无序性对脆性材料冲击破碎的影响

陈兴; 马刚; 周伟; 赖国伟; 来志强

doi:10.7498/aps.67.20180276

摘要

脆性材料受冲击荷载作用产生损伤开裂是一个连续介质离散化的过程.采用连续离散耦合方法模拟了一个脆性圆球以不同初始速度与刚性板的冲击，重点研究了无序性对脆性材料冲击破碎的影响，并对其内在机理进行了分析.本文不考虑材料细观结构的无序性，材料的无序仅体现在细观断裂参数的非均质性.数值实验同样揭示了脆性材料在冲击破坏中存在两种破坏模式，即低速时接触区域的局部损伤和高速时的整体碎裂.研究表明，材料无序性对临界冲击速度、破碎模式、碎片形态影响显著.随着无序度增加，材料的临界速度增大，损伤开裂由少量贯穿性裂纹主导转变为全域性的分叉裂纹.高无序度圆球冲击产生的碎片表面更粗糙，体型更为扁平细长.这与细观断裂的主导机制有关，无序度较高时剪切导致开裂的比重更大，碎片内部损伤裂纹面更多.

关键词:

Abstract

Brittle materials have many excellent properties for structural applications, whereas the brittleness and disorder due to defects and micro-cracks cause failure. Fragmentation may occur and often lead to a catastrophic damage, bring dangers to the users especially when brittle materials suffer dynamic loads like impact and explosion. The impact fragmentation of brittle material belongs to the continuum/discretization domain. The combined finite and discrete element method (FDEM) is used to investigate the impact fragmentation of disordered material in detail. In this work, structural disorder in the brittle material is not considered, and the disorder is only reflected in the strength heterogeneity. Assuming that the mesoscopic fracture parameters of brittle materials obey the Weibull distribution, the degree of disorder can be quantified by the Weibull modulus k. The impact of a brittle sphere against a rigid plate is simulated using the FDEM. The dynamic response can be classified into damage and fragmentation zones. In sphere with low material disorder, cracking pattern is mainly dominated by single or more penetrating cracks. Increasing the disorder degree by smaller k, branch cracks emerge. Finally, it changes into a global branch crack in highly disordered sphere. Besides, mass index analysis indicates that higher disordered sphere has a higher critical velocity in impact events, in which the critical impact velocities equal 10, 15, 40 and 80 m/s when the values of m are 10, 5, 2 and 1, respectively. Furthermore, the principal component analysis is adopted for digging the crack features from fragments morphology description. The statistics of two fragment shape indexes shows that fragments coming from the highly disordered spheres have greater variability with a rougher surface and higher flatness overall, corresponding to the fracture pattern. Finally, we conclude that the effects of disorder on impact fragmentation can be ascribed to the dominant cracking mechanism-specifically, the proportion of shear failure mechanism grows with the disorder degree, implying more non-penetrating branch cracks existing in the fragments. We demonstrate that the effect of disorder on impact fragmentation is probably a consequence of a continuous phase nucleation-avalanche-percolation transition as well.

Keywords:

作者及机构信息

1.
武汉大学水利水电学院, 水资源与水电工程国家重点实验室, 武汉 430072;

2.
武汉大学水利水电学院, 水工岩石力学教育部重点实验室, 武汉 430072

通信作者: 马刚, magang630@whu.edu.cn

基金项目: 国家重点研发计划（批准号：2016YFC0401907）和国家自然科学基金（批准号：51509190，51579193）资助的课题.

Authors and contacts

1.
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China;

2.
Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering, Ministry of Education, Wuhan University, Wuhan 430072, China

Corresponding author: Ma Gang, magang630@whu.edu.cn

Funds: Project supported by the National KeyResearch and Development Program of China (Grant No. 2016YFC0401907) and the National Natural Science Foundation of China (Grant Nos. 51509190, 51579193).

参考文献

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[2]	Biswas S, Ray P, Roy S 2017 Phys. Rev. E 96 63003
[3]	Li W, Bei H, Tong Y, Dmowski W, Gao Y F 2013 Appl. Phys. Lett. 103 171910
[4]	Zhang Y, Zhao D, Yue Y 2017 J. Am. Ceram. Soc. 100 3434
[5]	Wang J G, Zhao D Q, Pan M X, Shek C H, Wang W H 2009 Appl. Phys. Lett. 94 031904
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[8]	Kun F, Wittel F K, Herrmann H J, Kroplin B H, Maloy K J 2006 Phys. Rev. Lett. 96 025504
[9]	Wittel F, Kun F, Herrmann H J, Kroplin B H 2004 Phys. Rev. Lett. 93 035504
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[22]	Zhou W, Tang L, Liu X, Ma G, Chen M 2016 Int. J. Impact Eng. 95 165
[23]	Ma G, Zhou W, Chang X, Chen M 2016 Granul. Matter 18
[24]	Mahabadi O K, Cottrell B E, Grasselli G 2010 Rock Mech. Rock Eng. 43 707
[25]	Ma G, Zhou W, Ng T, Cheng Y, Chang X 2015 Acta Geotech. 10 481
[26]	Ma G, Zhou W, Chang X, Ng T, Yang L 2016 Powder Technol. 301 118
[27]	Ma G, Zhou W, Zhang Y, Wang Q, Chang X 2018 Powder Technol. 325 498
[28]	Ma G, Zhang Y, Zhou W, Ng T, Wang Q, Chen X 2018 Int. J. Impact Eng. 113 132
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[31]	Rao K S, Noferesti H 2008 Defence Sci. J. 58 285
[32]	Cui J, Hao H, Shi Y 2018 Constr. Build. Mater. 160 440
[33]	Ma G, Zhou W, Chang X 2014 Comput. Geotech. 61 132
[34]	Grange S, Forquin P, Mencacci S, Hild F 2008 Int. J. Impact Eng. 35 977
[35]	Pisano G, Carfagni G R 2015 Constr. Build. Mater. 98 741
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[37]	King D S, Fahrenholtz W G, Hilmas G E 2013 J. Eur. Ceram. Soc. 33 2943
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[39]	Siarampi E, Kontonasaki E, Andrikopoulos K S, Kantiranis N, Voyiatzis G A, Zorba T, Paraskevopoulos K M, Koidis P 2014 Dent. Mater. 30 E306
[40]	Guazzato M, Quach L, Albakry M, Swain M V 2005 J. Dent. 33 9
[41]	Yang W, Zhang G P, Zhu X F, Li X W, Meyers M A 2011 J. Mech. Behav. Biomed. 4 1514
[42]	Lin A Y, Meyers M A 2009 J. Mech. Behav. Biomed. 2 607
[43]	Gruber M, Kraleva I, Supancic P, Bielen J, Kiener D, Bermejo R 2017 J. Eur. Ceram. Soc. 37 4397
[44]	Wereszczak A A, Barnes A S, Breder K, Binapal S 2000 J. Mater. Sci. Mater. Electron. 11 291
[45]	Wittel F K, Kun F, Herrmann H J, Kroplin B H 2005 Phys. Rev. E 71 016108
[46]	Tomas J, Schreier M, Groger T, Ehlers S 1999 Powder Technol. 105 39
[47]	Khanal M, Schubert W, Tomas J 2004 Granul. Matter 5 177
[48]	Toussaint R, Hansen A 2006 Phys. Rev. E 73 046103
[49]	Shekhawat A, Zapperi S, Sethna J P 2013 Phys. Rev. Lett. 110 185505

施引文献

[1]	Halasz Z, Nakahara A, Kitsunezaki S, Kun F 2017 Phys. Rev. E 96 033006
[2]	Biswas S, Ray P, Roy S 2017 Phys. Rev. E 96 63003
[3]	Li W, Bei H, Tong Y, Dmowski W, Gao Y F 2013 Appl. Phys. Lett. 103 171910
[4]	Zhang Y, Zhao D, Yue Y 2017 J. Am. Ceram. Soc. 100 3434
[5]	Wang J G, Zhao D Q, Pan M X, Shek C H, Wang W H 2009 Appl. Phys. Lett. 94 031904
[6]	Fu Y F, Liang Z Z, Tang C 2000 Chinese J. Geot. Eng. 6 705 (in Chinese) [傅宇方, 梁正召, 唐春安 2000 岩土工程学报 6 705]
[7]	Oddershede L, Dimon P, Bohr J 1993 Phys. Rev. Lett. 71 3107
[8]	Kun F, Wittel F K, Herrmann H J, Kroplin B H, Maloy K J 2006 Phys. Rev. Lett. 96 025504
[9]	Wittel F, Kun F, Herrmann H J, Kroplin B H 2004 Phys. Rev. Lett. 93 035504
[10]	Pernas-Sanchez J, Artero-Guerrero J A, Varas D, Lopez-Puente J 2015 Exp. Mech. 55 1669
[11]	Parab N D, Guo Z, Hudspeth M C, Claus B J, Fezzaa K, Sun T, Chen W W 2017 Int. J. Impact Eng. 106 146
[12]	Kun F, Herrmann H J 1999 Phys. Rev. E 59 2623
[13]	Behera B, Kun F, Mcnamara S, Herrmann H J 2005 J. Phys.: Condens. Matter 17 S2439
[14]	Sator N, Mechkov S, Sausset F 2008 EPL 81 44002
[15]	Wittel F K, Carmona H A, Kun F, Herrmann H J 2008 Int. J. Fract. 154 105
[16]	Rabczuk T, Eibl J 2003 Int. J. Numer. Meth. Eng. 56 1421
[17]	Su T X, Ma L Q, Liu M B, Chang J Z 2013 Acta Phys. Sin. 62 064702 (in Chinese) [苏铁熊, 马理强, 刘谋斌, 常建忠 2013 物理学报 62 064702]
[18]	Silling S A, Askari E 2005 Comput. Struct. 83 1526
[19]	Li F, Pan J, Sinka C 2011 Int. J. Impact Eng. 38 653
[20]	Yu Y, He H L, Wang W Q, Lu T C 2014 Acta Phys. Sin. 63 246102 (in Chinese) [俞寅, 贺红亮, 王文强, 卢铁城 2014 物理学报 63 246102]
[21]	Munjiza A, Owen D, Bicanic N 1995 Eng. Comput. 12 145
[22]	Zhou W, Tang L, Liu X, Ma G, Chen M 2016 Int. J. Impact Eng. 95 165
[23]	Ma G, Zhou W, Chang X, Chen M 2016 Granul. Matter 18
[24]	Mahabadi O K, Cottrell B E, Grasselli G 2010 Rock Mech. Rock Eng. 43 707
[25]	Ma G, Zhou W, Ng T, Cheng Y, Chang X 2015 Acta Geotech. 10 481
[26]	Ma G, Zhou W, Chang X, Ng T, Yang L 2016 Powder Technol. 301 118
[27]	Ma G, Zhou W, Zhang Y, Wang Q, Chang X 2018 Powder Technol. 325 498
[28]	Ma G, Zhang Y, Zhou W, Ng T, Wang Q, Chen X 2018 Int. J. Impact Eng. 113 132
[29]	Carmona H A, Wittel F K, Kun F 2014 Eur. Phys. J.: Spec. Top 223 2369
[30]	Carmona H A, Wittel F K, Kun F, Herrmann H J 2008 Phys. Rev. E 77 051302
[31]	Rao K S, Noferesti H 2008 Defence Sci. J. 58 285
[32]	Cui J, Hao H, Shi Y 2018 Constr. Build. Mater. 160 440
[33]	Ma G, Zhou W, Chang X 2014 Comput. Geotech. 61 132
[34]	Grange S, Forquin P, Mencacci S, Hild F 2008 Int. J. Impact Eng. 35 977
[35]	Pisano G, Carfagni G R 2015 Constr. Build. Mater. 98 741
[36]	Joshi A A, Pagni P J 1994 Fire Safety J. 22 45
[37]	King D S, Fahrenholtz W G, Hilmas G E 2013 J. Eur. Ceram. Soc. 33 2943
[38]	Gorjan L, Ambrožič M 2012 J. Eur. Ceram. Soc. 32 1221
[39]	Siarampi E, Kontonasaki E, Andrikopoulos K S, Kantiranis N, Voyiatzis G A, Zorba T, Paraskevopoulos K M, Koidis P 2014 Dent. Mater. 30 E306
[40]	Guazzato M, Quach L, Albakry M, Swain M V 2005 J. Dent. 33 9
[41]	Yang W, Zhang G P, Zhu X F, Li X W, Meyers M A 2011 J. Mech. Behav. Biomed. 4 1514
[42]	Lin A Y, Meyers M A 2009 J. Mech. Behav. Biomed. 2 607
[43]	Gruber M, Kraleva I, Supancic P, Bielen J, Kiener D, Bermejo R 2017 J. Eur. Ceram. Soc. 37 4397
[44]	Wereszczak A A, Barnes A S, Breder K, Binapal S 2000 J. Mater. Sci. Mater. Electron. 11 291
[45]	Wittel F K, Kun F, Herrmann H J, Kroplin B H 2005 Phys. Rev. E 71 016108
[46]	Tomas J, Schreier M, Groger T, Ehlers S 1999 Powder Technol. 105 39
[47]	Khanal M, Schubert W, Tomas J 2004 Granul. Matter 5 177
[48]	Toussaint R, Hansen A 2006 Phys. Rev. E 73 046103
[49]	Shekhawat A, Zapperi S, Sethna J P 2013 Phys. Rev. Lett. 110 185505

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