Fractal correction of dynamic fracture parameters of black sandstone under impact loads

ZHANG Renfan; ZHU Zheming; WANG Fei; ZHOU Lei; WANG Meng; JIANG Yuanfeng

doi:10.11883/bzycj-2022-0051

Volume 42 Issue 7

Jul. 2022

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ZHANG Renfan, ZHU Zheming, WANG Fei, ZHOU Lei, WANG Meng, JIANG Yuanfeng. Fractal correction of dynamic fracture parameters of black sandstone under impact loads[J]. Explosion And Shock Waves, 2022, 42(7): 073101. doi: 10.11883/bzycj-2022-0051

Citation:

ZHANG Renfan, ZHU Zheming, WANG Fei, ZHOU Lei, WANG Meng, JIANG Yuanfeng. Fractal correction of dynamic fracture parameters of black sandstone under impact loads[J]. Explosion And Shock Waves, 2022, 42(7): 073101. doi: 10.11883/bzycj-2022-0051

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Fractal correction of dynamic fracture parameters of black sandstone under impact loads

doi: 10.11883/bzycj-2022-0051

Failure Mechanics and Engineering Disaster Prevention Key Laboratory of Sichuan Province, College of Architecture and Environment, Sichuan University, Chengdu 610065, Sichuan, China

Received Date: 2022-02-11
Rev Recd Date: 2022-04-15

Available Online: 2022-05-06

Publish Date: 2022-07-25

Abstract

Abstract

When studying the dynamic fracture behavior of cracked rock mass, dynamic fracture toughness is an important mechanical parameter to study the fracture characteristics of cracks, which can accurately reflect the energy required in the crack initiation and propagation stage. However, compared with the static fracture problem, it is difficult to obtain an analytical solution for dynamic fracture toughness. Therefore, many scholars measure the crack propagation speed by using crack propagation gauges, and then calculate the dynamic fracture toughness according to the universal function. In this way, the crack propagation speed plays a leading role in the calculation accuracy, but in the experiment, the crack propagation speed cannot be measured accurately due to the measuring instrument. In this paper, the fractal theory is used to correct this error. According to the fractal theory, the effects of deflected crack propagation trajectories on dynamic fracture properties of black sandstone under impact loads were studied. A traditional modified split Hopkinson pressure bar (SHPB) test device was used to conduct a dynamic impact test by using an improved single cleavage semi-circle (ISCSC) specimen, crack propagation speed and other fracture mechanics parameters were measured using crack propagation gauge (CPG). Subsequently, the fractal theory was applied to correct dynamic crack propagation speed and dynamic stress intensity factor, and the dynamic fracture toughness of black sandstone was also calculated using the experimental-numerical method. The research results indicate that the ISCSC specimen can be effectively applied to study the crack arrest behavior of rock materials. Crack propagation speed and dynamic fracture toughness after fractal correction are closer to the actual dynamic crack propagation characteristics. Comparisons between before and after the correction, the maximum error of the crack propagation speed of black sandstone material is 33.51%, and the maximum error of dynamic fracture toughness is 7.68%, indicating that it is more reasonable to use fractal theory to calculate dynamic fracture parameters such as crack propagation speed and dynamic fracture toughness.
- impact load,
- split Hopkinson pressure bar,
- fractal theory,
- crack propagation,
- dynamic stress intensity factor

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References(32)

References

[1]	GÓMEZ F J, ELICES M, BERTO F, et al. Local strain energy to assess the static failure of U-notches in plates under mixed mode loading [J]. International Journal of Fracture, 2007, 145(1): 29–45. DOI: 10.1007/s10704-007-9104-3.
[2]	COOK N G W. Natural joints in rock: mechanical, hydraulic and seismic behaviour and properties under normal stress [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1992, 29(3): 198–223. DOI: 10.1016/0148-9062(92)93656-5.
[3]	SOH A K, YANG C H. Numerical modeling of interactions between a macro-crack and a cluster of micro-defects [J]. Engineering Fracture Mechanics, 2004, 71(2): 193–217. DOI: 10.1016/S0013-7944(03)00097-3.
[4]	MISHURIS G, MOVCHAN A, MOVCHAN N, et al. Interaction of an interfacial crack with linear small defects under out-of-plane shear loading [J]. Computational Materials Science, 2012, 52(1): 226–230. DOI: 10.1016/j.commatsci.2011.01.023.
[5]	董玉清, 朱哲明, 王蒙, 等. 中低速冲击载荷作用下SCT岩石试样Ⅰ型裂纹的动态扩展行为 [J]. 中南大学学报(自然科学版), 2018, 49(11): 2821–2830. DOI: 10.11817/j.issn.1672-7207.2018.11.024. DONG Y Q, ZHU Z M, WANG M, et al. Mode Ⅰ crack dynamic propagation behavior of SCT specimens under medium-low speed impact load [J]. Journal of Central South University (Science and Technology), 2018, 49(11): 2821–2830. DOI: 10.11817/j.issn.1672-7207.2018.11.024.
[6]	周磊, 朱哲明, 董玉清, 等. 冲击加载下巷道内裂纹的扩展特性及破坏行为 [J]. 爆炸与冲击, 2018, 38(4): 785–794. DOI: 10.11883/bzycj-2016-0383. ZHOU L, ZHU Z M, DONG Y Q, et al. Propagation characteristics and failure behaviors of crack in tunnel under impact loads [J]. Explosion and Shock Waves, 2018, 38(4): 785–794. DOI: 10.11883/bzycj-2016-0383.
[7]	WANG F, WANG M, NEZHAD M M, et al. Rock dynamic crack propagation under different loading rates using improved single cleavage semi-circle specimen [J]. Applied Sciences, 2019, 9(22): 4944. DOI: 10.3390/APP9224944.
[8]	THEOCARIS P S, MILIOS J. Crack arrest modes of a transverse crack going through a longitudinal crack or a hole [J]. Journal of Engineering Materials and Technology, 1981, 103(2): 177–182. DOI: 10.1115/1.3224991.
[9]	MILIOS J, SPATHIS G. Dynamic interaction of a propagating crack with a hole boundary [J]. Acta Mechanica, 1988, 72(3/4): 283–295. DOI: 10.1007/BF01178314.
[10]	MURDANI A, MAKABE C, SAIMOTO A, et al. A crack-growth arresting technique in aluminum alloy [J]. Engineering Failure Analysis, 2008, 15(4): 302–310. DOI: 10.1016/j.engfailanal.2007.02.005.
[11]	AYATOLLAHI M R, RAZAVI S M J, YAHYA M Y. Mixed mode fatigue crack initiation and growth in a CT specimen repaired by stop hole technique [J]. Engineering Fracture Mechanics, 2015, 145: 115–127. DOI: 10.1016/j.engfracmech.2015.03.027.
[12]	CHEN N Z. A stop-hole method for marine and offshore structures [J]. International Journal of Fatigue, 2016, 88: 49–57. DOI: 10.1016/j.ijfatigue.2016.03.010.
[13]	WANG Y B, YANG R S, ZHAO G F. Influence of empty hole on crack running in PMMA plate under dynamic loading [J]. Polymer Testing, 2017, 58: 70–85. DOI: 10.1016/j.polymertesting.2016.11.020.
[14]	WANG M, WANG F, ZHU Z M, et al. Modelling of crack propagation in rocks under SHPB impacts using a damage method [J]. Fatigue and Fracture of Engineering Materials and Structures, 2019, 42(8): 1699–1710. DOI: 10.1111/ffe.13012.
[15]	王飞, 王蒙, 朱哲明, 等. 冲击荷载下岩石裂纹动态扩展全过程演化规律研究 [J]. 岩石力学与工程学报, 2019, 38(6): 1139–1148. DOI: 10.13722/j.cnki.jrme.2018.1172. WANG F, WANG M, ZHU Z M, et al. Study on evolution law of rock crack dynamic propagation in complete process under impact loading [J]. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(6): 1139–1148. DOI: 10.13722/j.cnki.jrme.2018.1172.
[16]	FUNATSU T, KURUPPU M, MATSUI K. Effects of temperature and confining pressure on mixed-mode (Ⅰ-Ⅱ) and mode Ⅱ fracture toughness of Kimachi sandstone [J]. International Journal of Rock Mechanics and Mining Sciences, 2014, 67: 1–8. DOI: 10.1016/j.ijrmms.2013.12.009.
[17]	周磊, 朱哲明, 董玉清, 等. 动态加载率对巷道内裂纹扩展速度及动态起裂韧度的影响 [J]. 振动与冲击, 2019, 38(4): 129–136. DOI: 10.13465/j.cnki.jvs.2019.04.021. ZHOU L, ZHU Z M, DONG Y Q, et al. Effect of dynamic loading rate on crack propagation velocity and dynamic fracture toughness in tunnels [J]. Journal of Vibration and Shock, 2019, 38(4): 129–136. DOI: 10.13465/j.cnki.jvs.2019.04.021.
[18]	ZHANG Q B, ZHAO J. Determination of mechanical properties and full-field strain measurements of rock material under dynamic loads [J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 60: 423–439. DOI: 10.1016/j.ijrmms.2013.01.005.
[19]	JIANG F C, VECCHIO K S. Hopkinson bar loaded fracture experimental technique: a critical review of dynamic fracture toughness tests [J]. Applied Mechanics Reviews, 2009, 62(6): 060802. DOI: 10.1115/1.3124647.
[20]	WANG Q Z, FENG F, NI M, et al. Measurement of mode Ⅰ and mode Ⅱ rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar [J]. Engineering Fracture Mechanics, 2011, 78(12): 2455–2469. DOI: 10.1016/j.engfracmech.2011.06.004.
[21]	AVACHAT S, ZHOU M. High-speed digital imaging and computational modeling of dynamic failure in composite structures subjected to underwater impulsive loads [J]. International Journal of Impact Engineering, 2015, 77: 147–165. DOI: 10.1016/j.ijimpeng.2014.11.008.
[22]	LEE D, TIPPUR H, BOGERT P. Dynamic fracture of graphite/epoxy composites stiffened by buffer strips: an experimental study [J]. Composite Structures, 2012, 94(12): 3538–3545. DOI: 10.1016/j.compstruct.2012.05.032.
[23]	MANDELBROT B B. The fractal geometry of nature [M]. New York, USA: W. H. Freeman and Company, 1982.
[24]	THEOCARIS P S, SAKELLARIOU M. A correction model for the incompatible deformations of the shear internal crack [J]. Engineering Fracture Mechanics, 1991, 38(4/5): 231–240. DOI: 10.1016/0013-7944(91)90001-H.
[25]	NAGAHAMA H. Fractal scalings of rock fragmentation [J]. Earth Science Frontiers, 2000, 7(1): 169–177. DOI: 10.3321/j.issn:1005-2321.2000.01.016.
[26]	谢和平. 动态裂纹扩展中的分形效应 [J]. 力学学报, 1995, 27(1): 18–27. DOI: 10.6052/0459-1879-1995-1-1995-401. XIE H P. Fractal effects of dynamic crack propagation [J]. Acta Mechanica Sinica, 1995, 27(1): 18–27. DOI: 10.6052/0459-1879-1995-1-1995-401.
[27]	谢和平. 脆性材料裂纹扩展的分形运动学 [J]. 力学学报, 1994, 26(6): 757–762. DOI: 10.6052/0459-1879-1994-6-1995-606. XIE H P. Fractal kinematics of crack propagation in brittle materials [J]. Acta Mechanica Sinica, 1994, 26(6): 757–762. DOI: 10.6052/0459-1879-1994-6-1995-606.
[28]	谢和平. 分形-岩石力学导论 [M]. 北京: 科学出版社, 1996: 168−261.
[29]	程靳, 赵树山. 断裂力学 [M]. 北京: 科学出版社, 2006: 9−55.
[30]	FREUND L B. Dynamic fracture mechanics [M]. Cambridge, UK: Cambridge University Press, 1990.
[31]	ROSE L R F. Recent theoretical and experimental results on fast brittle fracture [J]. International Journal of Fracture, 1976, 12(6): 799–813. DOI: 10.1007/BF00034620.
[32]	RAVI-CHANDAR K, KNAUSS W G. An experimental investigation into dynamic fracture: I. crack initiation and arrest [J]. International Journal of Fracture, 1984, 25: 247–262.10. DOI: 10.1007/BF00963460.