脆性材料动态断裂的介观格子模型

喻寅 李媛媛 贺红亮 王文强

喻寅, 李媛媛, 贺红亮, 王文强. 脆性材料动态断裂的介观格子模型[J]. 高压物理学报, 2019, 33(3): 030106. doi: 10.11858/gywlxb.20190707
引用本文: 喻寅, 李媛媛, 贺红亮, 王文强. 脆性材料动态断裂的介观格子模型[J]. 高压物理学报, 2019, 33(3): 030106. doi: 10.11858/gywlxb.20190707
YU Yin, LI Yuanyuan, HE Hongliang, WANG Wenqiang. Mesoscale Lattice Model for Dynamic Fracture of Brittle Materials[J]. Chinese Journal of High Pressure Physics, 2019, 33(3): 030106. doi: 10.11858/gywlxb.20190707
Citation: YU Yin, LI Yuanyuan, HE Hongliang, WANG Wenqiang. Mesoscale Lattice Model for Dynamic Fracture of Brittle Materials[J]. Chinese Journal of High Pressure Physics, 2019, 33(3): 030106. doi: 10.11858/gywlxb.20190707

脆性材料动态断裂的介观格子模型

doi: 10.11858/gywlxb.20190707
基金项目: 国家自然科学基金(11602244,11772090);冲击波物理与爆轰物理重点实验室装发部预研基金(6142A03020204);国防科技工业局稳定支持科研项目(LSD-KB1805)
详细信息
    作者简介:

    喻 寅(1986-),男,博士,副研究员,主要从事脆性材料的动态变形和断裂研究. E-mail: yuyun86@caep.cn

  • 中图分类号: O369; O346

Mesoscale Lattice Model for Dynamic Fracture of Brittle Materials

  • 摘要: 岩石、陶瓷、玻璃、固体炸药等脆性材料在爆炸与冲击施加的强动载荷作用下易发生迅速的裂纹扩展和灾难性的断裂破碎,造成材料、器件、装置的功能失效和事故危害。理解脆性断裂过程中介观裂纹网络演化与宏观动态响应的关联是提升脆性材料可靠性和安全性的关键,但同时也是计算建模与数值模拟研究面临的难点。为了解决爆炸与冲击加载下脆性材料中裂纹网络随机萌生、裂纹面挤压摩擦、大量裂纹交错扩展等复杂过程带来的算法困难,一种无网格/粒子方法—“格子模型”得到了持续的关注和长足的发展。本文综述了格子模型的原理和方法,介绍了运用格子模型开展脆性断裂研究的代表性成果,分析了格子模型存在的不足与改进的方向。

     

  • 图  格子模型示意图

    Figure  1.  Schematic of the lattice model

    图  格子模型中网格、微结构、缺陷设定示意图

    Figure  2.  Representatives of spring networks, microstructures and defects in the lattice model

    图  橡胶薄膜裂纹扩展的格子模型:(a)格点间的最近邻与次近邻相互作用,(b)不考虑次近邻作用时裂纹直线传播,(c)考虑次近邻作用以表现非局域效应后裂纹扩展路径出现正弦形振荡

    Figure  3.  Lattice model for the crack propagation in a rubber film: (a) the interaction among the nearest lattices and the next nearest neighbors; (b) the crack propagates linearly when the interaction with the next nearest neighbor were ignored; (c) the crack propagates oscillatorily when the nonlocal effect contributed by the next nearest neighbors was modeled

    图  格子模型和有限元网格结合示意图(a),炸药模型图(b)(其中蓝色基体为黏结剂,红色颗粒为炸药晶体),应力波扫过后黏结剂与炸药晶粒的摩擦升温(c)

    Figure  4.  (a) Schematic of a model combined by lattice model and finite element method; (b) the model of polymer-bonded explosives (Blue matrix represent binder, red particles represent HMX crystals); (c) the temperature rise induced by the friction between explosive particles and binders under dynamic loading

    图  裂纹扩展、气体扩散和燃烧反应耦合的格子模型计算结果

    Figure  5.  Simulations of crack extension, gas diffusion and combustion by lattice model

    图  多孔陶瓷冲击破坏的介观机制和宏观特征

    Figure  6.  Mesoscopic deformation and macroscopic response of shocked porous ceramics

  • [1] BUEHLER M J, GAO H. Dynamical fracture instabilities due to local hyperelasticity at crack tips [J]. Nature, 2006, 439(7074): 307–310. doi: 10.1038/nature04408
    [2] BUEHLER M J, ABRAHAM F F, GAO H. Hyperelasticity governs dynamic fracture at a critical length scale [J]. Nature, 2003, 426(6963): 141–146. doi: 10.1038/nature02096
    [3] RAVI-CHANDAR K, YANG B. On the role of microcracks in the dynamic fracture of brittle materials [J]. Journal of the Mechanics and Physics of Solids, 1997, 45(4): 535–563. doi: 10.1016/S0022-5096(96)00096-8
    [4] FINEBERG J, GROSS S P, MARDER M, et al. Instability in the propagation of fast cracks [J]. Physical Review B, 1992, 45(10): 5146–5154. doi: 10.1103/PhysRevB.45.5146
    [5] SHARON E, GROSS S P, FINEBERG J. Energy dissipation in dynamic fracture [J]. Physical Review Letters, 1996, 76(12): 2117–2120. doi: 10.1103/PhysRevLett.76.2117
    [6] 张庆明, 黄风雷. 超高速碰撞动力学引论 [M]. 北京: 科学出版社, 2000.
    [7] BAKER J R. Hypervelocity crater penetration depth and diameter—a linear function of impact velocity? [J]. International Journal of Impact Engineering, 1995, 17(1/2/3): 25–35.
    [8] CHHABILDAS L C, REINHART W D, THORNHILL T F, et al. Debris generation and propagation phenomenology from hypervelocity impacts on aluminum from 6 to 11 km/s [J]. International Journal of Impact Engineering, 2003, 29(1): 185–202. doi: 10.1016/j.ijimpeng.2003.09.016
    [9] 王新荣, 陈永波.有限元法基础及ANSYS应用 [M].北京: 科学出版社, 2008.
    [10] CAMACHO G T, ORTIZ M. Computational modeling of impact damage in brittle materials [J]. International Journal of Solids and Structures, 1996, 33(20/21/22): 2899–2938.
    [11] ESPINOSA H D, ZAVATTIERI P D. A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part I: theory and numerical implementation [J]. Mechanics of Materials, 2003, 35(3): 333–364.
    [12] ESPINOSA H D, ZAVATTIERI P D. A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part II: numerical examples [J]. Mechanics of Materials, 2003, 35(3): 365–394.
    [13] ZAVATTIERI P D, RAGHURAM P V, ESPINOSA H D. A computational model of ceramic microstructures subjected to multi-axial dynamic loading [J]. Journal of the Mechanics and Physics of Solids, 2001, 49(1): 27–68. doi: 10.1016/S0022-5096(00)00028-4
    [14] BOURNE N K, MILLETT J C F, CHEN M, et al. On the Hugoniot elastic limit in polycrystalline alumina [J]. Journal of Applied Physics, 2007, 102(7): 073514. doi: 10.1063/1.2787154
    [15] 马上. 超高速碰撞问题的三维物质点法 [D]. 北京: 清华大学, 2005.
    [16] SULSKY D, CHEN Z, SCHREYER H L. A particle method for history-dependent materials [J]. Computer Methods in Applied Mechanics and Engineering, 1994, 118(1/2): 179–196.
    [17] SULSKY D, ZHOU S J, SCHREYER H L. Application of a particle-in-cell method to solid mechanics [J]. Computer Physics Communications, 1995, 87(1/2): 236–252.
    [18] CHEN Z, HU W, SHEN L, et al. An evaluation of the MPM for simulating dynamic failure with damage diffusion [J]. Engineering Fracture Mechanics, 2002, 69(17): 1873–1890. doi: 10.1016/S0013-7944(02)00066-8
    [19] XU A, PAN X F, ZHANG G, et al. Material-point simulation of cavity collapse under shock [J]. Journal of Physics: Condensed Matter, 2007, 19(32): 326212. doi: 10.1088/0953-8984/19/32/326212
    [20] LI F, PAN J, SINKA C. Modelling brittle impact failure of disc particles using material point method [J]. International Journal of Impact Engineering, 2011, 38(7): 653–660. doi: 10.1016/j.ijimpeng.2011.02.004
    [21] DAPHALAPURKAR N P, LU H, COKER D, et al. Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method [J]. International Journal of Fracture, 2007, 143(1): 79–102. doi: 10.1007/s10704-007-9051-z
    [22] SULSKY D, SCHREYER L. MPM simulation of dynamic material failure with a decohesion constitutive model [J]. European Journal of Mechanics-A/Solids, 2004, 23(3): 423–445. doi: 10.1016/j.euromechsol.2004.02.007
    [23] SILLING S A. Reformulation of elasticity theory for discontinuities and long-range forces [J]. Journal of the Mechanics and Physics of Solids, 2000, 48(1): 175–209. doi: 10.1016/S0022-5096(99)00029-0
    [24] HELLAN K. Introduction to fracture mechanics [M]. New York: McGraw-Hill, 1985.
    [25] HA Y D, BOBARU F. Studies of dynamic crack propagation and crack branching with peridynamics [J]. International Journal of Fracture, 2010, 162(1/2): 229–244.
    [26] HA Y D, BOBARU F. Characteristics of dynamic brittle fracture captured with peridynamics [J]. Engineering Fracture Mechanics, 2011, 78(6): 1156–1168. doi: 10.1016/j.engfracmech.2010.11.020
    [27] SILLING S A, EPTON M, WECKNER O, et al. Peridynamic states and constitutive modeling [J]. Journal of Elasticity, 2007, 88(2): 151–184. doi: 10.1007/s10659-007-9125-1
    [28] GHAJARI M, IANNUCCI L, CURTIS P. A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media [J]. Computer Methods in Applied Mechanics and Engineering, 2014, 276: 431–452. doi: 10.1016/j.cma.2014.04.002
    [29] LIU W, HONG J W. A coupling approach of discretized peridynamics with finite element method [J]. Computer Methods in Applied Mechanics and Engineering, 2012, 245: 163–175.
    [30] HRENNIKOFF A. Solution of problems of elasticity by the framework method [J]. Journal of Applied Mechanics, 1941, 8(4): 169.
    [31] ASHURST W T, HOOVER W G. Microscopic fracture studies in the two-dimensional triangular lattice [J]. Physical Review B, 1976, 14(4): 1465. doi: 10.1103/PhysRevB.14.1465
    [32] KEATING P N. Theory of the third-order elastic constants of diamond-like crystals [J]. Physical Review, 1966, 149(2): 674. doi: 10.1103/PhysRev.149.674
    [33] KIRKWOOD J G. The skeletal modes of vibration of long chain molecules [J]. The Journal of Chemical Physics, 1939, 7(7): 506–509. doi: 10.1063/1.1750479
    [34] CUNDALL P A, STRACK O D L. A discrete numerical model for granular assemblies [J]. Geotechnique, 1979, 29(1): 47–65. doi: 10.1680/geot.1979.29.1.47
    [35] ALAVA M J, NUKALA P K V V, ZAPPERI S. Statistical models of fracture [J]. Advances in Physics, 2006, 55(3/4): 349–476.
    [36] PAZDNIAKOU A, ADLER P M. Lattice spring models [J]. Transport in Porous Media, 2012, 93(2): 243–262. doi: 10.1007/s11242-012-9955-6
    [37] FRENKEL D, SMIT B. FRENKEL D, et al. Understanding molecular simulation: from algorithms to applications [M]. Holand: Academic Press, 2001.
    [38] BEALE P D, SROLOVITZ D J. Elastic fracture in random materials [J]. Physical Review B, 1988, 37(10): 5500. doi: 10.1103/PhysRevB.37.5500
    [39] BUXTON G A, CARE C M, CLEAVER D J. A lattice spring model of heterogeneous materials with plasticity [J]. Modelling and Simulation in Materials Science and Engineering, 2001, 9(6): 485. doi: 10.1088/0965-0393/9/6/302
    [40] SROLOVITZ D J, BEALE P D. Computer simulation of failure in an elastic model with randomly distributed defects [J]. Journal of the American Ceramic Society, 1988, 71(5): 362–369. doi: 10.1111/jace.1988.71.issue-5
    [41] CALDARELLI G, CASTELLANO C, PETRI A. Criticality in models for fracture in disordered media [J]. Physica A: Statistical Mechanics and Its Applications, 1999, 270(1/2): 15–20.
    [42] PARISI A, CALDARELLI G. Physica A: statistical mechanics and its applications [J]. Physica A, 2000, 280(1/2): 161.
    [43] YAN H, LI G, SANDER L M. Fracture growth in 2d elastic networks with Born model [J]. Europhysics Letters, 1989, 10(1): 7. doi: 10.1209/0295-5075/10/1/002
    [44] GRAH M, ALZEBDEH K, SHENG P Y, et al. Brittle intergranular failure in 2D microstructures: experiments and computer simulations [J]. Acta Materialia, 1996, 44(10): 4003–4018. doi: 10.1016/S1359-6454(96)00044-4
    [45] LILLIU G, VAN MIER J G M. 3D lattice type fracture model for concrete [J]. Engineering Fracture Mechanics, 2003, 70(7/8): 927–941.
    [46] ZHAO G F, FANG J, ZHAO J. A 3D distinct lattice spring model for elasticity and dynamic failure [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2011, 35(8): 859–885. doi: 10.1002/nag.v35.8
    [47] YU Y, WANG W, HE H, et al. Modeling multiscale evolution of numerous voids in shocked brittle material [J]. Physical Review E, 2014, 89(4): 043309. doi: 10.1103/PhysRevE.89.043309
    [48] CASE S, HORIE Y. Discrete element simulation of shock wave propagation in polycrystalline copper [J]. Journal of the Mechanics and Physics of Solids, 2007, 55(3): 589–614. doi: 10.1016/j.jmps.2006.08.003
    [49] YANO K, HORIE Y. Discrete-element modeling of shock compression of polycrystalline copper [J]. Physical Review B, 1999, 59(21): 13672. doi: 10.1103/PhysRevB.59.13672
    [50] WANG Y C, YIN X C, KE F, et al. Numerical simulation of rock failure and earthquake process on mesoscopic scale [J]. Pure and Applied Geophysics, 2000, 157(11/12): 1905–1928.
    [51] OSTOJA-STARZEWSKI M. Lattice models in micromechanics [J]. Applied Mechanics Reviews, 2002, 55(1): 35–60. doi: 10.1115/1.1432990
    [52] GUSEV A A. Finite element mapping for spring network representations of the mechanics of solids [J]. Physical Review Letters, 2004, 93(3): 034302. doi: 10.1103/PhysRevLett.93.034302
    [53] GRIFFITH A A. VI The phenomena of rupture and flow in solids [J]. Philosophical Transactions of the Royal Society of London Series A, 1921, 221(582): 163–198.
    [54] YU Y, WANG W, HE H, et al. Mesoscopic deformation features of shocked porous ceramic: polycrystalline modeling and experimental observations [J]. Journal of Applied Physics, 2015, 117(12): 125901. doi: 10.1063/1.4916244
    [55] ZHANG Z, DING J, GHASSEMI A, et al. A hyperelastic-bilinear potential for lattice model with fracture energy conservation [J]. Engineering Fracture Mechanics, 2015, 142: 220–235. doi: 10.1016/j.engfracmech.2015.06.006
    [56] ZAPPERI S, VESPIGNANI A, STANLEY H E. Plasticity and avalanche behaviour in microfracturing phenomena [J]. Nature, 1997, 388(6643): 658. doi: 10.1038/41737
    [57] KALE S, OSTOJA-STARZEWSKI M. Elastic-plastic-brittle transitions and avalanches in disordered media [J]. Physical Review Letters, 2014, 112(4): 045503. doi: 10.1103/PhysRevLett.112.045503
    [58] KALE S, OSTOJA-STARZEWSKI M. Morphological study of elastic-plastic-brittle transitions in disordered media [J]. Physical Review E, 2014, 90(4): 042405. doi: 10.1103/PhysRevE.90.042405
    [59] OSTOJA-STARZEWSKI M, WANG G. Particle modeling of random crack patterns in epoxy plates [J]. Probabilistic Engineering Mechanics, 2006, 21(3): 267–275. doi: 10.1016/j.probengmech.2005.10.007
    [60] MASTILOVIC S, KRAJCINOVIC D. High-velocity expansion of a cavity within a brittle material [J]. Journal of the Mechanics and Physics of Solids, 1999, 47(3): 577–610. doi: 10.1016/S0022-5096(98)00040-4
    [61] WILNER B. Stress analysis of particles in metals [J]. Journal of the Mechanics and Physics of Solids, 1988, 36(2): 141–165. doi: 10.1016/S0022-5096(98)90002-3
    [62] WANG Y, ALONSO-MARROQUIN F. A finite deformation method for discrete modeling: particle rotation and parameter calibration [J]. Granular Matter, 2009, 11(5): 331–343. doi: 10.1007/s10035-009-0146-2
    [63] WANG Y, MORA P. Modeling wing crack extension: implications for the ingredients of discrete element model [M]// Earthquakes: Simulations, Sources and Tsunamis. Birkhäuser Basel, 2008: 609-620.
    [64] WANG Z L, KONIETZKY H, SHEN R F. Coupled finite element and discrete element method for underground blast in faulted rock masses [J]. Soil Dynamics and Earthquake Engineering, 2009, 29(6): 939–945. doi: 10.1016/j.soildyn.2008.11.002
    [65] DING J, ZHANG Z, GE X. Lattice structure: scaling of strain related energy density [J]. Theoretical and Applied Fracture Mechanics, 2015, 79: 84–90. doi: 10.1016/j.tafmec.2015.05.009
    [66] LIU X, MARTIN C L, DELETTE G, et al. Elasticity and strength of partially sintered ceramics [J]. Journal of the Mechanics and Physics of Solids, 2010, 58(6): 829–842. doi: 10.1016/j.jmps.2010.04.007
    [67] LIU X, MARTIN C L, BOUVARD D, et al. Strength of highly porous ceramic electrodes [J]. Journal of the American Ceramic Society, 2011, 94(10): 3500–3508. doi: 10.1111/j.1551-2916.2011.04669.x
    [68] LIU X, MARTIN C L, DELETTE G, et al. Microstructure of porous composite electrodes generated by the discrete element method [J]. Journal of Power Sources, 2011, 196(4): 2046–2054. doi: 10.1016/j.jpowsour.2010.09.033
    [69] 吕文银. 陶瓷材料压缩破坏的数值模拟 [D]. 宁波: 宁波大学, 2017.
    [70] 吴建奎. 冲击加载下裂纹高速扩展的数值模拟研究 [D]. 沈阳: 东北大学, 2016.
    [71] WANG W, CHEN S. Hyperelasticity, viscoelasticity, and nonlocal elasticity govern dynamic fracture in rubber [J]. Physical Review Letters, 2005, 95(14): 144301. doi: 10.1103/PhysRevLett.95.144301
    [72] 傅华. 材料在冲击荷载下细观变形特征的数值模拟初步研究 [D]. 绵阳: 中国工程物理研究院, 2006.
    [73] 王文强, 于继东, 尚海林. 撞击条件下炸药热点形成和燃烧的数值模拟研究[R]. 绵阳: 中国工程物理研究院流体物理研究所, 2012.
    [74] YU Y, WANG W, CHEN K, et al. Controllable fracture in shocked ceramics: shielding one region from severely fractured state with the sacrifice of another region [J]. International Journal of Solids and Structures, 2018, 135: 137–147. doi: 10.1016/j.ijsolstr.2017.11.016
  • 加载中
图(6)
计量
  • 文章访问数:  10893
  • HTML全文浏览量:  3375
  • PDF下载量:  54
出版历程
  • 收稿日期:  2019-01-10
  • 修回日期:  2019-03-25
  • 发布日期:  2019-08-25

目录

    /

    返回文章
    返回