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RDX基PBX的模型、结构、能量及其与感度关系的分子动力学研究[J]. 中国科学:化学, 2013, 43(5): 576-584.
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目录 contents

    摘要

    为研究晶体缺陷对奥克托今(HMX)基高聚物粘结炸药(PBX)性能的影响,分别建立了2种PBX“完美”模型和4种缺陷模型。采用分子动力学(MD)方法,对6种PBX模型进行了模拟计算,得到了感度、结合能、爆轰性能和力学性能参数并进行了对比。结果表明,晶体缺陷导致PBX炸药的键连双原子作用能和内聚能密度减小,分别下降2.46~5.72 kJ·mol-1和0.0251~0.0544 kJ·cm-3,表明缺陷模型的感度增加,安全性降低;缺陷模型的结合能下降509.61~1618.24 kJ·mol‑1,表明炸药的稳定性变差;缺陷模型的密度、爆速和爆压均下降,降幅分别为0.01~0.05 g·cm-3、36.35~185.69 m·s-1和0.36~1.79 GPa,其氧平衡和爆热的变化几乎可以忽略不计,表明缺陷模型的毁伤威力降低。晶体缺陷还导致PBX炸药的拉伸模量、体积模量和剪切模量分别下降0.062~1.772、0.261~1.188 GPa和0.012~0.685 GPa,体积模量与剪切模量之比增加0.002~0.366,位错和空位缺陷模型的柯西压分别下降0.822 GPa和0.479 GPa,掺杂和孪晶缺陷模型的柯西压分别上升0.114 GPa和0.491 GPa,表明缺陷模型的抗变形能力下降,柔韧性增强。

    Abstract

    To investigate the effect of crystal defects on properties of HMX‑based polymer bonded explosive (PBX), two defect‑free models and four defective models were established. Using molecular dynamics (MD) method, different models were simulated and the sensitivity, binding energy, detonation performance and mechanical properties of different models were calculated and compared. Results show that the crystal defects cause the interaction energy of trigger bond and cohesive energy density to decrease by 2.46-5.72 kJ·mol-1 and 0.0251-0.0544 kJ·cm-3, respectively, indicating that the sensitivity of defective models is increased and safety is decreased. The binding energy of defective models is decreased by 106.89-231.65 kJ·mol-1, meaning that their stability is deteriorated. The density, detonation velocity and detonation pressure of defective models are decreased by 0.01-0.05 g·cm-3, 36.35-185.69 m·s-1 and 0.36-1.79 GPa, respectively. But the variation of oxygen balance and detonation heat can be negligible. The variation of detonation parameter indicates that the damage power of defective models is weakened. Tensile modulus, bulk modulus, shear modulus of defective models are decreased by 0.062-1.772, 0.261-1.188 GPa and 0.012-0.685 GPa, respectively. The ratio of bulk modulus to shear modulus is increased by 0.002-0.366. The Cauchy pressure of dislocation and vacancy defective models is decreased by 0.822 GPa and 0.479 GPa, while it is increased by 0.114 GPa and 0.491 GPa in doping and twin defective models respectively, indicating that the deformation resistance of the defective models is decreased and the flexibility is enhanced.

    Graphic Abstract

    图文摘要

    html/hncl/CJEM2018298/media/6a5afb32-1315-4ffa-904d-2156cacb5c30-image014.png

    The defect‑free and defective models of HMX‑based PBX were established and the effect of defects on sensitivity, stability, detonation performance and mechanical properties were researched. The interaction energy of trigger bond, cohesive energy density, binding energy, detonation parameters and mechanical properties of different models were got and compared.

  • 1 引 言

    1

    高聚物粘结炸药(PBX)以爆炸威力大的单质高能炸药为主体,通过加入粘结剂、钝感剂和增塑剂制备而成。PBX既继承了高能炸药能量特性高的优点,又具有较低的机械感度以及良好的力学性能和安定性,并且易于加工成型。β‑奥克托今(β‑HMX)具有能量密度高、安定性好的优点,是目前军事上使用最广泛、综合性能最好的猛炸药,常用作PBX的主体炸药。

    受合成环境和工艺的制约,合成完美HMX晶体的可能性微乎其微,晶体缺陷是不能避免的。在晶体生长过程中,受外界环境影响,例如辐射、温度、撞击等,HMX晶体可能会被引入位错、孪晶、掺杂和空位等缺[1]。PBX在制备及应用过程中受到机械挤压和碰撞作用而产生的内应力也会造成晶体缺陷的出[2]。晶体缺陷会影响晶体内的分子弛豫,同时也会使能量局域化而形成“热点”,是影响含能材料性能的重要因[3,4,5]

    彭亚晶[5]利用第一性原理研究了分子空位缺陷对黑索今(RDX)的几何结构、电子结构及振动特性的影响,结果表明空位缺陷使其附近的N—N键变长,分子结构松弛,能带隙减小,体系活性增加,形成“热点”。Xue[6]采用ReaxFF‑MD模拟的方法探究了位错缺陷对RDX冲击波感度的影响,结果证实位错缺陷会提升RDX的冲击波感度,并且刃位错的影响程度大于螺位错的影响程度。Xiao[7]运用分子动力学(MD)方法研究了晶体缺陷对RDX晶体及以它为基的PBX的感度和力学性能的影响。但是关于晶体缺陷对HMX基PBX炸药的感度、稳定性、爆轰性能和力学性能的影响研究较少。

    基于此,本研究利用Materials Studio(以下简称MS)软件建立了主体炸药含有不同晶体缺陷的HMX基PBX模型。采用MD方法,计算得到了用于表征不同PBX模型的感度、稳定性、爆轰性能和力学性能等参数,并对结果进行了比较,探究主体炸药内的晶体缺陷对PBX性能的影响。

  • 2 计算方法

    2
  • 2.1 “完美”模型的搭建

    2.1

    Choi[8]通过中子晶体衍射实验获得了β‑HMX属于单斜晶系,空间群为P21/c,晶体结构参数为a=0.654 nm,b=1.105 nm,c=0.870 nm,α=γ=90°,β=124.30°。根据β‑HMX的结构参数以及PBX中HMX所占的质量分数,在MS程序中搭建β‑HMX的(5×4×5)超晶胞模型,共200个HMX分子。将β‑HMX超晶胞模型分别沿着(0 0 1)和(1 0 1)晶面方向进行“切割”,“切割”厚度分别设置为3.5935 nm和1.7392 nm,为了放置其他组分,其上层真空层高度设置为0.3 nm。将经过能量最小化优化后的氟橡胶(F2311)、梯恩梯(TNT)、石蜡(C22H46)、石墨、硝化棉(NC)通过吸附的方式添加到真空层中建立HMX基(0 0 1)面PBX“完美”模型和(1 0 1)面PBX“完美”模型,其中F2311、TNT、C22H46、石墨、NC为随意摆放,分别如图1a和图1b所示,为便于同缺陷模型之间进行比较,此两种模型分别标记为Model‑Ⅰ和Model‑Ⅱ。本文中主要研究缺陷率为10%的模型的性能,因此选取20个HMX分子用于缺陷模型的搭建。

    html/hncl/CJEM2018298/media/6a5afb32-1315-4ffa-904d-2156cacb5c30-image001.png

    a. (0 0 1) surface (Model‑Ⅰ)

    html/hncl/CJEM2018298/media/6a5afb32-1315-4ffa-904d-2156cacb5c30-image002.png

    b. (1 0 1) surface (Model‑Ⅱ)

    图1 HMX基PBX“完美”模型

    Fig.1 The defect‑free models of HMX‑based PBX

  • 2.2 缺陷模型的搭建

    2.2

    β‑HMX容易产生位错的晶面是(0 0 1),其位错滑移系为(0 0 1)[1 0 0],其中,(0 0 1)表示其滑移面,[1 0 0]表示其滑移的伯格斯矢[9]。如图2a所示,将“完美”型HMX基PBX中标记为黄色的HMX分子剪切掉,而后将20个标记为绿色的HMX分子沿着伯格斯矢量的正负两个方向移动0.327 nm(伯格斯矢量方向两分子之间距离的一半)。HMX基PBX的位错缺陷模型如图2b所示,为了便于同(0 0 1)面HMX基PBX“完美”模型之间进行比较,该模型标记为Model‑Ⅲ。

    html/hncl/CJEM2018298/media/6a5afb32-1315-4ffa-904d-2156cacb5c30-image003.png

    a. the defect‑free model of (0 0 1) surface (Model‑Ⅰ)

    html/hncl/CJEM2018298/media/6a5afb32-1315-4ffa-904d-2156cacb5c30-image004.png

    b. the dislocation model of (0 0 1) surface (Model‑Ⅲ)

    图2 HMX基PBX“完美”型与位错缺陷模型

    Fig.2 The defect‑free model (Model‑Ⅰ) and dislocation model (Model‑Ⅲ) of HMX‑based PBX

    在(0 0 1)面HMX基PBX“完美”模型的基础上,通过将图3a中标记为黄色的20个HMX分子剪切移除,建立含空位缺陷的HMX基PBX模型,如图3b所示,标记为Model‑Ⅳ。

    html/hncl/CJEM2018298/media/6a5afb32-1315-4ffa-904d-2156cacb5c30-image005.png

    a. the defect‑free model of (0 0 1) surface (Model‑Ⅰ)

    html/hncl/CJEM2018298/media/6a5afb32-1315-4ffa-904d-2156cacb5c30-image006.png

    b. the vacancy model of (0 0 1) surface (Model‑Ⅳ)

    图3 HMX基PBX“完美”型与空位缺陷模型

    Fig.3 The defect‑free model (Model‑Ⅰ) and vacancy model (Model‑Ⅳ) of HMX based PBX

    在(0 0 1)面HMX基PBX“完美”模型的基础上,通过将图3a中标记为黄色的20个HMX分子替换成RDX分子,建立含掺杂缺陷的HMX基PBX模型,如图4所示,标记为Model‑Ⅴ。

    图4
                            HMX基PBX掺杂缺陷模型

    图4 HMX基PBX掺杂缺陷模型

    Fig.4 The doping model of HMX based PBX

    β‑HMX晶胞容易发生孪晶的晶面是(1 0 1[9],为建立含有200个HMX分子的PBX孪晶模型,首先建立了β‑HMX(5×2×5)超晶胞初始模型,周期箱中分别含有100个HMX分子。将β‑HMX(5×2×5)超晶胞沿着(1 0 1)晶面方向进行“切割”,“切割”厚度设置为1.7392 nm。通过Build Layer命令将两个切割分面超晶胞模型拼接在一起建立了HMX超晶胞的孪晶模型,其上方的真空层的高度设置为0.3 nm,将经过能量最小化优化后的F2311、TNT、C22H46、石墨、NC添加到真空层中建立含孪晶缺陷的PBX炸药模型,如图5所示,标记为Model‑Ⅵ。图5中标记为绿色的面即为孪晶面。

    html/hncl/CJEM2018298/media/6a5afb32-1315-4ffa-904d-2156cacb5c30-image008.png

    a. the twin model of HMX

    html/hncl/CJEM2018298/media/6a5afb32-1315-4ffa-904d-2156cacb5c30-image009.png

    b. the twin model of PBX (Model‑Ⅵ)

    图5 HMX孪晶模型与HMX基PBX孪晶缺陷模型

    Fig.5 The twin models of HMX and HMX based PBX

  • 2.3 分子动力学模拟条件设置

    2.3

    由于COMPASS力场对HMX基PBX进行过成功的模拟计[10,11],因此对上述所建模型在COMPASS力场中采用Smart算法对初始模型进行优化,收敛精度设置为0.004 kJ·mol-1·Å-1。当优化结果显示的最大导数低于0.05时认为优化模型实现了能量极小化,内应力已被平衡。对优化后的晶胞模型进行模拟退火,退火精度设置为“Fine”,并选择能量最小的退火模型进行MD模拟。对PBX模型的MD模拟选择在恒压恒温(NPT)系综下进行,模拟的温度设置为298 K,压力设置为101 kPa精度设置为“Fine”。模拟过程中分别采用Nose[12]和Berendsen[13]方法对温度和压力进行控制,范德华(vdW)和静电作用(Coulomb)的加和方法分别采用Atom‑based[14]和Ewald[15],截断半径取1.55 nm,并对截断尾部进行矫正。原子运动的初始速度由Maxwell‑Boltzmann分布确定,并采用Verlet方[16]求解牛顿运动方程的积分。对所建模型进行了100 ps的MD模拟,前50 ps对模型体系进行平衡,后50 ps用于统计分析确定能量、力学参数和其它参数。每0.1 ps取样一次,共获得500帧轨迹。

  • 3 结果与讨论

    3
  • 3.1 平衡判别

    3.1

    只有当模拟体系达到平衡后,对原子运动轨迹进行统计分析才有意义。模拟体系平衡的标志是温度和能量随时间变化的波动幅度在5%~10%。以PBX位错缺陷模型的MD模拟为例,其温度和能量随时间变化的曲线图如图6所示。由图6可见,位错缺陷模型的温度和能量随时间的推移逐渐趋于平缓,温度和能量偏差较小,表明PBX初始模型已达到平衡状态。

    html/hncl/CJEM2018298/alternativeImage/6a5afb32-1315-4ffa-904d-2156cacb5c30-F010.jpg

    a. temperature curve vs. time

    html/hncl/CJEM2018298/media/6a5afb32-1315-4ffa-904d-2156cacb5c30-image011.png

    b. energy curves vs. time

    图6 温度和能量随时间的变化曲线

    Fig.6 Temperature and energy curves versus time

  • 3.2 安全性能

    3.2

    感度是指炸药在受到外界刺激后发生爆炸的难易程度,是体现含能材料安全性的一项重要内容。许多研究文[10,17,18,19,20]提出了评估含能材料感度的理论,尤其是Xiao[10]利用键连双原子作用能和内聚能密度作为判据评估HMX及以其为基的PBX的感度所得结果与实验事实相符。因此,本研究采用引发键键连双原子作用能和内聚能密度作为判据,来预测不同模型的感度,评估主体炸药内的晶体缺陷对PBX感度的影响。

  • 3.2.1 引发键键连双原子作用能

    3.2.1

    所谓引发键是指含能材料在受到外界刺激时,最先发生解离引发含能材料分解甚至爆炸的化学键。以HMX为基的PBX中,HMX所占比例最大,感度最高,是最易发生爆炸的组分。之前的研究表明,HMX的引发键为N—NO2基团中的N—N[18,21]

    键连双原子作用能(EN—N)是指引发键的键能,定义[22]

    ENN=E1-E2n
    (1)

    式中,E1表示平衡状态下,HMX基PBX模型的总能量,kJ·mol‑-1E2表示平衡状态下,PBX模型中HMX的引发键束缚的N原子被固定后的总能量,kJ·mol-1n表示PBX模型中N—N键的数量。根据MD模拟得到的能量参数以及公式(1)计算得到不同模型的引发键键连双原子作用能,如图7所示。

    从图7可以看出,Model‑Ⅲ、Model‑Ⅳ和Model‑Ⅴ的引发键的键连双原子作用能较Model‑Ⅰ减小,下降幅度分别为3.33、2.46 kJ·mol-1和2.90 kJ·mol-1;Model‑Ⅵ的引发键的键连双原子作用能较Model‑Ⅱ减小,降幅为5.72 kJ·mol-1。引发键键连双原子作用能的减小意味着PBX中的引发键束缚N原子的能力减弱,在受到外界刺激时更容易发生断裂诱发PBX分解甚至爆炸。这表明主体炸药内的位错、空位和掺杂晶体缺陷导致(0 0 1)面PBX模型的感度上升,安全性降低,孪晶缺陷导致(1 0 1)面PBX模型的感度上升,安全性降低。

    图7
                            不同HMX基PBX模型的键连双原子作用能

    图7 不同HMX基PBX模型的键连双原子作用能

    Fig.7 Interaction energy of trigger bond of different HMX‑based PBX models

  • 3.2.2 内聚能密度

    3.2.2

    内聚能密度(CED)是指单位体积内1 mol凝聚态物质汽化为气态物质所需要的能量。计算公[22]为:

    CED=ΔHV-RTVm
    (2)

    式中,ΔHV是指摩尔蒸发热,J·mol-1RT是指气化时所做的膨胀功,J·mol-1Vm是摩尔体积,cm3·mol-1

    内聚能密度是分子间相互作用的综合反映,是范德华力(vdW)和静电力(electrostatic force)之和,本质上是一种非键力。CED反映的是体系中分子间相互作用的强弱,与体系的感度之间存在一定的关[23]。通过MD模拟计算得到了不同HMX基PBX模型的CED值,如表1所示。

    表1 不同HMX基PBX模型的CED及其分量

    Table 1 CED and its components of different HMX‑based PBX modelskJ·cm-3

    ModelCEDvdWelectrostatic force
    0.68160.26660.4061
    0.71460.28940.4167
    0.64290.24440.3900
    0.65650.24480.4032
    0.65210.25680.3867
    0.66020.26880.3829

    从表1可以看出,Model‑Ⅲ、Model‑Ⅳ和Model‑Ⅴ的内聚能密度较Model‑Ⅰ减小,下降幅度分别为0.0387、0.0251 kJ·cm-3和0.0295 kJ·cm-3;Model‑Ⅵ的内聚能密度较Model‑Ⅱ减小,下降幅度为0.0544 kJ·cm-3。内聚能密度减小意味着PBX由凝聚态转化为气态所需的能量减小,受外界刺激作用时的敏感程度增加。这表明主体炸药内的晶体缺陷导致PBX的感度上升,安全性变差。这与以引发键的键连双原子作用能为判据分析主体炸药内的晶体缺陷对PBX感度性能的影响获得的结论一致。

    我们推测出现这种结果的原因是晶体缺陷破坏了PBX中的晶体结构,其晶格发生变形,晶胞中的分子重新排布,变得混乱无规则,PBX内分子间和分子内的相互作用减弱,势能减小。势能的净释放提高了PBX内分子的活化程度,在缺陷区域形成“热点”,感度升高,安全性降低。Model‑Ⅵ的内聚能和引发键键连双原子作用能的下降幅度最大的原因可能是因为孪晶缺陷对HMX晶体结构破坏最大,其缺陷模型的自由体积更大。

  • 3.3 稳定性

    3.3

    结合能(Eb)是指含能材料体系中不同组分之间的相互作用能,可用于评估PBX的稳定性。由于不同PBX模型的分子数不同,需要选择初始模型作为基准对其它模型的结合能进行归一化,得到修正结合能,其计算公式[24]

    Eb*=EbN0NiEb=Etotal-(mEHMX+Eadditive)
    (3)

    式中,Eb*表示修正结合能,kJ·mol-1N0表示基准模型中所有分子的个数;Ni表示修正模型中所有分子的个数;Eb是结合能,kJ·mol-1Etotal是平衡状态下,PBX体系的总能量,kJ·mol-1m表示PBX体系中主体炸药包含的HMX分子的个数;EHMX是单个HMX分子在平衡状态下的能量,kJ·mol-1Eadditive是平衡状态下,PBX模型体系中添加成分的能量,kJ·mol-1

    根据MD模拟计算得到的能量数据和公式(3)计算得到了HMX基PBX“完美”模型及其缺陷模型的结合能,如图8所示。

    图8
                            不同HMX基PBX模型的结合能

    图8 不同HMX基PBX模型的结合能

    Fig.8 Binding energy of different PBX models

    从图8可以看出,Model‑Ⅲ、Model‑Ⅳ和Model‑Ⅴ的结合能较Model‑Ⅰ减小,下降幅度分别为1618.24、989.43 kJ·mol-1和1358.01 kJ·mol-1;Model‑Ⅵ的结合能较Model‑Ⅱ下降了509.61 kJ·mol-1。这表明缺陷模型中的主体炸药与添加剂之间相互吸引的相互作用力减弱,缺陷模型的稳定性变差。由此可知,主体炸药内的晶体缺陷会导致PBX的稳定性变差。

  • 3.4 爆轰性能

    3.4

    爆轰性能主要反映含能材料的威力与能量密度,主要通过氧平衡系数(OB)、爆速(D)、爆压(p)和爆热(Q)等参数进行表征。本研究采用修正氮当量[25]和盖斯定[26]计算了炸药的爆轰参数,以此对其能量特性进行评估。

    对于化学式为CaHbOcNd的炸药,氧平衡系数计算公[27]如下:

    OB=c-(2a+b/2)Mr×16×100%
    (4)

    式中,abc分别为炸药分子中包含的C、H、O原子的数目;Mr为炸药的摩尔质量,g·mol-1

    根据修正氮当量理论,爆速(D)和爆压(p)的计算公[25]如下:

    D=(690+1160ρ)Nchp=1.106(ρNch)2-0.84Nch=100Mr(piNpi+BKNBK+GjNGj)
    (5)

    式中,D为炸药的爆速,m·s-1p为炸药的爆压,GPa;ρ为炸药的密度,g·cm-3;ΣNch为炸药的修正氮当量;pi为1 mol炸药爆炸时生成第i种爆轰产物的摩尔数;Npi为第i种爆轰产物的氮当量系数;BK为炸药分子中第K种化学键出现的次数;NBK为炸药分子中第K种化学键的氮当量系数;Gj为炸药分子中第j种基团出现的次数;NGj为炸药分子中第j种基团的氮当量系数。

    根据盖斯定律,爆热(Q)的计算公[26]为:

    Q=niΔHf,niθ-miΔHf,miθ
    (6)

    式中,ni是指爆轰产物中第i种产物的量,mol·kg-1ΔHf,niθ是指爆轰产物中第i种产物的生成焓,J·mol-1mi是指混合炸药中第i种组分的量,mol·kg-1ΔHf,miθ是指混合炸药中第i种组分的生成焓,J·mol-1

    根据修正氮当量法和盖斯定律,计算获得了不同模型的爆轰参数,结果如表2所示,表中炸药的密度值是MD模拟计算的结果。

    表2 不同HMX基PBX模型的爆轰参数

    Table 2 Detonation parameters of different HMX‑based PBX models

    ModelOB / %ρ / g·cm-3D / m·s-1p / GPaQ / kJ·kg-1
    -25.311.658160.1328.735553.46
    -25.311.638087.4328.025553.46
    -25.451.607974.4426.945551.25
    -25.691.628040.5127.595547.57
    -25.401.638084.9728.005553.82
    -25.311.628051.0827.665553.46

    分析公式(5)的结构可以看出,爆速和爆压受修正氮当量系数和密度两个因素制约。但是本节中探究的主体炸药内缺陷对HMX基PBX的修正氮当量系数的影响非常微小,最大降幅仅为0.0041,几乎可以忽略不计。因此,晶体缺陷对HMX基PBX爆速和爆压产生影响的主要因素是其对HMX基PBX密度的影响。根据表2中可以看出,位错(Model‑Ⅲ)、空位(Model‑Ⅳ)和掺杂(Model‑Ⅴ)缺陷导致(0 0 1)面HMX基PBX模型的密度下降了0.05、0.03 g·cm-3和0.02 g·cm-3,孪晶缺陷导致(1 0 1)面HMX基PBX模型的密度下降0.01 g·cm-3,位错(Model‑Ⅲ)、空位(Model‑Ⅳ)、掺杂(Model‑Ⅴ)和孪晶(Model‑Ⅵ)缺陷模型同各自的“完美”模型相比,爆速分别下降185.69、119.62、75.16 m·s-1和36.35 m·s-1,爆压分别下降1.79、1.14、0.73 GPa和0.36 GPa。这表明主体炸药内的晶体缺陷对HMX基PBX炸药的爆速和爆压产生不利影响,其中位错缺陷影响相对较重,孪晶缺陷影响相对较弱。分析公式(4)和(6)的结构可以看出,对炸药的氧平衡和爆热产生影响的因素是炸药中的分子组成的变化。由于孪晶缺陷模型的分子组成与(1 0 1)面HMX基PBX模型相比未发生改变,因此其氧平衡和爆热并未发生变化。位错、空位和掺杂三种缺陷均导致(0 0 1)面HMX基PBX更趋于负氧平衡,爆热下降,但是爆热受其影响的最大变化程度仅为0.11%,变化可忽略不计。由此看来,主体炸药内的晶体缺陷确实会导致PBX的毁伤威力减弱。

  • 3.5 力学性能

    3.5

    MS软件能够对经过分子动力学平衡后的体系进行小变形加载实验,并通过分析计算平衡体系的轨迹获得弹性系数。根据广义虎克定[28],通过最小二乘法拟合弹性系数得出平均的拉伸应力应变,获得体积模量(K)和剪切模量(G)。计算公式如下所示:

    σi=Cijεj
    (7)
    KR=S11+S22+S33+2(S12+S23+S31)-1
    (8)
    GR=154(S11+S22+S33)-4(S12+S23+S31)+3(S44+S55+S66)-1
    (9)

    式中,σ表示应力,Pa;ε表示应变;K表示体积模量,Pa;G表示剪切模量,Pa;下标R表示Reuss平均;Cijij=1,2,……,6)表示弹性系数矩阵;Sij表示柔量系数矩阵,等于Cij的逆矩阵,即S=C-1

    力学参数之间具有相互联系,关系式如公式(10)所示:

    E=2G(1+γ)=3K(1-2γ)
    (10)

    式中,E表示拉伸模量,Pa;γ是泊松比。

    根据公式(10)可以计算得到拉伸模量(E)以及泊松比(γ)。

    E=9GK3K+G
    (11)
    γ=3K-2G2(3K+G)
    (12)

    根据上述公式,求得HMX基PBX“完美”模型及其晶体缺陷模型的力学性能参数,结果如表3所示。

    表3 不同HMX基PBX模型的弹性系数及力学参数

    Table 3 Elasticity coefficient and mechanical parameters of different HMX‑based PBX models

    Model
    C1112.11111.6539.63111.14710.94110.941
    C2212.09511.3194.94110.93010.80711.393
    C3311.88110.7065.89211.23711.02711.803
    C442.5683.0992.3722.3532.2152.391
    C552.7653.0732.3782.8952.6532.941
    C662.6732.5872.3912.4042.4112.864
    C125.9595.6164.9415.2665.7205.633
    C136.4766.1115.8925.9405.8595.764
    C235.4085.8225.7785.4435.3905.723
    C150.153-0.6280.3450.062-0.0380.066
    C25-0.2860.231-0.029-0.1160.172-0.200
    C350.0770.5880.836-0.289-0.038-0.208
    C46-0.3520.2370.087-0.113-0.082-0.055
    E7.4907.4285.7186.8926.5407.383
    γ0.3430.3380.3590.3510.3530.338
    K7.9657.6336.7777.7047.4097.591
    G2.7882.7762.1032.5512.4172.759
    K/G2.8572.7493.2233.0203.0652.751
    C12C443.3912.7512.5692.9123.5053.242

    NOTE: The unit for E, K, G and Cijij=1,2,……,6) is GPa.

    从表3可以看出,缺陷模型的拉伸模量(E)、体积模量(K)和剪切模量(G)下降,降低幅度分别为0.062~1.772、0.261~1.188 GPa和0.012~0.685 GPa,表明缺陷模型的刚度、断裂强度和硬度减弱,其抗变形能力下降。缺陷模型的体积模量与剪切模量之比上升,上升幅度为0.002~0.366,表明缺陷模型的柔韧性增加,材料发生形变而不产生裂缝的能力增强。位错和空位缺陷模型的柯西压(C12C44)下降,降幅分别为0.822 GPa和0.479 GPa。掺杂和孪晶缺陷模型的柯西压上升,升幅分别为0.114 GPa和0.491 GPa。C12C44分别与正应力和切应力相关联,当C12大于C44时,更容易发生剪切形变产生切应力,产生粗糙的断裂面;反之,更容易发生正应变产生正应力,产生光滑的断裂[29]。这表明位错和空位缺陷模型更显脆性,在发生断裂的情况下,其断裂面比较光滑,而掺杂和孪晶缺陷模型的断裂面较为粗糙。

  • 4 结 论

    4

    (1)受主体炸药内含晶体缺陷的影响,HMX基PBX的键连双原子作用能和内聚能密度减小,显示PBX缺陷模型体系内的分子状态较各自“完美”模型的分子状态更活跃,表明缺陷模型的感度升高,安全性降低。因此,主体炸药内的晶体缺陷会对PBX的感度产生不利影响,降低PBX的安全性。

    (2)主体炸药内的晶体缺陷导致HMX基PBX的主体炸药与添加剂之间的结合能下降,显示PBX主体炸药与添加剂之间相互吸引的相互作用力减弱,表明缺陷模型的稳定性变差。因此,主体炸药内的晶体缺陷会破坏PBX的稳定性。

    (3)HMX基PBX缺陷模型的密度、爆速和爆压均下降,氧平衡和爆热的变化可忽略不计,表明主体炸药内的晶体缺陷降低了PBX炸药的毁伤威力。

    (4)HMX基PBX缺陷模型的刚度、硬度和断裂强度下降,抗变形能力变差;其体积模量与剪切模量之比上升,发生形变时不产生裂缝的能力增强。位错和空位缺陷模型的柯西压下降,掺杂和孪晶缺陷的柯西压上升,表明位错和空位缺陷模型发生断裂时的界面更加光滑,掺杂和孪晶缺陷模型的断裂界面更加粗糙。

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      欧育湘. 炸药学[M]. 北京: 北京理工大学出版社, 2006: 344.

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    • 27

      王玉玲, 余文力. 炸药与火工品[M]. 西安: 西北工业大学出版社, 2011: 31, 27.

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    • 28

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      YU Mao‑hong. Mechanics of Materials[M]. Beijing: Higher Education Press, 2015: 283-284.

    • 29

      Xiao J J, Wang W R, Chen J, et al. Study on structure, sensitivity and mechanical properties of HMX and HMX‑based PBXs with molecular dynamics simulation[J]. Computational and Theoretical Chemistry, 2012, 999(11):21-27.

苗爽

机 构:火箭军工程大学 核工程学院, 陕西 西安 710025

Affiliation:School of Nuclear Engineering, Rocket Force University of Engineering, Xi′an 710025, China

作者简介:苗爽(1994-),男,硕士研究生,主要从事含能材料晶体缺陷研究。e‑mail:2474524959@qq.com

王涛

机 构:火箭军工程大学 核工程学院, 陕西 西安 710025

Affiliation:School of Nuclear Engineering, Rocket Force University of Engineering, Xi′an 710025, China

角 色:通讯作者

Role:Corresponding author

邮 箱:wtao009@163.com

作者简介:王涛(1978-),男,副教授,主要从事含能材料晶体缺陷研究。e‑mail:wtao009@163.com

王玉玲

机 构:火箭军工程大学 核工程学院, 陕西 西安 710025

Affiliation:School of Nuclear Engineering, Rocket Force University of Engineering, Xi′an 710025, China

杭贵云

机 构:火箭军工程大学 核工程学院, 陕西 西安 710025

Affiliation:School of Nuclear Engineering, Rocket Force University of Engineering, Xi′an 710025, China

戚春保

机 构:火箭军工程大学 核工程学院, 陕西 西安 710025

Affiliation:School of Nuclear Engineering, Rocket Force University of Engineering, Xi′an 710025, China

鲁昌兵

机 构:空军驻中国工程物理研究院军事代表办公室, 四川 绵阳 621999

Affiliation:Military Representative Office in China Institute of Engineering Physics of Air Force, Mianyang 621999, China

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ModelCEDvdWelectrostatic force
0.68160.26660.4061
0.71460.28940.4167
0.64290.24440.3900
0.65650.24480.4032
0.65210.25680.3867
0.66020.26880.3829
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ModelOB / %ρ / g·cm-3D / m·s-1p / GPaQ / kJ·kg-1
-25.311.658160.1328.735553.46
-25.311.638087.4328.025553.46
-25.451.607974.4426.945551.25
-25.691.628040.5127.595547.57
-25.401.638084.9728.005553.82
-25.311.628051.0827.665553.46
Model
C1112.11111.6539.63111.14710.94110.941
C2212.09511.3194.94110.93010.80711.393
C3311.88110.7065.89211.23711.02711.803
C442.5683.0992.3722.3532.2152.391
C552.7653.0732.3782.8952.6532.941
C662.6732.5872.3912.4042.4112.864
C125.9595.6164.9415.2665.7205.633
C136.4766.1115.8925.9405.8595.764
C235.4085.8225.7785.4435.3905.723
C150.153-0.6280.3450.062-0.0380.066
C25-0.2860.231-0.029-0.1160.172-0.200
C350.0770.5880.836-0.289-0.038-0.208
C46-0.3520.2370.087-0.113-0.082-0.055
E7.4907.4285.7186.8926.5407.383
γ0.3430.3380.3590.3510.3530.338
K7.9657.6336.7777.7047.4097.591
G2.7882.7762.1032.5512.4172.759
K/G2.8572.7493.2233.0203.0652.751
C12C443.3912.7512.5692.9123.5053.242

图1 HMX基PBX“完美”模型 -- a. (0 0 1) surface (Model‑Ⅰ)

Fig.1 The defect‑free models of HMX‑based PBX -- a. (0 0 1) surface (Model‑Ⅰ)

图1 HMX基PBX“完美”模型 -- b. (1 0 1) surface (Model‑Ⅱ)

Fig.1 The defect‑free models of HMX‑based PBX -- b. (1 0 1) surface (Model‑Ⅱ)

图2 HMX基PBX“完美”型与位错缺陷模型 -- a. the defect‑free model of (0 0 1) surface (Model‑Ⅰ)

Fig.2 The defect‑free model (Model‑Ⅰ) and dislocation model (Model‑Ⅲ) of HMX‑based PBX -- a. the defect‑free model of (0 0 1) surface (Model‑Ⅰ)

图2 HMX基PBX“完美”型与位错缺陷模型 -- b. the dislocation model of (0 0 1) surface (Model‑Ⅲ)

Fig.2 The defect‑free model (Model‑Ⅰ) and dislocation model (Model‑Ⅲ) of HMX‑based PBX -- b. the dislocation model of (0 0 1) surface (Model‑Ⅲ)

图3 HMX基PBX“完美”型与空位缺陷模型 -- a. the defect‑free model of (0 0 1) surface (Model‑Ⅰ)

Fig.3 The defect‑free model (Model‑Ⅰ) and vacancy model (Model‑Ⅳ) of HMX based PBX -- a. the defect‑free model of (0 0 1) surface (Model‑Ⅰ)

图3 HMX基PBX“完美”型与空位缺陷模型 -- b. the vacancy model of (0 0 1) surface (Model‑Ⅳ)

Fig.3 The defect‑free model (Model‑Ⅰ) and vacancy model (Model‑Ⅳ) of HMX based PBX -- b. the vacancy model of (0 0 1) surface (Model‑Ⅳ)

图4 HMX基PBX掺杂缺陷模型

Fig.4 The doping model of HMX based PBX

图5 HMX孪晶模型与HMX基PBX孪晶缺陷模型 -- a. the twin model of HMX

Fig.5 The twin models of HMX and HMX based PBX -- a. the twin model of HMX

图5 HMX孪晶模型与HMX基PBX孪晶缺陷模型 -- b. the twin model of PBX (Model‑Ⅵ)

Fig.5 The twin models of HMX and HMX based PBX -- b. the twin model of PBX (Model‑Ⅵ)

图6 温度和能量随时间的变化曲线 -- a. temperature curve vs. time

Fig.6 Temperature and energy curves versus time -- a. temperature curve vs. time

图6 温度和能量随时间的变化曲线 -- b. energy curves vs. time

Fig.6 Temperature and energy curves versus time -- b. energy curves vs. time

图7 不同HMX基PBX模型的键连双原子作用能

Fig.7 Interaction energy of trigger bond of different HMX‑based PBX models

表1 不同HMX基PBX模型的CED及其分量

Table 1 CED and its components of different HMX‑based PBX modelskJ·cm-3

图8 不同HMX基PBX模型的结合能

Fig.8 Binding energy of different PBX models

表2 不同HMX基PBX模型的爆轰参数

Table 2 Detonation parameters of different HMX‑based PBX models

表3 不同HMX基PBX模型的弹性系数及力学参数

Table 3 Elasticity coefficient and mechanical parameters of different HMX‑based PBX models

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The unit for E, K, G and Cijij=1,2,……,6) is GPa.

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