Parthasarathi, N., S. Srinivasa Senthil, M. Prakash, and K. S. Satyanarayanan. 2018. “Analytical and experimental study on reinforced concrete arch by photoelasticity technique.” Asian J. Civ. Eng. 19 (5): 647–650. https://doi.org/10.1007/s42107-018-0049-9.
Qiao, D., W. Cheng, J. Xie, J. Wang, F. Huang, Y. Mo, and J. Peng. 2019. “Analysis of the influence of gradation on the strength of a cemented filling body and the cementation strength model.” Integr. Ferroelectr. 199 (1): 12–21. https://doi.org/10.1080/10584587.2019.1592593.
Shou, Y., X. Zhou, and F. Berto. 2019. “3D numerical simulation of initiation, propagation and coalescence of cracks using the extended non-ordinary state-based peridynamics.” Theor. Appl. Fract. Mech. 101: 254–268. https://doi.org/10.1016/j.tafmec.2019.03.006.
Tang, H. D., Z. D. Zhu, M. L. Zhu, and H. X. Lin. 2016. “Mechanical behavior of 3D crack growth in transparent rock-like material containing preexisting flaws under compression.” Adv. Mater. Sci. Eng. 2015: 1–10.
Tijssens, M. G. A., B. L. J. Sluys, and E. van der Giessen. 2000. “Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces.” Eur. J. Mech. A. Solids 19 (5): 761–779. https://doi.org/10.1016/S0997-7538(00)00190-X.
Wang, H. J., A. V. Dyskin, A. Hsieh, and P. Dight. 2012. “The mechanism of the deformation memory effect and the deformation rate analysis in layered rock in the low stress region.” Comput. Geotech. 44: 83–92. https://doi.org/10.1016/j.compgeo.2012.03.006.
Wang, H. J., S. Y. Yu, R. Ren, L. Tang, X. Y. Li, and Y. Jia. 2019a. “Study on failure of brittle solids with circular hole and internal crack based on 3D-ILC.” Rock Soil Mech. 40 (06): 2200–2212.
Wang, H. J., J. D. Zhang, R. Ren, L. Tang, and L. W. Zhong. 2019b. “Embedded cracks in brittle solids induced by laser-medium interaction (3D-ILC).” Chin. J. Geotech. Eng. 41 (12): 2345–2352.
Wang, H. J., H. Z. Li, L. Tang, X. Ren, Q. Meng, and C. Zhu. 2022a. “Fracture of two three-dimensional parallel internal cracks in brittle solid under ultrasonic fracturing.” J. Rock Mech. Geotech. Eng. 14 (3): 757–769. https://doi.org/10.1016/j.jrmge.2021.11.002.
Wang, H. J., H. Z. Li, L. Tang, J. C. Li, and X. H. Ren. 2022b. “Fracturing behavior of brittle solids containing 3D internal crack of different depths under ultrasonic fracturing.” Int. J. Min. Sci. Technol. 32 (6): 1245–1257. https://doi.org/10.1016/j.ijmst.2022.09.008.
Wang, J., W. S. Zhu, and H. P. Ma. 2014. “Crack propagation of jointed rock and application.” Appl. Mech. Mater. 117–119: 476–479.
Wang, X., J. Li, X. Zhao, and Y. Liang. 2022. “Propagation characteristics and prediction of blast-induced vibration on closely spaced rock tunnels.” Tunnelling Underground Space Technol. 123: 104416. https://doi.org/10.1016/j.tust.2022.104416.
Wang, Y., S. Gao, D. Liu, and C. Li. 2020a. “Anisotropic fatigue behaviour of interbeded marble subjected to uniaxial cyclic compressive loads.” Fatigue Fract. Eng. Mater. Struct. 43 (6): 1170–1183. https://doi.org/10.1111/ffe.13191.
Wang, Y., D. Liu, J. Han, C. Li, and H. Liu. 2020b. “Effect of fatigue loading-confining stress unloading rate on marble mechanical behaviors: An insight into fracture evolution analyses.” J. Rock Mech. Geotech. Eng. 12 (6): 1249–1262. https://doi.org/10.1016/j.jrmge.2020.08.002.
Wong, L. N. Y., and H. H. Einstein. 2009. “Crack coalescence in molded gypsum and carrara marble: Part 2—Microscopic observations and interpretation.” Rock Mech. Rock Eng. 42 (3): 513–545. https://doi.org/10.1007/s00603-008-0003-3.
Xiao, B., Q. Liu, G. Hu, and Y. Shi. 2017. “Research on transient dynamic characteristics of three-stage axial-flow multi-phase pumps influenced by gas volume fractions.” Adv. Mech. Eng. 9 (12): 1–10.
Xiroudakis, G., M. Stavropoulou, and G. Exadaktylos. 2019. “Three-dimensional elastic analysis of cracks with the g2 constant displacement discontinuity method.” Int. J. Numer. Anal. Methods Geomech. 43: 2355–2382. https://doi.org/10.1002/nag.2971.
Yang, S.-Q. 2011. “Crack coalescence behavior of brittle sandstone samples containing two coplanar fissures in the process of deformation failure.” Eng. Fract. Mech. 78 (17): 3059–3081. https://doi.org/10.1016/j.engfracmech.2011.09.002.
Yin, P., R. H. C. Wong, and K. T. Chau. 2014. “Coalescence of two parallel pre-existing surface cracks in granite.” Int. J. Rock Mech. Min. Sci. 68 (6): 66–84. https://doi.org/10.1016/j.ijrmms.2014.02.011.
Yin, Q., R. Liu, H. Jing, H. Su, L. Yu, and L. He. 2019. “Experimental study of nonlinear flow behaviors through fractured rock samples after high-temperature exposure.” Rock Mech. Rock Eng. 52: 2963–2983. https://doi.org/10.1007/s00603-019-1741-0.
Yin, Q., J. Wu, C. Zhu, Q. Wang, and J. Xie. 2021. “The role of multiple heating and water cooling cycles on physical and mechanical responses of granite rocks.” Geomech. Geophys. Geo-Energy Geo-Resour. 7: 69. https://doi.org/10.1007/s40948-021-00267-0.
Zhang, X.-P., Q. Liu, S. Wu, and X. Tang. 2015. “Crack coalescence between two non-parallel flaws in rock-like material under uniaxial compression.” Eng. Geol. 199: 74–90. https://doi.org/10.1016/j.enggeo.2015.10.007.
Zhang, Y., and H. A. Mang. 2020. “Global cracking elements: A novel tool for Galerkin-based approaches simulating quasi-brittle fracture.” Int. J. Numer. Methods Eng. 121 (11): 2462–2480. https://doi.org/10.1002/nme.6315.
Zhang, Y., and X. Zhuang. 2019. “Cracking elements method for dynamic brittle fracture.” Theor. Appl. Fract. Mech. 102: 1–9. https://doi.org/10.1016/j.tafmec.2018.09.015.
Zhao, Y.-Q., Y.-J. Deng, F. Lin, M.-M. Zhu, and X. Zhen. 2018. “Transient dynamic characteristics of a non-pneumatic mechanical elastic wheel rolling over a ditch.” Int. J. Automot. Technol. 19 (3): 499–508. https://doi.org/10.1007/s12239-018-0048-6.
Zhou, Y. 2016. “A method for calculating the stability of unstable rocks on Three Gorges Reservoir by fracture mechanics.” Rock Soil Mech. 37 (S1): 495–499.
Zhou, T., and J. Zhu. 2017. “An experimental investigation of tensile fracturing behavior of natural and artificial rocks in static and dynamic Brazilian disc tests.” Procedia Eng. 191: 992–998. https://doi.org/10.1016/j.proeng.2017.05.271.
Zhou, T., J. B. Zhu, Y. Ju, and H. P. Xie. 2019. “Volumetric fracturing behavior of 3D printed artificial rocks containing single and double 3D internal flaws under static uniaxial compression.” Eng. Fract. Mech. 205: 190–204. https://doi.org/10.1016/j.engfracmech.2018.11.030.
Zhu, J. B., T. Zhou, Z. Y. Liao, L. Sun, X. B. Li, and R. Chen. 2018. “Replication of internal defects and investigation of mechanical and fracture behaviour of rock using 3D printing and 3D numerical methods in combination with X-ray computerized tomography.” Int. J. Rock Mech. Min. Sci. 106: 198–212. https://doi.org/10.1016/j.ijrmms.2018.04.022.
Zhuang, X., C. E. Augarde, and K. M. Mathisen. 2012. “Fracture modeling using meshless methods and level sets in 3D: Framework and modeling.” Int. J. Numer. Methods Eng. 92 (11): 969–998. https://doi.org/10.1002/nme.4365.
Zhuang, X., C. Augarde, and S. Bordas. 2011. “Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling.” Int. J. Numer. Methods Eng. 86 (2): 249–268. https://doi.org/10.1002/nme.3063.
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International Journal of Geomechanics
Volume 23 • Issue 4 • April 2023
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© 2023 American Society of Civil Engineers.
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Received: Aug 22, 2021
Accepted: Nov 9, 2022
Published online: Jan 23, 2023
Published in print: Apr 1, 2023
Discussion open until: Jun 23, 2023
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