Mesoscale Lattice Model for Dynamic Fracture of Brittle Materials

YU Yin; LI Yuanyuan; HE Hongliang; WANG Wenqiang

doi:10.11858/gywlxb.20190707

Volume 33 Issue 3

Jun 2019

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Chinese Journal of High Pressure Physics > 2019 > 33(3): 030106.

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

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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

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Mesoscale Lattice Model for Dynamic Fracture of Brittle Materials

doi: 10.11858/gywlxb.20190707

National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, CAEP, Mianyang 621999, China

Received Date: 10 Jan 2019
Rev Recd Date: 25 Mar 2019
Publish Date: 25 Aug 2019

Abstract

Abstract

Rapid crack propagation and catastrophic fragmentation frequently occur in brittle materials, such as rocks, ceramics, glass and solid explosives, under intense dynamic loading imposed by the explosion and impact. Understanding the correlation between the evolution of mesoscopic crack network and the macroscopic dynamic response plays a key role to improve the reliability and the safety of brittle materials, while it still poses a great challenge to such modeling and simulation. In order to overcome the algorithm difficulties caused by complex processes, such as the random initiation of crack network, the extrusion and friction of crack surfaces, and the staggered propagation of a large number of cracks in brittle materials subjected to explosion and impact loading, the lattice model, one of meshfree methods, has received sustained attention and considerable development. In this paper, we introduce the theory and implement of the lattice model and its representative results on brittle fracture research. Its shortcomings and the direction of improvement have also been discussed.
- lattice model,
- brittle materials,
- dynamic fracture,
- crack network,
- meshfree method

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References(74)

References

[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

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Mesoscale Lattice Model for Dynamic Fracture of Brittle Materials

doi: 10.11858/gywlxb.20190707

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Mesoscale Lattice Model for Dynamic Fracture of Brittle Materials

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