非均质炸药冲击载荷作用下热点形成的离散元模拟研究
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摘要
冲击波作用下非均质炸药中热点的形成机制是炸药冲击起爆的关键。热点的形成是炸药内部细观尺度结构相互作用的结果,在多尺度响应中处于承上(宏观)启下(微观)的地位,因此细观数值模拟研究是解决与应用问题有关的炸药安全性和起爆问题的有效途径。本文用离散元方法对非均质炸药在冲击加载条件下的细观变形以及热点形成过程进行了数值模拟研究。细观数值模拟仅计算到热点生成为止,未考虑化学反应。
本文的研究内容以及数值模拟结果主要包括:
(1)通过对离散元方法的原理以及计算流程进行调研,将二维离散元程序DM2升级为三维离散元程序DEM3D,并用换算后的Hugoniot关系取代原有的中心作用力关系,用link-cell方法取代原有直接查找邻居单元的方法,提高了计算效率;
(2)利用Voronoi方法建立了可以近似反映高聚物粘结炸药PBX实际细观结构的三维离散元几何模型。
(3)在此基础上对炸药在冲击载荷下热点的生成过程进行了细观离散元模拟,得到如下结果:对于受到冲击载荷作用的PBX炸药,高温区域集中在炸药晶体与粘结剂的结合部位,且HMX晶体温升低于粘结剂,晶体边界温升高于内部;相对于HMX(炸药,粘结剂比较软,起到缓冲作用,导致PBX中HMX炸药温度明显低于颗粒炸药;含孔洞炸药在冲击作用下由于孔洞塌缩形成的热点温度明显高于不含孔洞炸药受冲击后的温度,对比三维和二维模拟结果可以得知三维模拟计算得到的炸药温度高于相应二维模拟的温度;对于含孔洞的HMX炸药,大尺寸孔洞塌缩形成的热点温度高于同样形状小尺寸孔洞塌缩形成的热点温度;球形孔洞塌缩形成的热点温度比相同尺寸立方体孔洞塌缩得到的热点温度高;
(4)发展了有限元和离散元相结合的三维计算程序,用该方法对部分算例进行了计算,得到的结果和离散元模拟结果基本相符。
Hot spot mechanism in plastic bonded explosives (PBX) under shock loading is the key of shock initiation in explosives. The formation of hot spot is the result of the interaction of mesoscale structure which can link the macroscale and microscale in the multiscale responses of explosives, so mesoscale numerical simulation is an effective approach to solve initiation problems in explosives. In this work, mesoscale responses and hot spots formation processes of heterogeneous explosives under shock loading have been investigated using the discrete element method. The mesoscale numerical simulation reveals mechanism of hot spots formation without considering chemical reaction.
The main points of this paper and results of the numerical simulations are as follows:
(1) By investigating the theory and calculation process, we upgrade the two-dimensional discrete element code DM2 to three-dimensional code DEM3D. And the central force was replaced by a modified Hugoniot relation. In addition, the calculation efficiency was improved after replacing the intrinsic neighbor calculation method by the link-cell method.
(2) The three-dimensional geometrical model which can approximatively mimics the mesoscopic structure of the plastic bonded explosives was created based on the Voronoi tessellation.
(3) Based on the above progress, hot spots formation processes of explosives under shock loading have been investigated using the discrete element method. In the case of shocked PBX explosives high temperature regions mostly locate near the interface between HMX crystals and binder, the temperature rise of HMX crystals is lower than the binder, and the surrounding parts of HMX crystals have higher temperature rise than the inner parts. The binder is softer than HMX explosives, so it can cushion the explosive, causing the temperature of HMX in PBX much lower than that of HMX crystal. Temperature of hot spot under shock loading in explosives containing a void is much higher than that in explosives without void. We also find that temperature from three-dimensional simulation is higher than that from two-dimensional simulation. For pure HMX explosives, higher hot spot temperature is obtained due to void collapsing from big void than from small void, and temperature obtained from spherical void is higher than from cubic void with the same size.
(4) We also developed a three-dimensional combined finite-discrete element code. A part of models that mentioned above are also calculated using this code, and the calculated results almost agree with the discrete element method.
本文的研究内容以及数值模拟结果主要包括:
(1)通过对离散元方法的原理以及计算流程进行调研,将二维离散元程序DM2升级为三维离散元程序DEM3D,并用换算后的Hugoniot关系取代原有的中心作用力关系,用link-cell方法取代原有直接查找邻居单元的方法,提高了计算效率;
(2)利用Voronoi方法建立了可以近似反映高聚物粘结炸药PBX实际细观结构的三维离散元几何模型。
(3)在此基础上对炸药在冲击载荷下热点的生成过程进行了细观离散元模拟,得到如下结果:对于受到冲击载荷作用的PBX炸药,高温区域集中在炸药晶体与粘结剂的结合部位,且HMX晶体温升低于粘结剂,晶体边界温升高于内部;相对于HMX(炸药,粘结剂比较软,起到缓冲作用,导致PBX中HMX炸药温度明显低于颗粒炸药;含孔洞炸药在冲击作用下由于孔洞塌缩形成的热点温度明显高于不含孔洞炸药受冲击后的温度,对比三维和二维模拟结果可以得知三维模拟计算得到的炸药温度高于相应二维模拟的温度;对于含孔洞的HMX炸药,大尺寸孔洞塌缩形成的热点温度高于同样形状小尺寸孔洞塌缩形成的热点温度;球形孔洞塌缩形成的热点温度比相同尺寸立方体孔洞塌缩得到的热点温度高;
(4)发展了有限元和离散元相结合的三维计算程序,用该方法对部分算例进行了计算,得到的结果和离散元模拟结果基本相符。
Hot spot mechanism in plastic bonded explosives (PBX) under shock loading is the key of shock initiation in explosives. The formation of hot spot is the result of the interaction of mesoscale structure which can link the macroscale and microscale in the multiscale responses of explosives, so mesoscale numerical simulation is an effective approach to solve initiation problems in explosives. In this work, mesoscale responses and hot spots formation processes of heterogeneous explosives under shock loading have been investigated using the discrete element method. The mesoscale numerical simulation reveals mechanism of hot spots formation without considering chemical reaction.
The main points of this paper and results of the numerical simulations are as follows:
(1) By investigating the theory and calculation process, we upgrade the two-dimensional discrete element code DM2 to three-dimensional code DEM3D. And the central force was replaced by a modified Hugoniot relation. In addition, the calculation efficiency was improved after replacing the intrinsic neighbor calculation method by the link-cell method.
(2) The three-dimensional geometrical model which can approximatively mimics the mesoscopic structure of the plastic bonded explosives was created based on the Voronoi tessellation.
(3) Based on the above progress, hot spots formation processes of explosives under shock loading have been investigated using the discrete element method. In the case of shocked PBX explosives high temperature regions mostly locate near the interface between HMX crystals and binder, the temperature rise of HMX crystals is lower than the binder, and the surrounding parts of HMX crystals have higher temperature rise than the inner parts. The binder is softer than HMX explosives, so it can cushion the explosive, causing the temperature of HMX in PBX much lower than that of HMX crystal. Temperature of hot spot under shock loading in explosives containing a void is much higher than that in explosives without void. We also find that temperature from three-dimensional simulation is higher than that from two-dimensional simulation. For pure HMX explosives, higher hot spot temperature is obtained due to void collapsing from big void than from small void, and temperature obtained from spherical void is higher than from cubic void with the same size.
(4) We also developed a three-dimensional combined finite-discrete element code. A part of models that mentioned above are also calculated using this code, and the calculated results almost agree with the discrete element method.
引文
1 章冠人,陈大年.凝聚炸药起爆动力学[M].北京:国防工业出版社,1991:89-128.
2 Campell A W,Davis W G,Travis J R.Shock initiation of detonation in liquid explosives[J].Physics of Fluids,1961,4(4):498.
3 Walker F E,Wasley R J.Initiation of nitromethane with relatively long duration,low amplitude shock waves[J].Combustion and Flame,1970,15(1):233.
4 孙承纬,卫玉章,周之奎.应用爆轰物理[M].北京:国防工业出版社,2000:430-433.
5 孙锦山,朱建士.理论爆轰物理[M].北京:国防工业出版社,1995:327-341.
6 R.W.Armstrong,H.L.Ammon,W.L.Elban,D.H.Tsai.Investigation of hot spot characteristics in energetic crystals[J].Thermochimica Acta 384(2002) 303-313.
7 John.E.Field.Hot spot ignition mechanisms for explosives[J].Acc.Chem.Res.1992,25,489-496.
8 K.Yano,Y.Horie,D.Greening.Mechanistic model of hot-spot:A unifying framework[J].Shock Compression of Condensed Matter,2001:983-986.
9 Charles L.Mader.Shock and Hot Spot Initiation of Homogeneous Explosives[J].The Physics of Fluids,1963,6(3):375-381.
10 Charles L.Mader.Initiation of Detonation by the Interaction of Shocks with Density Discontinuities [J].The Physics of Fluids,1965,8(10):1811-1816.
11 P.A.Conley,D.J.Benson.Microstructural effets in shock initiation[A].Proceedings of the 11th International Detonation Symposium[C].Snowmass,CO,United States,1998:768-780.
12 R.Menikoff,E.Kober.Compaction Waves in Granular HMX[A].American Physical Society,Conference on Shock Compression of Condensed Matter[C].Snowbird,Utah,United States,1999.
13 R.Menikoff.Granular explosives and initiation sensitivity[J].Los Alamos National Laboratory,1999.
14 R.Menikoff.Pore Collapse and Hot Spots in HMX[A].Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter.AIP Conference Proceedings[C].Portland,Oregon,United States,2004,706:393-396.
15 J.E.Reaugh.Multi-scale Computer Simulations to Study the Reaction Zone of Solid Explosives[A].Presented at 13th International Detonation Symposium[C].Norfolk,VA,United States,2006.
16 M.R.Baer.Modeling heterogeneous energetic materials at the mesoscale[J].Thermochimica Acta,2002,384:351-367.
17 Hua Fu,Cangli Liu,Wenqiang Wang,Duowang Tan,Tao Li.A combined discrete/finite element method applied to energetic materials at the meso-scale simulation under shock loading[A].Presented at 13th International Detonation Symposium[C].Norfolk,VA,United States,2006.
18 傅华.材料在冲击荷载下细观变形特征的数值模拟探索研究[D].硕士学位论文,绵阳:中国工程物理研究院,2006.
19 于继东.炸药冲击响应的二维细观离散元模拟[D].硕士学位论文,绵阳:中国工程物理研究院,2007.
20 A.G.Xu,X.F.Pan,G.C.Zhang.Material-point simulation of cavity collapse under shock[J].Journal of Physics:Condensed Matter,2007,19:1-11.
21 P.A.Cundall.A computer model for simulating progressive,large-scale movements in blocky rock systems[A].In:Proceedings ISRM Symposium on Rock Fracture[C].Nancy,1971:11-18.
22 刘凯欣,高凌天.离散元法研究的评述[J].力学进展,2003,33(4):483-490.
23 Cundall PA.Rational Design of Tunnel Supports:A Computer Model for Rock Mass Behavior Using Interactive Graphics for the Input and Output of Geometrical Data[R].Tech.Report MRD-2-74,Missouri River Division,U.S.Army Corps of Engineers,1974,NTIS Reports No.AD/A-001 602,1974.
24 Cundall P A,Marti J,Beresford P J,Last N C,Assign M I.Computer Modeling of Jointed Rock Masses[R].Tech.Report N-78-4 U.S.Army Engineer Waterways Experiment Station,Vicksburg,Mississippi,August 1978.
25 Cundall P A.BALL-A Program to Model granular Media Using the Distinct Element Method[J].Dames & Moore Advanced Technology Group,London,April 20,1978.
26 Drescher A,De Jossein de Jong.Photoelastic Verification of a Mechanical Model for the Flow of a Granular Material[J].J.Mech.Physics Solids,Vol,.20,337-351,1972.
27 3DEC—3-D Distinct Element Code,ITASCA Consulting Group,1987.
28 Cundall P A,Strack O D L.The Distinct Element Method as a Tool for Research in Granular Media,Part Ⅱ.Department of Civil and Mineral Engineering,University of Minnesota,National Science Foundation,October 1979.
29 王泳嘉.离散单元法——一种适用于节理岩石力学分析的数值方法[A].第一届全国岩石力学数值计算及模型试验讨论会论文集[C],1986.32-37.
30 剑万禧.离散单元法的基本原理及其在岩体工程中的应用[A].第一届全国岩石力学数值计算及模型试验讨论会论文集[C],1986.43-46.
31 王泳嘉,宋文洲,赵艳娟.离散单元法软件系统2D-block的现代化特点[J].岩石力学与工程学报,2000,6(增刊):1057-1060.
32 王泳嘉,刘连峰.三维离散单元法软件系统TRUDEC的研制[J].岩石力学与工程学报,1996,15:200-210.
33 Z.P.Tang,Y.Horie,S.G.Psakhic.Discrete meso-element modeling of shock processes in porous materials,Vol.1,Theory and model calculations[R].Technical Report,North Carolina State University,1995.
34 唐志平.三维离散元方法及其在冲击动力学中的应用[J].中国科学(E辑),2003,33(11):989-998.
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[D].博士学位论文,合肥:中国科学技术大学,2000.
36 刘红,刘军.离散元法中三种球形颗粒接触发现算法的比较[J].黑龙江科技学院学报.2006,16(6):360-363
37 Zhenhua Yao,Jiansheng Wang,Guirong Liu,Min Cheng.Improved neighbor list algorithm in molecular simulations using cell decomposition and data sorting method[J].Computer Physics Communications,2004,161:27-35.
38 William Mattson,Betsy M.Rice.Near-neighbor calculations using a modified cell-linked list method [J].Computer Physics Communications,1999,119:135-148.
39 Kholmirzo Kholmurdov,William Smith,Kenji Yasuoka,Toshikazu Ebisuzaki.A highly vectorised "link-cell" FORTRAN code for the DL_POLY molecular dynamics simulation package[J].Computer Physics Communications,2000,125:167-192.
40 经福谦.实验物态方程导引(第二版)[M].北京:科学出版社,1999:95.
41 Rajesh Ramamurthy,Rida T.Farouki.Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I:Theoretical foundations[J].Journal of Computational and Applied Mathematics,1999,102:119-141.
42 张有会,浅野哲夫,小保方幸次.关于一般图形Voronoi近似构造法的研究[J].数值计算与计算机应用,2002,3:216-225.
43 刘雪娜.三维点集Voronoi图的算法实现[J].计算机辅助工程,2006,15(1):1-4.
44 R.Menikoff,T.D.Sewell.Constituent properties of HMX needed for mesoscale simulations[J].Combustion theory and Modeling,2002,6:103-125.
45 Ante Munjiza.The Combined Finite-Discrete Element Method[M].Queen Mary,University of London,London,UK,2004.
46 Roland W.Lewis,David T.Gethin,Xinshe S.Yang,Ray C.Rowe.A combined finite-discrete element method for simulating pharmaceutical powder tableting[J].International Journal for Numerical Methods in Engineering,2005,62:853-869.
47 G.R.Liu,S.S.Quek.The Finite Element Method:A Practical Course[M].Oxford:Linacre House,Jordan Hill,2003.
48 Guido Dhondt.The Finite Element Method for Three-dimensional Thermo Mechanical Application [M].England:John Wiley & Sons Ltd,The Atrium,2004.
49 John O.Hallquist.LS-DYNA Theory Manual[M].California:Livermore Software Technology Corporation,2005.
50 P.A.Conley,D.J.Benson.An estimate of the linear strain rate dependence of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine[J].Journal of Applied Physics,1999,86(12):6717-6728.
51 Takahiro Hatano.Spatiotemporal behavior of void collapse in shocked solids[J].Physical Review Letters,2004,92(1):015503-1-4.
2 Campell A W,Davis W G,Travis J R.Shock initiation of detonation in liquid explosives[J].Physics of Fluids,1961,4(4):498.
3 Walker F E,Wasley R J.Initiation of nitromethane with relatively long duration,low amplitude shock waves[J].Combustion and Flame,1970,15(1):233.
4 孙承纬,卫玉章,周之奎.应用爆轰物理[M].北京:国防工业出版社,2000:430-433.
5 孙锦山,朱建士.理论爆轰物理[M].北京:国防工业出版社,1995:327-341.
6 R.W.Armstrong,H.L.Ammon,W.L.Elban,D.H.Tsai.Investigation of hot spot characteristics in energetic crystals[J].Thermochimica Acta 384(2002) 303-313.
7 John.E.Field.Hot spot ignition mechanisms for explosives[J].Acc.Chem.Res.1992,25,489-496.
8 K.Yano,Y.Horie,D.Greening.Mechanistic model of hot-spot:A unifying framework[J].Shock Compression of Condensed Matter,2001:983-986.
9 Charles L.Mader.Shock and Hot Spot Initiation of Homogeneous Explosives[J].The Physics of Fluids,1963,6(3):375-381.
10 Charles L.Mader.Initiation of Detonation by the Interaction of Shocks with Density Discontinuities [J].The Physics of Fluids,1965,8(10):1811-1816.
11 P.A.Conley,D.J.Benson.Microstructural effets in shock initiation[A].Proceedings of the 11th International Detonation Symposium[C].Snowmass,CO,United States,1998:768-780.
12 R.Menikoff,E.Kober.Compaction Waves in Granular HMX[A].American Physical Society,Conference on Shock Compression of Condensed Matter[C].Snowbird,Utah,United States,1999.
13 R.Menikoff.Granular explosives and initiation sensitivity[J].Los Alamos National Laboratory,1999.
14 R.Menikoff.Pore Collapse and Hot Spots in HMX[A].Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter.AIP Conference Proceedings[C].Portland,Oregon,United States,2004,706:393-396.
15 J.E.Reaugh.Multi-scale Computer Simulations to Study the Reaction Zone of Solid Explosives[A].Presented at 13th International Detonation Symposium[C].Norfolk,VA,United States,2006.
16 M.R.Baer.Modeling heterogeneous energetic materials at the mesoscale[J].Thermochimica Acta,2002,384:351-367.
17 Hua Fu,Cangli Liu,Wenqiang Wang,Duowang Tan,Tao Li.A combined discrete/finite element method applied to energetic materials at the meso-scale simulation under shock loading[A].Presented at 13th International Detonation Symposium[C].Norfolk,VA,United States,2006.
18 傅华.材料在冲击荷载下细观变形特征的数值模拟探索研究[D].硕士学位论文,绵阳:中国工程物理研究院,2006.
19 于继东.炸药冲击响应的二维细观离散元模拟[D].硕士学位论文,绵阳:中国工程物理研究院,2007.
20 A.G.Xu,X.F.Pan,G.C.Zhang.Material-point simulation of cavity collapse under shock[J].Journal of Physics:Condensed Matter,2007,19:1-11.
21 P.A.Cundall.A computer model for simulating progressive,large-scale movements in blocky rock systems[A].In:Proceedings ISRM Symposium on Rock Fracture[C].Nancy,1971:11-18.
22 刘凯欣,高凌天.离散元法研究的评述[J].力学进展,2003,33(4):483-490.
23 Cundall PA.Rational Design of Tunnel Supports:A Computer Model for Rock Mass Behavior Using Interactive Graphics for the Input and Output of Geometrical Data[R].Tech.Report MRD-2-74,Missouri River Division,U.S.Army Corps of Engineers,1974,NTIS Reports No.AD/A-001 602,1974.
24 Cundall P A,Marti J,Beresford P J,Last N C,Assign M I.Computer Modeling of Jointed Rock Masses[R].Tech.Report N-78-4 U.S.Army Engineer Waterways Experiment Station,Vicksburg,Mississippi,August 1978.
25 Cundall P A.BALL-A Program to Model granular Media Using the Distinct Element Method[J].Dames & Moore Advanced Technology Group,London,April 20,1978.
26 Drescher A,De Jossein de Jong.Photoelastic Verification of a Mechanical Model for the Flow of a Granular Material[J].J.Mech.Physics Solids,Vol,.20,337-351,1972.
27 3DEC—3-D Distinct Element Code,ITASCA Consulting Group,1987.
28 Cundall P A,Strack O D L.The Distinct Element Method as a Tool for Research in Granular Media,Part Ⅱ.Department of Civil and Mineral Engineering,University of Minnesota,National Science Foundation,October 1979.
29 王泳嘉.离散单元法——一种适用于节理岩石力学分析的数值方法[A].第一届全国岩石力学数值计算及模型试验讨论会论文集[C],1986.32-37.
30 剑万禧.离散单元法的基本原理及其在岩体工程中的应用[A].第一届全国岩石力学数值计算及模型试验讨论会论文集[C],1986.43-46.
31 王泳嘉,宋文洲,赵艳娟.离散单元法软件系统2D-block的现代化特点[J].岩石力学与工程学报,2000,6(增刊):1057-1060.
32 王泳嘉,刘连峰.三维离散单元法软件系统TRUDEC的研制[J].岩石力学与工程学报,1996,15:200-210.
33 Z.P.Tang,Y.Horie,S.G.Psakhic.Discrete meso-element modeling of shock processes in porous materials,Vol.1,Theory and model calculations[R].Technical Report,North Carolina State University,1995.
34 唐志平.三维离散元方法及其在冲击动力学中的应用[J].中国科学(E辑),2003,33(11):989-998.
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[D].博士学位论文,合肥:中国科学技术大学,2000.
36 刘红,刘军.离散元法中三种球形颗粒接触发现算法的比较[J].黑龙江科技学院学报.2006,16(6):360-363
37 Zhenhua Yao,Jiansheng Wang,Guirong Liu,Min Cheng.Improved neighbor list algorithm in molecular simulations using cell decomposition and data sorting method[J].Computer Physics Communications,2004,161:27-35.
38 William Mattson,Betsy M.Rice.Near-neighbor calculations using a modified cell-linked list method [J].Computer Physics Communications,1999,119:135-148.
39 Kholmirzo Kholmurdov,William Smith,Kenji Yasuoka,Toshikazu Ebisuzaki.A highly vectorised "link-cell" FORTRAN code for the DL_POLY molecular dynamics simulation package[J].Computer Physics Communications,2000,125:167-192.
40 经福谦.实验物态方程导引(第二版)[M].北京:科学出版社,1999:95.
41 Rajesh Ramamurthy,Rida T.Farouki.Voronoi diagram and medial axis algorithm for planar domains with curved boundaries I:Theoretical foundations[J].Journal of Computational and Applied Mathematics,1999,102:119-141.
42 张有会,浅野哲夫,小保方幸次.关于一般图形Voronoi近似构造法的研究[J].数值计算与计算机应用,2002,3:216-225.
43 刘雪娜.三维点集Voronoi图的算法实现[J].计算机辅助工程,2006,15(1):1-4.
44 R.Menikoff,T.D.Sewell.Constituent properties of HMX needed for mesoscale simulations[J].Combustion theory and Modeling,2002,6:103-125.
45 Ante Munjiza.The Combined Finite-Discrete Element Method[M].Queen Mary,University of London,London,UK,2004.
46 Roland W.Lewis,David T.Gethin,Xinshe S.Yang,Ray C.Rowe.A combined finite-discrete element method for simulating pharmaceutical powder tableting[J].International Journal for Numerical Methods in Engineering,2005,62:853-869.
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