炸药冲击响应的二维细观离散元模拟
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摘要
细观结构对炸药的冲击响应具有重要影响,颗粒尺度的数值模拟是目前研究这一问题的主要手段。本文用离散元方法模拟了冲击作用下颗粒炸药和塑料粘结炸药中热点的形成和发展。
首先利用Voronoi拼图建立了可近似反映炸药实际细观结构的离散元几何模型。相应地改进了离散元程序DM2,使之适应本文模拟的要求。并改进了原有的法向作用力模型,即用换算后的Hugoniot关系取代原有的中心作用力关系,用物理的体积粘性取代原有的法向振荡阻尼。此外,引入“代表体元”的概念对体应变和剪应变进行了新的定义和计算。
在此基础上,开展了炸药冲击响应的二维细观离散元模拟。利用文献给出的物理参数,得到了基本合理的计算结果。在可对比的算例中,热点的温度范围与文献给出的基本一致。在本文的算例中,粘塑性变形是温度局域化的主要原因,而摩擦和体积粘性等机制影响很小。通过对比颗粒炸药和塑料粘结炸药,发现粘结剂的缓冲作用可降低炸药颗粒的热点温度。对不同几何形状炸药部件与固壁碰撞的模拟表明,加载方式和边界条件对热点的温度影响较大,而对热点的空间分布影响相对较小。对孔洞塌缩的热点形成机制的计算结果表明,孔洞塌缩可使当地温度显著提高,温升主要是由于应力波对孔洞周围的加载—卸载—再加载导致炸药颗粒剧烈的粘塑性变形。
Mesoscopic structures significantly affect the shock response of explosives. Presently this problem is mostly investigated through grain scale numerical simulations. In this thesis, the discrete element method has been used to simulate the formation and development of hot spots in shock loaded granular and plastic bonded explosives.
The geometrical part of the discrete element model that mimics the mesoscopic structure of explosives was created based on the Voronoi tessellation. Correspondingly, the discrete element code DM2 was modified to satisfy the special needs of this study. Improvements were also made on the original normal force model. That is, the central force was replaced by a modified Hugoniot relation, and the artificial damping was replaced by the physical volumetric viscosity. In addition, the idea of representative volume element has been used to redefine both the volumetric and the shear strains.
Based on the above efforts, two dimensional mesoscale discrete element simulation of shock response of explosives has been performed. Reasonable results were obtained by using the physical parameters from the literature. The temperature scale of hot spots is comparable to that in other works. In this study, viscoplastic deformation is the main cause for temperature localization, whereas the effects of friction and volumetric viscosity are very small. By comparing the granular and the plastic bonded explosives, it was found that the cushioning effect of the binder can reduce the temperatures of hot spots. Simulations of explosives of different shapes impacting on a rigid wall showed that the loading method and boundary condition affected the temperatures of hot spots more than affecting their spatial distribution. For explosive sample with a void inside, it was found that void collapse can significantly raise the local temperature. The reason for this is the severe viscoplastic deformation in materials surrounding the void due to loading, unloading, and reloading of the stress wave.
首先利用Voronoi拼图建立了可近似反映炸药实际细观结构的离散元几何模型。相应地改进了离散元程序DM2,使之适应本文模拟的要求。并改进了原有的法向作用力模型,即用换算后的Hugoniot关系取代原有的中心作用力关系,用物理的体积粘性取代原有的法向振荡阻尼。此外,引入“代表体元”的概念对体应变和剪应变进行了新的定义和计算。
在此基础上,开展了炸药冲击响应的二维细观离散元模拟。利用文献给出的物理参数,得到了基本合理的计算结果。在可对比的算例中,热点的温度范围与文献给出的基本一致。在本文的算例中,粘塑性变形是温度局域化的主要原因,而摩擦和体积粘性等机制影响很小。通过对比颗粒炸药和塑料粘结炸药,发现粘结剂的缓冲作用可降低炸药颗粒的热点温度。对不同几何形状炸药部件与固壁碰撞的模拟表明,加载方式和边界条件对热点的温度影响较大,而对热点的空间分布影响相对较小。对孔洞塌缩的热点形成机制的计算结果表明,孔洞塌缩可使当地温度显著提高,温升主要是由于应力波对孔洞周围的加载—卸载—再加载导致炸药颗粒剧烈的粘塑性变形。
Mesoscopic structures significantly affect the shock response of explosives. Presently this problem is mostly investigated through grain scale numerical simulations. In this thesis, the discrete element method has been used to simulate the formation and development of hot spots in shock loaded granular and plastic bonded explosives.
The geometrical part of the discrete element model that mimics the mesoscopic structure of explosives was created based on the Voronoi tessellation. Correspondingly, the discrete element code DM2 was modified to satisfy the special needs of this study. Improvements were also made on the original normal force model. That is, the central force was replaced by a modified Hugoniot relation, and the artificial damping was replaced by the physical volumetric viscosity. In addition, the idea of representative volume element has been used to redefine both the volumetric and the shear strains.
Based on the above efforts, two dimensional mesoscale discrete element simulation of shock response of explosives has been performed. Reasonable results were obtained by using the physical parameters from the literature. The temperature scale of hot spots is comparable to that in other works. In this study, viscoplastic deformation is the main cause for temperature localization, whereas the effects of friction and volumetric viscosity are very small. By comparing the granular and the plastic bonded explosives, it was found that the cushioning effect of the binder can reduce the temperatures of hot spots. Simulations of explosives of different shapes impacting on a rigid wall showed that the loading method and boundary condition affected the temperatures of hot spots more than affecting their spatial distribution. For explosive sample with a void inside, it was found that void collapse can significantly raise the local temperature. The reason for this is the severe viscoplastic deformation in materials surrounding the void due to loading, unloading, and reloading of the stress wave.
引文
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[2]M.Kornhauser,Correlation of explosive sensitivity to compressional inputs,Proc.of 9th(Int.)Symp.on Detonation,1989,1451-1459.
[3]R.L.Gustavsen,S.A.Sheffield,R.R.Alcon.Measurements of shock initiation in the tri-amino-trinitro-benzene based explosive PBX 9502 Wave forms from embedded gauges and comparison of four different material lots.J.Appl.Phys.99,114907(2006).
[4]C.M.Tarver,J.Hallquist,and L.M.Erickson.Eighth Symposium(International)on Detonation,Naval Surface Weapons Center NSWC MP86-194,Albuquerque,NM,1985,pp.951-961.
[5]J.N.Johnson,P.K.Tang,C.A.Forest.Shock-wave initiation of heterogeneous reactive solids.J.Appl.Phys.57,4323(1985).
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[11]T.N.Dey and J.R.Kamm.Numerical modeling of shear band formation in PBX-9501.Proceedings of the 11th Symposium(International)on Detonation,pp.725-734(1998)
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[15]M.R.Baer and W.M.Trott.Theoretical and experimental mesoscale studies of impact-loaded granular explosive and simulant materials.Presented at the 12th Symposium(International)on Detonation (2002)
[16]S.G.Bardenhagen,et al.Direct numerical simulation of weak shocks in granular material.Presented at the 12th Symposium(International)on Detonation(2002)
[17]S.G.Bardenhagen,et al.Shear deformation in granular material.Proceedings of the 11th Symposium(International)on Detonation,pp.547-555(1998)
[18]S.G.Bardenhagen,et al.The material-point method for granular materials.Comput.Methods Appl.Mech.Engrg.pp.529-541,187(2000)
[19]UCRL-MI-125901 Rev.1,2000
[20]P.A.Cundall,O D L.Strack.A discrete numerical model for granular assemblies[J].Geotechnique,1979,29;47-65.
[21]F.V.Donze,et al.Numerical study of compressive behavior of concrete at high strain rates[J].Journal of Engineering Mechanics,1999,125(10);1154-1163.
[22]F.V.Donze,et al.Modeling fractures in rock blasting[J].Int.J.Rock Mech.Min.Sci.,1997,34(8);1153-1163.
[23]W.G.Buttlar,Z.You.Discrete element modeling of asphalt concrete;a micro-fabric approach[A].Annual Meeting of the Transportation Research Board,Washinton,D.C.,2001.
[24]L.I.Slepyan.Models and Phenomena in Fracture Mechanics[M].Berlin;Springer,2002.
[25]J.Fineberg,Marder M.Physics Reports,1999,313;1-.
[26]L.M.Sander,S.V.Ghaisas.Physical Review Letters,1999,83(10);1994-.
[27]O.Kresse,L.Truskinovsky.Journal of the Mechanics and Physics of Solids,2004,52;521-.
[28]L.Truskinovsky,A.Vainchtein.Journal of the Mechanics and Physics of Solids,2004,52;1421-.
[29]S.Case,Y.Horie.Discrete element simulation of shock wave propagation in polycrystalline copper[J],Journal of the Mechanics and Physics of Solids,2006,10.1016/j.jmps.2006.08.003.
[30]P.A.Cundall.A computer model for simulating progressive large scale movement in block rock system,Symposium ISRM,1971,Proc 2;129-136
[31]唐志平.三维离散元方法及其在冲击力学中的应用.中国科学,2003,17;899.
[32]Tang Z P,Horie Y and Psakhie S G.Discrete meso-element dynamic simulation of shock response of reactive,porous solids[A].in Shock Compression of Condensed Matter-1995[C].AIP,1996.657.
[33]Tang Z P,HorieY and Psakhie S G.Discrete Meso-element modeling of shock processes in powders[A]Graham R A,et al.Shock Compression of Solids,Ⅳ,[M].Springer-Verlag,1997.143-176.
[34]Tang Z P,et al.Discrete meso-element modeling of shock processes in powders,Vol.1,Theory and model calculations[R]Technical Report,NCSU,1995.
[35]王文强.离散元方法及其在材料和结构力学响应分析中的应用.博士学位论文,中国科学技术大学,2000.
[36]H.Tan,C.Liu,et al.The cohesive law for the particle/matrix interfaces in high explosives[J],J.Mech.Phys.Solids 53,1892-1917.
[37]J.E.Reaugh Grain-scale Dynamics in Explosive.UCRL-ID-150388.
[38]陈鹏万.高聚物粘结炸药的细观结构和力学性能.中国科学院力学研究所博士后研究工作报告,2001.
[39]D.P.Bentz,E.J.Garboczi,and K.A.Snyder,"A Hard Core / Soft Shell Microstructural Model for Studying Percolation and Transport in Three-Dimensional Composite Media," National Institute of Standards and Technology report NISTR 6265,Gaithersburg,MD,January 1999.
[40]R.Menikoff,T.D.Sewell,et al.Constituent Properties of HMX Needed for Meso-Scale Simulations[R],LA-UR-00-3804-rev.
[41]C.L.Mader,Numerical Modeling of Detonations,University of California Press,Berkeley,CA,1979.
[42]R.Menikoff.Pore collapse and hot spots in HMX,in Shock Compression of Condensed Matter,2003,M.D.Furnish,Y.M.Gupta,J.W.Forbes eds.,AIP Press,2003,pp.393-396.
[43]A.M.Milne,N.K.Bourne.Experimental and Numerical Study of Temperatures in Cavity Collapse.in Shock Compression of Condensed Matter,2001,Y.Horie,N.Thadani,M.Furnish,eds),pp.914-917.
[44]G.L.Ball,B.P.Leighton,M.J.Schofield.Shock-Induced Collapse of a Cylindrical Air Cavity in Water;A Free-Lagrange Simulation.Shock Waves 10,265,2000.
[45]P.W.Randles,L.D.Libersky.Normalized SPH with Stress Points.Int.J.Num.Meth.Engng.,48,1445,2000.
[46]A.A.Gusev,Finite Element Mapping for Spring Network Representations of the Mechanics of Solids.Phys.Rev.Lett.93,034302(2004).
[2]M.Kornhauser,Correlation of explosive sensitivity to compressional inputs,Proc.of 9th(Int.)Symp.on Detonation,1989,1451-1459.
[3]R.L.Gustavsen,S.A.Sheffield,R.R.Alcon.Measurements of shock initiation in the tri-amino-trinitro-benzene based explosive PBX 9502 Wave forms from embedded gauges and comparison of four different material lots.J.Appl.Phys.99,114907(2006).
[4]C.M.Tarver,J.Hallquist,and L.M.Erickson.Eighth Symposium(International)on Detonation,Naval Surface Weapons Center NSWC MP86-194,Albuquerque,NM,1985,pp.951-961.
[5]J.N.Johnson,P.K.Tang,C.A.Forest.Shock-wave initiation of heterogeneous reactive solids.J.Appl.Phys.57,4323(1985).
[6]C.M.Tarver.Next Generation Experiments and Models for Shock Initiation and Detonation of Solid Explosives[C],in Shock Compression of Condensed Matter-1999,M.D.Furnish,L.C.Chhabildas,and R.S.Hixson,eds,AIP Press,New York,1999,pp.873-877.
[7]F.P.Bowden,A.lb.Yoffe.Initiation and Growth of Explosion in Liquids and Solids,Cambridge Press,MA,1985.
[8]C.B.Skidmore,et al.The evolution of microstructural changes in pressed HMX explosives.Proceedings of the 11th Symposium(International)on Detonation,pp.556-564(1998)
[9]J.K.Dienes,et al.Progress in statistical crack mechanics;an approach to initiation.Presented at the 12th Symposium(International)on Detonation(2002)
[10]J.K.Dienes and J.D.Kershner.Multiple-shock initiation via statistical crack mechanics.Proceedings of the 11th Symposium(International)on Detonation,pp.717-724(1998)
[11]T.N.Dey and J.R.Kamm.Numerical modeling of shear band formation in PBX-9501.Proceedings of the 11th Symposium(International)on Detonation,pp.725-734(1998)
[12]P.A.Conley,et al.Microstructural effets in shock initiation.Proceedings of the 11th Symposium(International)on Detonation,pp.768-780(1998)
[13]Ralph Menikoff.Granular explosives and initiation sensitivity.Los Alamos National Laboratory,1999.
[14]M.R.Baer,et al.Micromechanical modeling of heterogeneous energetic materials.Proceedings of the 11th Symposium(International)on Detonation,pp.788-797(1998)
[15]M.R.Baer and W.M.Trott.Theoretical and experimental mesoscale studies of impact-loaded granular explosive and simulant materials.Presented at the 12th Symposium(International)on Detonation (2002)
[16]S.G.Bardenhagen,et al.Direct numerical simulation of weak shocks in granular material.Presented at the 12th Symposium(International)on Detonation(2002)
[17]S.G.Bardenhagen,et al.Shear deformation in granular material.Proceedings of the 11th Symposium(International)on Detonation,pp.547-555(1998)
[18]S.G.Bardenhagen,et al.The material-point method for granular materials.Comput.Methods Appl.Mech.Engrg.pp.529-541,187(2000)
[19]UCRL-MI-125901 Rev.1,2000
[20]P.A.Cundall,O D L.Strack.A discrete numerical model for granular assemblies[J].Geotechnique,1979,29;47-65.
[21]F.V.Donze,et al.Numerical study of compressive behavior of concrete at high strain rates[J].Journal of Engineering Mechanics,1999,125(10);1154-1163.
[22]F.V.Donze,et al.Modeling fractures in rock blasting[J].Int.J.Rock Mech.Min.Sci.,1997,34(8);1153-1163.
[23]W.G.Buttlar,Z.You.Discrete element modeling of asphalt concrete;a micro-fabric approach[A].Annual Meeting of the Transportation Research Board,Washinton,D.C.,2001.
[24]L.I.Slepyan.Models and Phenomena in Fracture Mechanics[M].Berlin;Springer,2002.
[25]J.Fineberg,Marder M.Physics Reports,1999,313;1-.
[26]L.M.Sander,S.V.Ghaisas.Physical Review Letters,1999,83(10);1994-.
[27]O.Kresse,L.Truskinovsky.Journal of the Mechanics and Physics of Solids,2004,52;521-.
[28]L.Truskinovsky,A.Vainchtein.Journal of the Mechanics and Physics of Solids,2004,52;1421-.
[29]S.Case,Y.Horie.Discrete element simulation of shock wave propagation in polycrystalline copper[J],Journal of the Mechanics and Physics of Solids,2006,10.1016/j.jmps.2006.08.003.
[30]P.A.Cundall.A computer model for simulating progressive large scale movement in block rock system,Symposium ISRM,1971,Proc 2;129-136
[31]唐志平.三维离散元方法及其在冲击力学中的应用.中国科学,2003,17;899.
[32]Tang Z P,Horie Y and Psakhie S G.Discrete meso-element dynamic simulation of shock response of reactive,porous solids[A].in Shock Compression of Condensed Matter-1995[C].AIP,1996.657.
[33]Tang Z P,HorieY and Psakhie S G.Discrete Meso-element modeling of shock processes in powders[A]Graham R A,et al.Shock Compression of Solids,Ⅳ,[M].Springer-Verlag,1997.143-176.
[34]Tang Z P,et al.Discrete meso-element modeling of shock processes in powders,Vol.1,Theory and model calculations[R]Technical Report,NCSU,1995.
[35]王文强.离散元方法及其在材料和结构力学响应分析中的应用.博士学位论文,中国科学技术大学,2000.
[36]H.Tan,C.Liu,et al.The cohesive law for the particle/matrix interfaces in high explosives[J],J.Mech.Phys.Solids 53,1892-1917.
[37]J.E.Reaugh Grain-scale Dynamics in Explosive.UCRL-ID-150388.
[38]陈鹏万.高聚物粘结炸药的细观结构和力学性能.中国科学院力学研究所博士后研究工作报告,2001.
[39]D.P.Bentz,E.J.Garboczi,and K.A.Snyder,"A Hard Core / Soft Shell Microstructural Model for Studying Percolation and Transport in Three-Dimensional Composite Media," National Institute of Standards and Technology report NISTR 6265,Gaithersburg,MD,January 1999.
[40]R.Menikoff,T.D.Sewell,et al.Constituent Properties of HMX Needed for Meso-Scale Simulations[R],LA-UR-00-3804-rev.
[41]C.L.Mader,Numerical Modeling of Detonations,University of California Press,Berkeley,CA,1979.
[42]R.Menikoff.Pore collapse and hot spots in HMX,in Shock Compression of Condensed Matter,2003,M.D.Furnish,Y.M.Gupta,J.W.Forbes eds.,AIP Press,2003,pp.393-396.
[43]A.M.Milne,N.K.Bourne.Experimental and Numerical Study of Temperatures in Cavity Collapse.in Shock Compression of Condensed Matter,2001,Y.Horie,N.Thadani,M.Furnish,eds),pp.914-917.
[44]G.L.Ball,B.P.Leighton,M.J.Schofield.Shock-Induced Collapse of a Cylindrical Air Cavity in Water;A Free-Lagrange Simulation.Shock Waves 10,265,2000.
[45]P.W.Randles,L.D.Libersky.Normalized SPH with Stress Points.Int.J.Num.Meth.Engng.,48,1445,2000.
[46]A.A.Gusev,Finite Element Mapping for Spring Network Representations of the Mechanics of Solids.Phys.Rev.Lett.93,034302(2004).
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