Abstract
The former studies indicate that loading rates significantly affect dynamic behavior of brittle materials, for instance, the dynamic compressive and tensile strength increase with loading rates. However, there still are many unknown or partially unknown aspects. For example, whether loading rates have effect on crack dynamic propagating behavior (propagation toughness, velocity and arrest, etc). To further explore the effect of loading rates on crack dynamic responses, a large-size single-cleavage trapezoidal open (SCTO) specimen was proposed, and impacting tests using the SCTO specimen under drop plate impact were conducted. Crack propagation gauges (CPGs) were employed in measuring impact loads, crack propagation time and velocities. In order to verify the testing result, the corresponding numerical model was established using explicit dynamic software AUTODYN, and the simulation result is basically consistent with the experimental results. The ABAQUS software was used to calculate the dynamic SIFs. The universal function was calculated by fractal method. The experimental-numerical method was employed in determining initiation toughness and propagation toughness. The results indicate that crack propagating velocities, dynamic fracture toughness and energy release rates increase with loading rates; crack delayed initiation time decreases with loading rates.
摘要
通常,加载率会显著影响脆性材料的抗压强度和拉伸强度等力学行为,但是对其它动态力学性 能的影响仍然存在许多未知或部分未知的情况,比如,加载率是否会影响裂纹的动态扩展行为(扩展 韧度,裂纹速度和裂纹止裂等)。为了进一步探讨加载率对裂纹动态响应的影响,提出梯形开口的侧 开单裂纹构型试样,并在落锤冲击装置下对该试样进行了冲击试验。利用裂纹扩展计测量冲击载荷、 裂纹扩展时间和裂纹速度。为了验证测试结果,采用显式动力软件AUTODYN 建立了相应的数值模 型,数值仿真结果与实验结果基本一致。利用有限元程序ABAQUS 计算动态应力强度因子,并采用 普适函数进行修正,最后基于实验-数值方法确定裂纹起始韧度和裂纹扩展韧度。结果表明,裂纹扩 展速度、动态断裂韧度和能量释放率均随着加载率的增加而增加,裂纹的延迟起裂时间随着加载率的 增加而缩短。
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References
HUANG B, LIU J. The effect of loading rate on the behavior of samples composed of coal and rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 61: 23–30. DOI: https://doi.org/10.1016/j.ijrmms.2013.02.002.
LI X B, LOK T S, ZHAO J. Dynamic characteristics of granite subjected to intermediate loading rate [J]. Rock Mechanics and Rock Engineering, 2004, 38: 21–39. DOI: https://doi.org/10.1007/s00603-004-0030-7.
KIM D J, SIRIJAROONCHAI K, EL-TAWIL S. NAAMAN A E. Numerical simulation of the split Hopkinson pressure bar test technique for concrete under compression [J]. International Journal of Impact Engineering, 2010, 37: 141–149. DOI: https://doi.org/10.1016/j.ijimpeng.2009.06.012.
CAO A, JING G, DING Y, LIU S. Mining-induced static and dynamic loading rate effect on rock damage and acoustic emission characteristic under uniaxial compression [J]. Safety Science, 2019, 116: 86–96. DOI: https://doi.org/10.1016/j.ssci.2019.03.003.
KOMURLU E. Loading rate conditions and specimen size effect on strength and deformability of rock materials under uniaxial compression [J]. International Journal of Geo-Engineering, 2018, 9(1): 1–11. DOI: https://doi.org/10.1186/s40703-018-0085-z.
ELMER VII W, TACIROGLU E, MCMICHAEL L. Dynamic strength increase of plain concrete from high strain rate plasticity with shear dilation [J]. International Journal of Impact Engineering, 2012, 45: 1–15. DOI: https://doi.org/10.1016/j.ijimpeng.2012.01.003.
HEIDARI-RARANI M, ALIHA M R M, SHOKRIEH M, AYATOLLAHI M R. Mechanical durability of an optimized polymer concrete under various thermal cyclic loadings-An experimental study [J]. Construction and Building Materials, 2014, 64: 308–315. DOI: https://doi.org/10.1016/j.conbuildmat.2014.04.031.
KIM E, CHANGANI H. Effect of water saturation and loading rate on the mechanical properties of red and buff sandstones [J]. International Journal of Rock Mechanics and Mining Sciences, 2016, 88: 23–28. DOI: https://doi.org/10.1016/j.ijrmms.2016.07.005.
YIN Zhi-qiang, CHEN Wen-su, HAO Hong, CHANG Ju-cai, ZHAO Guang-ming, CHEN Zhi-yu, PENG Kang. Dynamic compressive test of gas-containing coal using a modified split Hopkinson pressure bar system [J]. Rock Mechanics and Rock Engineering, 2020, 53: 815–829. DOI: https://doi.org/10.1007/s00603-019-01955-w.
ZHU Z M, XU W T, FENG R Q. A new method for measuring mode-I dynamic fracture toughness of rock under blasting loads [J]. Experimental Techniques, 2016, 40(3): 889–905. DOI: https://doi.org/10.1007/s40799-016-0093-x.
HUANG Hua, YUAN Yu-jie, ZHANG Wei, GAO Zi-chen. Bond behavior between lightweight aggregate concrete and normal weight concrete based on splitting-tensile test [J]. Construction and Building Materials, 2019, 209: 306–314. DOI: https://doi.org/10.1016/j.conbuildmat.2019.03.125.
GUL A J, FATEHI M S, YASMEEN G, SHARIFAH M M, NORAM I R. Uniaxial compression and tensile splitting tests on adobe with embedded steel wire reinforcement [J]. Construction and Building Materials, 2018, 176: 383–393. DOI: https://doi.org/10.1016/j.conbuildmat.2018.05.006.
WANG Q Z, YANG J R, ZHANG C G, ZHOU Y, LI L, ZHU Z M, WU L Z. Sequential determination of dynamic initiation and propagation toughness of rock using an experimental-numerical- analytical method [J]. Engineering Fracture Mechanics, 2015, 141: 78–94. DOI: https://doi.org/10.1016/j.engfracmech.2015.04.025.
WANG X M, ZHU Z M, WANG M, YING P, ZHOU L, DONG Y Q. Study of rock dynamic fracture toughness by using VB-SCSC specimens under medium-low speed impacts [J]. Engineering Fracture Mechanics, 2017, 181: 52–64. DOI: https://doi.org/10.1016/j.engfracmech.2017.06.024.
KURUPPU M D, OBARA Y, AYATOLLAHI M R, CHONG K P, FUNATSU T. ISRM-suggested method for determining the mode I static fracture toughness using semi-circular bend specimen [J]. Rock Mechanics and Rock Engineering, 2014, 47(1): 267–274. DOI: https://doi.org/10.1007/s00603-013-0422-7.
ALIHA M R M, AYATOLLAHI M R. Rock fracture toughness study using cracked chevron notched Brazilian disc specimen under pure modes I and II loading-A statistical approach [J]. Theoretical and Applied Fracture Mechanics, 2014, 69(2): 17–25. DOI: https://doi.org/10.1016/j.tafmec.2013.11.008.
GUO H, AZIZ N I, SCHMIDT L C. Rock fracture-toughness determination by the Brazilian test [J]. Engineering Geology, 1993, 33(3): 177–188. DOI: https://doi.org/10.1016/0013-7952(93)90056-I.
AKBARDOOST J, GHADIRIAN H R, SANGSEFIDI M. Calculation of the crack tip parameters in the holed-cracked flattened Brazilian disk (HCFBD) specimens under wide range of mixed mode I/II loading [J]. Fatigue & Fracture of Engineering Materials & Structures, 2017, 40: 1416–1427. DOI: https://doi.org/10.1111/ffe.12585.
WANG M, ZHU Z M, DONG Y Q, ZHOU L. Study of mixed-mode I/II fractures using single cleavage semicircle compression specimens under impacting loads [J]. Engineering Fracture Mechanics, 2017, 177: 33–44, DOI: https://doi.org/10.1016/j.engfracmech.2017.03.042.
ZHOU L, ZHU Z M, QIU H, ZHANG X S, LANG L. Study of the effect of loading rates on crack propagation velocity and rock fracture toughness using cracked tunnel specimens [J]. International Journal of Rock Mechanics and Mining Sciences, 2018, 112: 25–34. DOI: https://doi.org/10.1016/j.ijrmms.2018.10.01.
YING P, ZHU Z M, WANG F, WANG M, NIU C, ZHOU L. The characteristics of dynamic fracture toughness and energy release rate of rock under impact [J]. Measurement, 2019, 147: 106884. DOI: https://doi.org/10.1016/j.measurement.2019.106884.
TANG S B. The effect of T-stress on the fracture of brittle rock under compression [J]. International Journal of Rock Mechanics & Mining Sciences, 2015, 79: 86–98. DOI: https://doi.org/10.1016/j.ijrmms.2015.06.009.
LANG L, ZHU Z, ZHANG X, QIU H, ZHOU C L. Investigation of crack dynamic parameters and crack arresting technique in concrete under impacts [J]. Construction and Building Materials, 2019, 199: 321–334. DOI: https://doi.org/10.1016/j.conbuildmat.2018.12.029.
TANG S B. Stress intensity factors for a Brazilian disc with a central crack subjected to compression [J]. International Journal of Rock Mechanics & Mining Sciences, 2017, 93: 38–45. DOI: https://doi.org/10.1016/j.ijrmms.2017.01.003.
TANG S B, BAO C Y, LIU H Y. Brittle fracture of rock under combined tensile and compressive loading conditions [J]. Canadian Geotechnical Journal, 2017, 54(1): 88–101. DOI: https://doi.org/10.1139/cgj-2016-0214.
ZHANG Z X, KOU S Q, JIANG L G, LINDQVIST P A. Effects of loading rate on rock fracture: Fracture characteristics and energy partitioning [J]. International Journal of Rock Mechanics & Mining Sciences, 2000, 37: 745–762. DOI: https://doi.org/10.1016/S1365-1609(00)00008-3.
ZHAO Y, GONG S, HAO X, PENG Y, JIANG Y. Effects of loading rate and bedding on the dynamic fracture toughness of coal: Laboratory experiments [J]. Engineering Fracture Mechanics, 2017, 178: 375–391. DOI: https://doi.org/10.1016/j.engfracmech.2017.03.011.
SATYANARAYANA A, GATTU M. Effect of displacement loading rates on mode-I fracture toughness of fiber glass-epoxy composite laminates [J]. Engineering Fracture Mechanics, 2019, 218: 1–19. DOI: https://doi.org/10.1016/j.engfracmech.2019.106535.
FREW D J, FORRESTAL M J, CHEN W. A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock materials [J]. Experimental Mechanics, 2001, 41(1): 40–46. DOI: https://doi.org/10.1007/BF02323102.
NASSERI M H B, MOHANTY B. Fracture toughness anisotropy in granitic rocks [J]. International Journal of Rock Mechanics & Mining Sciences, 2008, 45(2): 167–193. DOI: https://doi.org/10.1016/j.ijrmms.2007.04.005.
ZHOU Z, LI X, LIU A, ZOU Y. Stress uniformity of split Hopkinson pressure bar under half-sine wave loads [J]. International Journal of Rock Mechanics & Mining Sciences, 2011, 48(4): 697–701. DOI: https://doi.org/10.1016/j.ijrmms.2010.09.006.
ZHANG Q B, ZHAO J. Effect of loading rate on fracture toughness and failure micromechanisms in marble [J]. Engineering Fracture Mechanics, 2013, 102(2): 288–309. DOI: https://doi.org/10.1016/j.engfracmech.2013.02.009.
IMANI M, NEJATI H R, GOSHTASBI K. Dynamic response and failure mechanism of Brazilian disk specimens at high strain rate [J]. Soil Dynamics and Earthquake Engineering, 2017, 100: 261–269. DOI: https://doi.org/10.1016/j.soildyn.2017.06.007.
YANG R, CHEN J, YANG L, FANG S, LIU J. An experimental study of high strain-rate properties of clay under high consolidation stress [J]. Soil Dynamics and Earthquake Engineering, 2017, 92: 46–51. DOI: https://doi.org/10.1016/j.soildyn.2016.09.036.
WANG Q Z, FENG F, NI M, GOU X P. 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: https://doi.org/10.1016/j.engfracmech.2011.06.004.
HAERI H, SHAHRIAR K, MARJI M F, MOAREFVAND P. Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks [J]. International Journal of Rock Mechanics & Mining Sciences, 2013, 67(4): 20–28. DOI: https://doi.org/10.1016/j.ijrmms.2014.01.008.
FAYE A, PARAMESWARAN V, BASU S. Dynamic fracture initiation toughness of PMMA: A critical evaluation [J]. Mechanics of Materials, 2016, 94: 156–169. DOI: https://doi.org/10.1016/j.mechmat.2015.12.002.
HAERI H, SARFARAZI V, ZHU Z. Effect of normal load on the crack propagation from preexisting joints using particle flow code (PFC) [J]. Computers and Concrete, 2017, 19(1): 99–110. DOI: https://doi.org/10.12989/cac.2017.19.1.099.
LANG L, ZHU Z M, DENG S, WANG L, NIU C Y, XIAO D J. Study on the arresting mechanism of two arrest-holes on moving crack in brittle material under impacts [J]. Engineering Fracture Mechanics, 2020, 229(39): 1–14. DOI: https://doi.org/10.1016/j.engfracmech.2020.10693.
ZHU Z. Numerical prediction of crater blasting and bench blasting [J]. International Journal of Rock Mechanics & Mining Sciences, 2009, 46(6): 1088–1096. DOI: https://doi.org/10.1016/j.ijrmms.2009.05.009.
ZHU Z, WANG C, KANG J, LI Y, WANG M. Study on the mechanism of zonal disintegration around an excavation [J]. International Journal of Rock Mechanics & Mining Sciences, 2014, 67(4): 88–95. DOI: https://doi.org/10.1016/j.ijrmms.2013.12.017.
YE W P. Origin 9.1 science and technology drawing and data analysis [M]. Beijing: Mechanical Industry Press, 2015: 299–319.
ZHOU Y X, XIA K, LI X B, LI H B, MA G W, ZHAO J, ZHOU Z L, DAI F. Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials [J]. International Journal of Rock Mechanics & Mining Sciences, 2012, 49(1): 105–112. DOI: https://doi.org/10.1016/j.ijrmms.2011.10.004.
XIE H P, SANDERSON D J. Fractal kinematics of crack propagation in geomaterials [J]. Engineering Fracture Mechanics, 1995, 50(4): 529–536. DOI: https://doi.org/10.1016/0013-7944(94)00203-T.
XIE H P, SANDERSON D J. Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities [J]. International Journal of Fracture, 1986, 74: 29–42. DOI: https://doi.org/10.1007/BF00018573.
ROSE L R F. On the initial motion of a Griffith crack [J]. International Journal of Fracture, 1976, 12(6): 829–841. DOI: https://doi.org/10.1007/bf00034622.
BHAT H S, ROSAKIS A J, SAMMIS C G. A micromechanics based constitutive model for brittle failure at high strain rates [J]. Journal of Applied Mechanics, 2012, 79(3): 031016. DOI: https://doi.org/10.1115/1.4005897.
FREUND L B. Dynamic fracture mechanics [M]. Cambridge University Press, 1990.
RAVI-CHANDAR K. Dynamic fracture [M]. Elsevier, 2004.
FREUND L B, HUTCHINSON J W. Dynamic fracture mechanics [J]. Journal of Applied Mechanics, 1992, 59(1): 245. DOI: https://doi.org/10.1115/1.2899458.
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Foundation item: Projects(11672194, U19A2098) supported by the National Natural Science Foundation of China; Project(2018SCU12047) supported by Fundamental Research Funds for the Central Universities, China; Project(2018JZ0036) supported by the Project of Science and Technology of Sichuan Province, China
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Lang, L., Zhu, Zm., Wang, Hb. et al. Effect of loading rates on crack propagating speed, fracture toughness and energy release rate using single-cleavage trapezoidal open specimen under impact loads. J. Cent. South Univ. 27, 2440–2454 (2020). https://doi.org/10.1007/s11771-020-4460-5
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DOI: https://doi.org/10.1007/s11771-020-4460-5
Key words
- crack velocity
- dynamic fracture toughness
- particle velocity
- loading rate
- single-cleavage trapezoidal open (SCTO) specimen