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PBX炸药冲击起爆的改进细观反应速率模型

  • 白志玲1

    机 构：北京理工大学 爆炸科学与技术国家重点实验室， 北京 100081

    邮 箱：zhilingbai@yeah.net

    作者简介：白志玲（1989-），女，博士生，主要从事爆炸与冲击动力学研究。e‑mail：zhilingbai@yeah.net

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  • 段卓平1

    机 构：北京理工大学 爆炸科学与技术国家重点实验室， 北京 100081

    角 色：通讯作者

    邮 箱：duanzp@bit.edu.cn

    作者简介：段卓平（1965-），男，研究员，博士生导师，主要从事爆炸与冲击动力学研究。e‑mail：duanzp@bit.edu.cn

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  • 温丽晶2

    机 构：环境保护部核与辐射安全中心， 北京 100082

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  • 张震宇3

    机 构：国防科技大学理学院技术物理研究所， 湖南 长沙 410073

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  • 欧卓成1

    机 构：北京理工大学 爆炸科学与技术国家重点实验室， 北京 100081

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  • 黄风雷1

    机 构：北京理工大学 爆炸科学与技术国家重点实验室， 北京 100081

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1. 北京理工大学 爆炸科学与技术国家重点实验室， 北京 100081； 2. 环境保护部核与辐射安全中心， 北京 100082； 3. 国防科技大学理学院技术物理研究所， 湖南 长沙 410073

中图分类号: TJ55； O381

DOI:10.11943/CJEM2018354

A Modified Mesoscopic Reaction Rate Model for Shock Initiation of PBXs

  • BAI Zhi‑ling1

    Affiliation：The State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

    Email：zhilingbai@yeah.net

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  • DUAN Zhuo‑ping1

    Affiliation：The State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

    Role：Corresponding author

    Email：duanzp@bit.edu.cn

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  • WEN Li‑jing2

    Affiliation：Nuclear and Radiation Safety Center, Ministry of Environmental Protection, Beijing 100082, China

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  • ZHANG Zhen‑yu3

    Affiliation：Institute of Technical Physics, College of Science, National University of Defense Technology, Changsha 410073, China

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  • OU Zhuo‑cheng1

    Affiliation：The State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

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  • HUANG Feng‑lei1

    Affiliation：The State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

    ×

1. The State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China； 2. Nuclear and Radiation Safety Center, Ministry of Environmental Protection, Beijing 100082, China； 3. Institute of Technical Physics, College of Science, National University of Defense Technology, Changsha 410073, China

CLC: TJ55； O381

DOI:10.11943/CJEM2018354

参考文献 1
LiuY R, DuanZ P, ZhangZ Y, et al. A mesoscopic reaction rate rodel for shock initiation of multi‑component PBX explosives[J]. Journal of Hazardous Materials, 2016, 317: 44-51.
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参考文献 2
QiuL, XiaoH M. Molecular dynamics study of binding energies, mechanical properties, and detonation performances of bicyclo‑HMX‑based PBXs[J]. Journal of Hazardous Materials, 2009, 164(1): 329-336.
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TalawarM B, AgarwalA P, AnniyappanM, et al. Method for preparation of fine TATB (2-5 microm) and its evaluation in plastic bonded explosive (PBX) formulations[J]. Journal of Hazardous Materials, 2006, 137(3): 1848-1852.
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MassoniJ, SaurelR, BaudinG, et al. A mechanistic model for shock initiation of solid explosives[J]. Physics of Fluids, 1999, 11(3): 710-736.
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FieldJ E. Hot spot ignition mechanisms for explosives[J]. Accounts of Chemical Research, 1992, 25(11): 489-496.
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FreyR B. Cavity collapse in energetic materials[C]//The 8th Symposium (International) on Detonation, Albuquerque, New Mexico, 1985: 68-80.
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KimK. Development of a model of reaction rates in shocked multicomponent explosives[C]//The 9th International Detonation Symposium, Prtland, OR, USA: Office of the Chief of Naval Researche, 1989: 593-603.
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KimK, SohnC H. Modeling of reaction bulidup processes in shocked porous explosives[C]//The 8th International Detonation Symposium, Albuquerque, NM, 1985: 926-933.
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CookM D, HaskinsP J, StennettC. Development and implementation of an ignition and growth model for homogeneous and heterogeneous explosives[C]//The 11th International Detonation Symposium, Snowmass, Colorado, USA: Office of Naval Research, 1998: 589-598.
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参考文献 11
HandleyC A. The CREST reactive burn model[C]//Shock Compression of Condensed Matter, AIP Publishing, 2007: 373-376.
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HoweP M, BensonD C. Exploitation of some micro‑mechanical concepts to develop an engineering model of initiation[C]//The 12th International Detonation Symposium, San Diego, USA: Office of Naval Research, 2002.
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参考文献 13
JohnsonJ N, TangP K, ForestC A. Shock‑wave initiation of heterogeneous reactive solids[J]. Journal of Applied Physics, 1985, 57(9): 4323-4334.
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LeeE L, TarverC M. Phenomenological model of shock initiation in heterogeneous explosives[J]. Physics of Fluids, 1980, 23(12): 2362-2372.
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MaderC L, ForestC A. Two‑dimensional homogeneous and heterogeneous detonation wave propagation[C]//The 6th International Detonation Symposium, San Diego, CA, USA ,1976.
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StarkenbergJ, DorseyT M. An assessment of the performance of the history variable reactive burn explosive initiation model in the CTH code[C]//The 11th International Detonation Symposium, Snowmass, CO, USA: Office of Naval Research, 1998: 621-631.
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参考文献 17
DuanZ P, WenL J, LiuY R, et al. A pore collapse model for hot‑spot ignition in shocked multi‑component explosives[J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2010, 11(Suppl): 19-24.
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参考文献 18
田占东, 张震宇. PBX‑9404炸药冲击起爆细观反应速率模型[J]. 含能材料, 2007, 15(5): 464-467.
TIANZhan‑dong, ZHANGZhen‑yu. A mesomechanic model of shock initiation in PBX‑9404 explosive [J]. Chinese Journal of Energetic Materials（Hanneng Cailiao）, 2007, 15(5): 464-467.
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参考文献 19
WENLi‑jing, DUANZhuo‑ping, ZHANGLian‑sheng, et al. Effects of HMX particle size on the shock initiation of PBXC03 explosive[J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2012, 13(2): 189-194.
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参考文献 20
温丽晶, 段卓平, 张震宇, 等. 不同加载压力下炸药冲击起爆过程实验和数值模拟研究[J]. 兵工学报, 2013, 34(3): 283-288.
WENLi‑jing, DUANZhuo‑ping, ZHANGZhen‑yu, et al. Experimental and numerical study on the shock initiation of PBXC03 explosive under the different loading pressures [J]. Acta Armanentarh, 2013, 34(3): 283-288.
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DuanZ P, LiuY R, ZhangZ Y, et al. Prediction of initial temperature effects on shock initiation of solid explosives by using mesoscopic reaction rate model[J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2014, 15(5): 299-305.
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温丽晶. PBX炸药冲击起爆细观反应速率模型研究[D]. 北京：北京理工大学, 2011.
WENLi‑jing. Research on mesoscopic reaction rate model of shock initiation of PBX[D]. Beijing: Beijing Institute of Technology, 2011.
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参考文献 23
温丽晶，段卓平，张震宇，等. 采用遗传算法确定炸药爆轰产物JWL状态方程参数[J]. 爆炸与冲击，2013, 33(s1): 130-134.
WENLi‑jing, DUANZhuo‑ping, ZHANGZhen‑yu, et al. Determination of JWL‑EOS parameters for explosive detonation products using genetic algorithm[J]. Explosion and Shock Waves, 2013, 33(s1): 130-134.
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WhirleyR G, EngelmannB E. DYNA2D: A nonlinear, explicit, two‑dimensional finite element code for solid mechanics: user manual: UCRL‑MA‑110630[R]. United States, Lawrence Livermore National Laborotary,1992.
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TarverC M, ChidesterS K, NicholsA L. Critical conditions for impact‑ and shock‑induced hot spots in solid explosives[J]. Journal of Physical Chemistry, 1996, 100(14): 5794-5799.
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GrebenkinK F. Comparative analysis of physical mechanisms of detonation initiation in HMX and in a low‑sensitive explosive (TATB)[J]. Combustion Explosion and Shock Waves, 2009, 45(1): 78-87.
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目录 contents

    摘要

    为了系统研究载荷和炸药细观结构对高聚物粘结炸药(Polymer Bonded Explosive，PBX)冲击起爆爆轰成长的影响规律，考虑到炸药低压慢反应阶段的燃烧拓扑结构包含颗粒内部孔隙表面燃烧和颗粒外表面燃烧形式，以及装药密度的影响，引入燃耗因子和装药密度影响因子，改进了Duan‑Zhang‑Kim（DZK）细观反应速率模型。采用同一套反应速率模型参数，数值模拟各实验状态下HMX基PBXC03（87% HMX,7% TATB,6% Viton）的冲击起爆过程，数值模拟结果与实验测试结果均吻合较好，表明改进DZK反应速率模型可更好地描述和预测载荷和炸药细观结构对PBXC03冲击起爆爆轰成长过程的影响规律。在本研究装药和加载条件下，中等密度的炸药冲击起爆和爆轰成长最快；颗粒度越小，炸药越难点火，但一旦点火，爆轰成长最快。

    Abstract

    To systemly investigate the influence of the mesostructure and the shock loadings on the shock initiation and detonation of polymer bonded explosives (PBXs), a modified Duan‑Zhang‑Kim（DZK）mesoscopic reaction rate model is proposed. A burn‑up and a porosity factors are introduced to describe effects of the outer burning on the surfaces of grains of the explosive at the low‑pressure slow reactive stage and the initial charge density, respectively. The calculated pressure‑time histories inside the HMX‑based PBXC03 explosive samples using the modified model with one set of parameters are in good agreement with the experimental data, which indicates that this model can be used to well predicate the influence of the particle size, the porosity and the shock loading on the shock initiation (i.e., ignition and detonation growth) processes of PBXs. Moreover, it is also observed that the detonation grows fastest in the explosive with a moderate porosity. And the smaller the particle size of the explosive is, the more difficult the explosive can be ignited, in which the detonation grows fastest once the explosive is ignited.

    Graphic Abstract

    图文摘要

    html/hncl/CJEM2018354/media/1cb37c64-827c-4fe7-9286-2508d077390a-image003.png

    Based on experiments and pore collapse “hot‑spot” ignition mechanism, a modified mesoscopic reaction rate model (modified DZK model) for a polymer bonded explosive (PBX) is proposed. A burn‑up and a porosity factors are introduced to describe effects of the outer burning on the surfaces of explosive grains at the low‑pressure slow reactive stage and the initial charge density, respectively. The new model is used to investigate the influence of shock loading and mesostructure on the shock initiation and detonation characteristic of a HMX‑based PBX explosive.

  • 1 引 言

    为解决弹药威力与安全性的矛盾，国内外均致力于开发新型炸药，其中高聚物粘结炸药（Polymer Bonded Explosive，PBX）是由主体炸药（如黑索今(RDX)、奥克托今(HMX)和三氨基三硝基苯(TATB)等）或其混合物与聚合物粘结剂混合制成的非均质固体炸药，具有优异的高能、钝感等特性[1,2,3]。PBX的冲击起爆过程明显不同于均质炸药，归因于其细观非均质性[4,5]，而目前对非均质炸药在细观尺度的冲击响应认识尚处于发展阶段，适时开展非均质炸药冲击起爆的细观机理研究，建立具有一定普适性的宏细观结合的爆轰反应流模型，探索炸药细观结构特征对其冲击起爆性能的影响规律是当前爆轰领域的重要研究方向。

    研究表明，孔隙塌缩是非均质固体炸药冲击起爆“热点”形成的主导机制[4,5,6,7]，“热点”点火后进入爆轰成长过程，主要由表面燃烧机理描述[5,8,9]。早期，基于“热点”机制的爆轰反应流模型研究多数为致力于构造现象学的宏观连续介质力学模型[10,11,12,13,14,15,16]，通过实验数据标定模型经验参数，可较好地再现炸药冲击起爆实验现象，但这些模型无法适应炸药细观结构特征对冲击起爆过程的影响。Duan等[17]基于Kim模型[8,9]建立了描述PBX“热点”形成的弹粘塑性双球壳塌缩模型，并结合低压慢反应项和田占东等[18]的高压快反应项建立了描述PBX冲击起爆和爆轰成长过程的Duan‑Zhang‑Kim（DZK）细观反应速率模型，可较好地反映初始温度、加载压力、颗粒度和粘结剂强度及含量等对冲击起爆过程的影响[19,20]，但进一步研究表明，DZK模型计算的低压慢反应阶段的压力增长速率较实验测试波形偏快，且不能较好地预测装药密度（孔隙度）变化对其冲击起爆爆轰成长过程的影响规律。

    为进一步分析非均质固体炸药冲击起爆的细观反应机理，本研究改进DZK细观反应速率模型，结合实验数据，确定一套模型参数，并验证改进DZK模型用来描述和预测不同加载压力、不同炸药颗粒度和不同孔隙度PBX炸药冲击起爆爆轰成长规律的适应性。

  • 2 改进DZK细观反应速率模型

    段卓平等[17]提出的DZK反应速率模型：

    dλx,tdt=dλhdt+3λ2/3roapn+Gpm1-λs
    (1)

    式中，λ(x,t)、p分别表示t时刻位于宏观流体动力学坐标x处的球壳胞元内炸药反应度（已反应炸药的体积分数）和实时压力(Mbar)；ro是球壳外半径，cm，表示炸药平均颗粒度。等号右边第一项描述冲击作用下弹粘塑性双球壳塌缩变形生成“热点”的过程，其中λh表示“热点”点火反应度；第二项描述热点形成后早期低压阶段的慢反应，假设反应从球壳内表面以表面燃烧的形式向外传播；第三项为高压快反应速率方程，描述炸药整体爆轰反应。“热点”点火项参数[19]（见表1）均为炸药自身的热力学参数，不包含未知参数；a、n、G、m和s为待定系数，通过炸药冲击起爆实验数据标定。

    表1 常温下PBXC03的改进DZK反应速率模型参数

    Table 1 Parameters of the modified DZK reaction rate model for PBXC03 at room temperature

    hot‑spot ignition term[19]the second and third terms (the present work)
    Z/ μs-15.0e13a0.017
    T*/ K26500b1.86
    T0/ K298n0.965
    Cp/ cm2·μs-2·K-11.4e‑5c0.0128
    Q/ cm2·μs-25.439e‑2y0.125
    k*/ cm·μs-1·K-18.0e‑14G590.0
    γe/ GPa2.6m3.195
    ke/ GPa8e‑3s1.00

    NOTE: Z is the pre‑exponential factor in Arrhenius kinetics. T* is the activation temperature. T0 is the initial temperature; Cp is the heat capacity. Q is the reaction heat of the explosive. k* is the thermal conductivity. γe is the viscous factor of the explosive. ke is the shear yield strength of the explosive.

    DZK反应速率模型可反映初始温度、加载压力、炸药颗粒度、孔隙度、粘结剂强度及含量等对冲击起爆过程的影响[19,21,22]，但该模型计算冲击起爆过程的压力历史曲线与实验测试曲线特征有较大差异，实验测试的压力增长经历缓慢‑快速‑缓慢过程直至最大值，呈现“鼓包”特征，而计算压力曲线增长速率持续增大直至峰值，呈现“尖峰”特征。原因是该模型的低压慢反应阶段仅考虑了颗粒内部孔隙表面燃烧，随着反应进行，燃烧表面积增长速率持续增大，孔内压力保持持续快速增大，直到炸药反应完全，压力达到峰值后衰减。但实际上炸药内部是多热点燃烧过程，燃烧拓扑结构包含颗粒内部孔隙表面燃烧和颗粒外表面燃烧形式，随着反应进行，内部孔隙燃烧表面积增大，而颗粒燃烧外表面积减小，因此，低压慢反应阶段整体燃烧表面积增长速率变缓，压力增长速率变缓。于是，在低压慢反应阶段增加了表征颗粒外表面燃烧影响的燃耗因子(1‑λ)b，b是待定常系数，同时参考Lee‑Taver模型[14]，进一步增加装药密度（孔隙度）影响因子1‑|1‑ρ0/ρT‑c|y，其中ρ0、ρT分别为炸药装药密度和理论密度，c、y是待定常数系数，最后改进DZK反应速率模型如下：

    dλdt=dλhdt+3λ2/31-λbroapn1-1-ρ0ρT-cy+Gpm1-λs
    (2)

    点火项参数均是炸药自身热力学参数[19]，后两项参数通过任意一发实验数据确定，如表1所示，本研究所有数值模拟时反应速率模型参数均采用表1数据。

    此外，炸药爆轰产物状态方程和未反应炸药状态方程均采用含温度形式的Jones‑Wilkins‑Lee (JWL)状态方程[22,23]：

    pg,s=Aexp-R1V¯+Bexp-R2V¯+ωcvV¯T
    (3)

    式中，pg,s、V¯、T分别表示爆轰产物或冲击波后未反应炸药的压力（p=λpg+(1‑λ)ps）、相对比容、温度；A，B，R1，R2，ω，cv为待定系数。炸药装药密度改变，其爆轰性能（如爆速、爆压等）也随之变化。温丽晶等[22,23]采用遗传优化算法确定了中等密度（ρ0=1.849 g·cm-3）HMX基PBXC03（87% HMX, 7% TATB， 6% Viton）爆轰产物状态方程和未反应炸药状态方程参数，当PBXC03装药密度变化较小时，R1，R2，ω保持与中等密度时一致，根据相容关系[22]即可确定A，B，cv值，如表2,3所示。

    表2 常温下不同密度PBXC03爆轰产物JWL状态方程参数

    Table 2 Parameters of the JWL EOS for the detonation products of PBXC03 with different densities at room temperature

    parameters

    ρ0=1.836 g·cm-3

    (the present work)

    		ρ0=1.849 g·cm-3[22]

    ρ0=1.855 g·cm-3

    (the present work)

    A/GPa1002.7235102.5451031.4249
    B/GPa22.9311522.5723.48774
    R14.914.914.91
    R21.371.371.37
    ω0.290.290.29
    cv/GPa·K-11.0e‑31.0e‑31.0e‑3
    E0/GPa9.559.589.60

    表3 常温下不同密度PBXC03未反应炸药JWL状态方程参数

    Table 3 Parameters of the JWL EOS for the unreacted PBXC03 with different densities at room temperature

    parameters

    ρ0=1.836 g·cm-3

    (the present work)

    		ρ0=1.849 g·cm-3[22]

    ρ0=1.855 g·cm-3

    (the present work)

    A/GPa26554595.027213759.027750964.0
    B/GPa-73.4289-73.8544-73.8959
    R119.8719.8719.87
    R21.9871.9871.987
    ω1.991.991.99
    cv/GPa·K-11.68714e‑21.6932e‑21.69749e‑2

  • 3 数值模拟与实验结果对比分析

    采用DYNA2D程序，建立一维拉格朗日模型，模拟实验状态下PBXC03炸药的冲击起爆爆轰成长过程[22]，实验用PBXC03炸药的物理参数见表4。考虑到实验时炸药内嵌有锰铜压阻传感器和聚四氟乙烯膜，建模时，炸药内对应拉格朗日位置处同样加入锰铜材料和聚四氟乙烯材料。此外，锰铜压阻传感器及聚四氟乙烯模型均采用Grüeneisen状态方程，参数见表5[24]。

    表4 PBXC03的物理参数[22]

    Table 4 Physical parameters of PBXC03[22]

    density / g·cm-3mean particle size / μmpressure / GPa
    1.83620-30 (fine particle)5.9
    1.84970-90 (medium particle)5.2
    1.855110-130 (coarse particle)4.5

    表5 Grüeneisen状态方程参数[24]

    Table 5 Parameters in the Grüneisen equations of state [24]

    materials

    ρ0

    / g·cm-3

    C

    / cm·μs-1

    		S1S2S3γ0a
    manganin8.140.3941.489001.990
    teflon2.120.1341.930000.900

    NOTE: ρ0 is the the initial density. C is the intercept of the shock wave velocity‑particle velocity curve. S1, S2, and S3 are slope coefficients of the particle velocity curve. γ0 is the Grüeneisen coefficient. a is the first‑order volume correction factor.

  • 3.1 载荷的影响

    在冲击载荷作用下，炸药临界点火温度Tcr(K)、反应热点的临界直径dcr(μm)与前导冲击波阵面压力pf(GPa)满足关系式[25,26]:

    dcr=T1T0+θpf1γ
    (4)
    Tcr=T1dcrγ
    (5)

    式中，T0是炸药初始温度,K；T1(K),γ,θ(K·GPa-1)是常数系数。可见，炸药前导冲击波阵面压力pf越大，临界点火温度Tcr越高，反应热点的临界直径dcr越小。

    中等密度（ρ0=1.849 g·cm-3）粗颗粒（110~130 μm）的PBXC03在不同加载压力（p0）下冲击起爆过程的数值模拟与文献[22]中实验结果比较如图1所示，图2为前导冲击波阵面压力成长历史的数值模拟与文献[22]中实验结果比较。由图1、图2可知，其数值模拟结果与实验测试结果均符合较好，表明改进DZK模型能较好地预测载荷对PBXC03冲击起爆和爆轰成长过程的影响规律。加载压力越高，前导冲击波阵面压力增长越明显，并且波后压力成长越快，压力高峰不断追赶波阵面而最早形成爆轰。因为加载压力越高，炸药潜在热点的温度越高，反应热点的临界尺寸越小，于是炸药内部能发生反应的热点数量多，热点点火反应快且燃烧反应（爆轰成长）也快，到爆轰时间最早，到爆轰距离最短。

    html/hncl/CJEM2018354/media/1cb37c64-827c-4fe7-9286-2508d077390a-image005.png

    a. p0=5.9 GPa

    html/hncl/CJEM2018354/media/1cb37c64-827c-4fe7-9286-2508d077390a-image006.png

    b. p0=5.2 GPa

    html/hncl/CJEM2018354/media/1cb37c64-827c-4fe7-9286-2508d077390a-image007.png

    c. p0=4.5 GPa

    图1 不同加载压力下PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较

    Fig.1 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 under different loading pressures

    图2 不同加载压力下PBXC03前导冲击波阵面压力历史的数值模拟结果与实验结果[22]比较

    图2 不同加载压力下PBXC03前导冲击波阵面压力历史的数值模拟结果与实验结果[22]比较

    Fig.2 Comparison of experimental data[22] and numerical results for the pressure growth on the precursory shock wave front of PBXC03 under different loading pressures

  • 3.2 颗粒度的影响

    不同颗粒度的中等密度（ρ0=1.849 g·cm-3）PBXC03炸药在加载压力p0=5.9 GPa下冲击起爆过程的数值模拟与文献[22]实验结果比较如图3所示，前导冲击波阵面压力成长历史的数值模拟结果与文献[22]实验结果比较如图4所示。由图3、图4可知，其数值模拟结果与实验测试结果均符合较好。在本研究加载条件下，细颗粒（20~30 μm）炸药前导冲击波阵面压力前期增长缓慢，但后期成长较快，而粗颗粒（110~130 μm）炸药前导冲击波阵面压力前期有相对较大的增长趋势，后期则成长较慢, 粗颗粒炸药在9 mm位置附近形成爆轰的时间比细颗粒滞后0.328 μs。因为细颗粒炸药潜在热点尺寸小，反应热点的数量少，热点反应速度慢，释能缓慢，热点点火反应在波阵面附近的贡献不大，但热点点火后，细颗粒炸药燃烧比表面积最大，化学反应最快，波后压力成长最快；而粗颗粒炸药潜在热点尺寸大，反应热点数量多，快速释放的能量直接推动了波阵面压力增长，但随后的燃烧反应最慢，波后压力成长最慢。上述结果表明：在本研究装药和加载条件下，细颗粒炸药难点火，但一旦点火爆轰成长较快；粗颗粒炸药更容易点火，但后期爆轰成长缓慢。

    html/hncl/CJEM2018354/media/1cb37c64-827c-4fe7-9286-2508d077390a-image009.png

    a. fine particle

    html/hncl/CJEM2018354/media/1cb37c64-827c-4fe7-9286-2508d077390a-image010.png

    b. medium particle

    html/hncl/CJEM2018354/media/1cb37c64-827c-4fe7-9286-2508d077390a-image011.png

    c. coarse particle

    图3 不同颗粒度PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较

    Fig.3 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 with different particle sizes

    图4 不同颗粒度PBXC03冲击起爆前导冲击波阵面压力历史的数值模拟结果与实验结果[22]比较

    图4 不同颗粒度PBXC03冲击起爆前导冲击波阵面压力历史的数值模拟结果与实验结果[22]比较

    Fig.4 Comparison of experimental data[22] and numerical results for the pressure growth on precursory shock wave front of PBXC03 with different particle sizes

  • 3.3 孔隙度的影响

    图5为不同孔隙度（装药密度）的细颗粒PBXC03在加载压力p0=5.9 GPa下冲击起爆过程的数值模拟与实验测试结果[22]比较，图6为前导冲击波阵面压力成长历史的数值模拟与实验数据[22]比较。由图5、图6可知，其数值模拟结果与实验测试结果均吻合较好。结果显示：中等密度（ρ0=1.849 g·cm-3）炸药波后压力成长最快，到爆轰时间最早，低密度（ρ0=1.836 g·cm-3）次之，高密度（ρ0=1.855 g·cm-3）最低，其中高密度炸药在9 mm位置附近形成爆轰的时间比中等密度滞后0.336 μs。可见在本研究装药和加载条件下，装药密度对炸药冲击起爆爆轰性能的影响不单调。装药密度低时，孔隙度大，潜在热点数量多或尺寸大，在相同外载条件下，形成的反应热点温度较低，热点反应区内激发的化学反应速率慢；而装药密度大时，孔隙度小，潜在热点数量少或尺寸小，临界点火温度较高，能够发生点火反应的热点数量少，也将导致反应速率下降。

    html/hncl/CJEM2018354/media/1cb37c64-827c-4fe7-9286-2508d077390a-image014.png

    a. ρ0=1.836 g·cm-3

    html/hncl/CJEM2018354/media/1cb37c64-827c-4fe7-9286-2508d077390a-image015.png

    b. ρ0=1.849 g·cm-3

    html/hncl/CJEM2018354/media/1cb37c64-827c-4fe7-9286-2508d077390a-image016.png

    c. ρ0=1.855 g·cm-3

    图5 不同孔隙度的PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较

    Fig.5 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 with different porosities

    图6 不同孔隙度PBXC03的前导冲击波阵面压力历史的数值模拟结果与实验结果[22]比较

    图6 不同孔隙度PBXC03的前导冲击波阵面压力历史的数值模拟结果与实验结果[22]比较

    Fig.6 Comparison of experimental data[22] and numerical results for the pressure growth on the precursory shock wave front of PBXC03 with different porosities

    非均质固体炸药的冲击起爆是由上述热点点火过程和后续燃烧反应过程共同作用控制，装药密度范围不同，孔隙度对炸药冲击起爆过程的影响可能不同；载荷范围不同，炸药冲击起爆随孔隙度变化规律可能不同。比如，在高压载荷作用下，炸药冲击起爆主要受燃烧反应控制，冲击起爆过程随着装药密度增大而单调变慢。

  • 4 结 论

    本研究系统地关注了加载压力和炸药细观结构（颗粒度和孔隙度）对PBXC03装药冲击起爆过程的影响规律。改进了DZK反应速率模型，获得了一套反应流计算模型参数，数值模拟不同颗粒度、不同孔隙度及不同载荷条件下PBXC03冲击起爆过程与实验结果均吻合较好，验证了改进DZK模型的合理性和一定程度的普适性，并得到以下结论：

    （1）细颗粒炸药难点火，但一旦点火爆轰成长较快，而粗颗粒炸药更容易点火，但后期爆轰成长缓慢。

    （2）在本研究装药和加载条件下，装药密度对炸药冲击起爆爆轰性能的影响不单调，这是热点点火过程与燃烧反应过程共同作用的结果。

    (责编：肖依依）

  • 参考文献

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      Liu Y R, Duan Z P, Zhang Z Y, et al. A mesoscopic reaction rate rodel for shock initiation of multi‑component PBX explosives[J]. Journal of Hazardous Materials, 2016, 317: 44-51.

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      Talawar M B, Agarwal A P, Anniyappan M, et al. Method for preparation of fine TATB (2-5 microm) and its evaluation in plastic bonded explosive (PBX) formulations[J]. Journal of Hazardous Materials, 2006, 137(3): 1848-1852.

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      Grebenkin K F. Comparative analysis of physical mechanisms of detonation initiation in HMX and in a low‑sensitive explosive (TATB)[J]. Combustion Explosion and Shock Waves, 2009, 45(1): 78-87.

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      Massoni J, Saurel R, Baudin G, et al. A mechanistic model for shock initiation of solid explosives[J]. Physics of Fluids, 1999, 11(3): 710-736.

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      Field J E. Hot spot ignition mechanisms for explosives[J]. Accounts of Chemical Research, 1992, 25(11): 489-496.

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      Frey R B. Cavity collapse in energetic materials[C]//The 8th Symposium (International) on Detonation, Albuquerque, New Mexico, 1985: 68-80.

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      Kim K. Development of a model of reaction rates in shocked multicomponent explosives[C]//The 9th International Detonation Symposium, Prtland, OR, USA: Office of the Chief of Naval Researche, 1989: 593-603.

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      Cook M D, Haskins P J, Stennett C. Development and implementation of an ignition and growth model for homogeneous and heterogeneous explosives[C]//The 11th International Detonation Symposium, Snowmass, Colorado, USA: Office of Naval Research, 1998: 589-598.

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      Johnson J N, Tang P K, Forest C A. Shock‑wave initiation of heterogeneous reactive solids[J]. Journal of Applied Physics, 1985, 57(9): 4323-4334.

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      Mader C L, Forest C A. Two‑dimensional homogeneous and heterogeneous detonation wave propagation[C]//The 6th International Detonation Symposium, San Diego, CA, USA ,1976.

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      Starkenberg J, Dorsey T M. An assessment of the performance of the history variable reactive burn explosive initiation model in the CTH code[C]//The 11th International Detonation Symposium, Snowmass, CO, USA: Office of Naval Research, 1998: 621-631.

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      Duan Z P, Wen L J, Liu Y R, et al. A pore collapse model for hot‑spot ignition in shocked multi‑component explosives[J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2010, 11(Suppl): 19-24.

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      田占东, 张震宇. PBX‑9404炸药冲击起爆细观反应速率模型[J]. 含能材料, 2007, 15(5): 464-467.

      TIAN Zhan‑dong, ZHANG Zhen‑yu. A mesomechanic model of shock initiation in PBX‑9404 explosive [J]. Chinese Journal of Energetic Materials（Hanneng Cailiao）, 2007, 15(5): 464-467.

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      WEN Li‑jing, DUAN Zhuo‑ping, ZHANG Lian‑sheng, et al. Effects of HMX particle size on the shock initiation of PBXC03 explosive[J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2012, 13(2): 189-194.

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      WEN Li‑jing, DUAN Zhuo‑ping, ZHANG Zhen‑yu, et al. Experimental and numerical study on the shock initiation of PBXC03 explosive under the different loading pressures [J]. Acta Armanentarh, 2013, 34(3): 283-288.

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      温丽晶. PBX炸药冲击起爆细观反应速率模型研究[D]. 北京：北京理工大学, 2011.

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  • 基本信息

    DOI:10.11943/CJEM2018354

    中图分类号: TJ55； O381

    文献标识码: A

    引用信息

    白志玲,段卓平,温丽晶,等. PBX炸药冲击起爆的改进细观反应速率模型[J]. 含能材料, DOI:10.11943/CJEM2018354.

    BAI Zhi‑ling,DUAN Zhuo‑ping,WEN Li‑jing,et al. A Modified Mesoscopic Reaction Rate Model for Shock Initiation of PBXs[J]. Chinese Journal of Energetic Materials（Hanneng Cailiao）, DOI:10.11943/CJEM2018354.

    基金信息

    国家自然科学基金（U1630113）；材料与结构冲击动力学创新小组（11521062）

    稿件历史

    网刊发布 : 2019-04-22
    收稿日期 : 2018-12-18
    修回日期 : 2019-01-22

    • 白志玲

    机 构：北京理工大学 爆炸科学与技术国家重点实验室， 北京 100081

    Affiliation：The State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

    邮 箱：zhilingbai@yeah.net

    作者简介：白志玲（1989-），女，博士生，主要从事爆炸与冲击动力学研究。e‑mail：zhilingbai@yeah.net

    段卓平

    机 构：北京理工大学 爆炸科学与技术国家重点实验室， 北京 100081

    Affiliation：The State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

    角 色：通讯作者

    Role：Corresponding author

    邮 箱：duanzp@bit.edu.cn

    作者简介：段卓平（1965-），男，研究员，博士生导师，主要从事爆炸与冲击动力学研究。e‑mail：duanzp@bit.edu.cn

    温丽晶

    机 构：环境保护部核与辐射安全中心， 北京 100082

    Affiliation：Nuclear and Radiation Safety Center, Ministry of Environmental Protection, Beijing 100082, China

    张震宇

    机 构：国防科技大学理学院技术物理研究所， 湖南 长沙 410073

    Affiliation：Institute of Technical Physics, College of Science, National University of Defense Technology, Changsha 410073, China

    欧卓成

    机 构：北京理工大学 爆炸科学与技术国家重点实验室， 北京 100081

    Affiliation：The State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

    黄风雷

    机 构：北京理工大学 爆炸科学与技术国家重点实验室， 北京 100081

    Affiliation：The State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

    hot‑spot ignition term[19]the second and third terms (the present work)
    Z/ μs-15.0e13a0.017
    T*/ K26500b1.86
    T0/ K298n0.965
    Cp/ cm2·μs-2·K-11.4e‑5c0.0128
    Q/ cm2·μs-25.439e‑2y0.125
    k*/ cm·μs-1·K-18.0e‑14G590.0
    γe/ GPa2.6m3.195
    ke/ GPa8e‑3s1.00
    parameters

    ρ0=1.836 g·cm-3

    (the present work)

    		ρ0=1.849 g·cm-3[22]

    ρ0=1.855 g·cm-3

    (the present work)

    A/GPa1002.7235102.5451031.4249
    B/GPa22.9311522.5723.48774
    R14.914.914.91
    R21.371.371.37
    ω0.290.290.29
    cv/GPa·K-11.0e‑31.0e‑31.0e‑3
    E0/GPa9.559.589.60
    parameters

    ρ0=1.836 g·cm-3

    (the present work)

    		ρ0=1.849 g·cm-3[22]

    ρ0=1.855 g·cm-3

    (the present work)

    A/GPa26554595.027213759.027750964.0
    B/GPa-73.4289-73.8544-73.8959
    R119.8719.8719.87
    R21.9871.9871.987
    ω1.991.991.99
    cv/GPa·K-11.68714e‑21.6932e‑21.69749e‑2
    density / g·cm-3mean particle size / μmpressure / GPa
    1.83620-30 (fine particle)5.9
    1.84970-90 (medium particle)5.2
    1.855110-130 (coarse particle)4.5
    materials

    ρ0

    / g·cm-3

    C

    / cm·μs-1

    		S1S2S3γ0a
    manganin8.140.3941.489001.990
    teflon2.120.1341.930000.900
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    表1 常温下PBXC03的改进DZK反应速率模型参数

    Table 1 Parameters of the modified DZK reaction rate model for PBXC03 at room temperature

    表2 常温下不同密度PBXC03爆轰产物JWL状态方程参数

    Table 2 Parameters of the JWL EOS for the detonation products of PBXC03 with different densities at room temperature

    表3 常温下不同密度PBXC03未反应炸药JWL状态方程参数

    Table 3 Parameters of the JWL EOS for the unreacted PBXC03 with different densities at room temperature

    表4 PBXC03的物理参数[22]

    Table 4 Physical parameters of PBXC03[22]

    表5 Grüeneisen状态方程参数[24]

    Table 5 Parameters in the Grüneisen equations of state [24]

    图1 不同加载压力下PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较 -- a. p0=5.9 GPa

    Fig.1 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 under different loading pressures -- a. p0=5.9 GPa

    图1 不同加载压力下PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较 -- b. p0=5.2 GPa

    Fig.1 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 under different loading pressures -- b. p0=5.2 GPa

    图1 不同加载压力下PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较 -- c. p0=4.5 GPa

    Fig.1 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 under different loading pressures -- c. p0=4.5 GPa

    图2 不同加载压力下PBXC03前导冲击波阵面压力历史的数值模拟结果与实验结果[22]比较

    Fig.2 Comparison of experimental data[22] and numerical results for the pressure growth on the precursory shock wave front of PBXC03 under different loading pressures

    图3 不同颗粒度PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较 -- a. fine particle

    Fig.3 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 with different particle sizes -- a. fine particle

    图3 不同颗粒度PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较 -- b. medium particle

    Fig.3 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 with different particle sizes -- b. medium particle

    图3 不同颗粒度PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较 -- c. coarse particle

    Fig.3 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 with different particle sizes -- c. coarse particle

    图4 不同颗粒度PBXC03冲击起爆前导冲击波阵面压力历史的数值模拟结果与实验结果[22]比较

    Fig.4 Comparison of experimental data[22] and numerical results for the pressure growth on precursory shock wave front of PBXC03 with different particle sizes

    图5 不同孔隙度的PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较 -- a. ρ0=1.836 g·cm-3

    Fig.5 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 with different porosities -- a. ρ0=1.836 g·cm-3

    图5 不同孔隙度的PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较 -- b. ρ0=1.849 g·cm-3

    Fig.5 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 with different porosities -- b. ρ0=1.849 g·cm-3

    图5 不同孔隙度的PBXC03冲击起爆过程的数值模拟结果与实验结果[22]比较 -- c. ρ0=1.855 g·cm-3

    Fig.5 Comparison of experimental data[22] and numerical results for the shock initiation process of PBXC03 with different porosities -- c. ρ0=1.855 g·cm-3

    图6 不同孔隙度PBXC03的前导冲击波阵面压力历史的数值模拟结果与实验结果[22]比较

    Fig.6 Comparison of experimental data[22] and numerical results for the pressure growth on the precursory shock wave front of PBXC03 with different porosities

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    Z is the pre‑exponential factor in Arrhenius kinetics. T* is the activation temperature. T0 is the initial temperature; Cp is the heat capacity. Q is the reaction heat of the explosive. k* is the thermal conductivity. γe is the viscous factor of the explosive. ke is the shear yield strength of the explosive.

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    ρ0 is the the initial density. C is the intercept of the shock wave velocity‑particle velocity curve. S1, S2, and S3 are slope coefficients of the particle velocity curve. γ0 is the Grüeneisen coefficient. a is the first‑order volume correction factor.

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