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目录 contents

    摘要

    以1,3,5‑三氨基‑2,4,6‑三硝基苯(TATB)基高聚物粘结炸药(PBX)材料为研究对象,在-40~75 ℃下开展了准静态的单轴拉伸、压缩试验,获得了预设17个温度点下的应力应变关系数据;以温度、应变为自变量,应力为因变量,基于支持向量机(SVM)算法对拉伸压缩条件下的应力应变关系进行了描述,并对构建的关系式进行了误差分析。结果表明,在-40~75 ℃内,材料的拉伸强度和压缩强度均随温度的升高而劣化,应力应变曲线的非线性和拉压非对称性特征变化明显;同时,采用一组参数基于SVM算法实现了不同温度下TATB基PBX拉伸压缩应力应变关系的描述,解决了模型参数常随温度变化的问题,构建的关系式平均绝对百分比误差不超过7.77%,相关系数均大于0.998,表现出了良好的适用性。

    Abstract

    Taking 1,3,5‑triamino‑2,4,6‑trinitrobenzene (TATB)‑based high polymer bonded explosive (PBX) material as research object, the quasi‑static uniaxial tension and compression tests were carried out at -40-75 ℃, and the stress‑strain relationship data at 17 preset temperature points were obtained. Setting temperature and strain as independent variables, stress as dependent variable, the stress‑strain relationship under the tension and compression conditions was described based on support vector machine (SVM) algorithm, and the error analysis of the constructed relationship was carried out. The results show that the tensile strength and compressive strength of the materials deteriorate with increasing the temperature in the temperature range of -40-75 ℃ and the non‑linearity of stress‑strain curve and asymmetry of tension compression change obviously. Meanwhile, a set of parameters based on SVM algorithm is used to realize the description of the tensile and compressive strain‑strain relationship of TATB‑based PBX at different temperatures, which solves the problem that the model parameters often change with temperature. The average absolute percentage error of the constructed relationship is not more than 7.77%, and the correlation coefficients are all greater than 0.998, showing a good applicability.

  • 1 引 言

    本构模型作为不同应力状态、不同加卸载路径和不同温度环境下材料本构行[1]的普适性描述,一直以来都是材料力学行为研究领域中的热点;应力应变关系的描述作为本构模型建立的重要基础工作,向来备受关[2,3,4]。高聚物粘结炸药(PBX)本构模型的研究最早可追溯到上世纪80年[5,6],并随着代表性模型的建立取得了长足进展。其中,Visco‑SCRAM[7]模型考虑了微裂纹的张开、闭合、剪切以及材料粘性的影响,较好地反映了单轴应力下的力学行为;但因考虑因素过多,参数确定十分困难,导致实际应用效果并不理想。对于唯像的Ramberg‑Osgood[8]与Johnson‑Cook[9]模型,两者参数更为精简,可对单轴准静态拉伸或压缩载荷下PBX的应力应变关系进行描述,Johnson‑Cook模型同时考虑了应变率和温度的影响;但二者均无法使用一套参数同时对拉伸和压缩状态下的应力应变关系进行描述。为解决上述问题,有学者提出采用Boltzmann函[10]来建立炸药材料的高精度本构模[11],但所适用的温度范围有限。目前PBX本构模型的总体研究现状正如Devin Shunk在国防报[12]的描述,“虽然开展了大量的探索性工作,但仍很缺乏”。

    宽温域下应力应变关系的描述,常采用在一定假设前提下得到的理论推导表达式,进而通过拟合确定参数,存在描述精度不佳或参数确定困难的问题在所难免。机器学习算法对数据规律的挖掘不受主观预设模型的影响,“智能”且便利,为宽温域下拉伸压缩应力应变关系的描述带来了新思[13]。支持向量机(SVM)算法不仅收敛性优于人工神经网络(ANN)算[14],而且具有完整的数学解[15],便于模型的二次开发运用,现广泛应用于材料失效面建[16],结构损伤检[17],地面沉降分[18]以及混合炸药爆轰性能预[19]等领域。

    本研究针对传统应力应变关系中参数确定困难,以及参数的温度相关性(参数随温度变化而改变)问题,以1,3,5‑三氨基‑2,4,6‑三硝基苯(TATB)基PBX为研究对象,在获取宽温域(-40~75 ℃)准静态单轴拉伸、压缩实验数据的基础上,以期通过构建训练集、关系式参数寻优以及误差分析等步骤,采用SVM算法描述拉伸压缩应力应变关系,并进行误差分析。

  • 2 实验部分

  • 2.1 材料与仪器

    本研究使用的TATB基PBX,由质量比超过94%的TATB炸药晶体与质量比低于6%的氟橡胶制成。参照GJB772A-1997标准,单轴拉伸实验样品为Φ15 mm×65 mm的哑铃状,单轴压缩实验样品为Φ20 mm×20 mm的圆柱状。

    实验在Instron‑5582型材料实验机上进行。

  • 2.2 准静态单轴拉压实验方案

    实验分为单轴拉伸和单轴压缩两部分,实验加载速度为0.5 mm·min-1,折算应变率为4.16×10-4,属于准静态范围。依据最大温度间隔不超过10 ℃,在常用温度范围和粘结剂性能转变点附[20]密集选点的原则,在-40~75 ℃内,设计了-40,-30,-20,-15,-5,5,15,20,25,35,40,45,50,55,60,65,75 ℃17个实验温度点,每种实验条件的有效样本不低于3发,共计实验样本数超过102发。

  • 2.3 实验结果

    曲线变化规律类似,仅选取-20 ℃和20 ℃下,单轴压缩载荷(图1)与拉伸载荷(图2)的应力应变曲线进行分析。

    html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F005.jpg

    a. -20 ℃

    html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F006.jpg

    b. 20 ℃

    图1 -20 ℃与20 ℃下单轴压缩应力应变曲线

    Fig.1 Uniaxial compressive stress‑strain curves at -20 ℃ and 20 ℃

    html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F007.jpg

    a. -20 ℃

    html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F008.jpg

    b. 20 ℃

    图2 -20 ℃与20 ℃下单轴拉伸应力应变曲线

    Fig.2 Uniaxial tensile stress‑strain curves at -20 ℃ and 20 ℃

    为得到同温度,拉伸与压缩载荷下的应力应变曲线,首先按单轴拉伸应力为正,单轴压缩应力为负对实验数据进行标记,然后将最小拉伸和最小压缩应力位置设为零点,最后在同一坐标系下重构拉伸压缩应力应变曲线,如图3。可以看出该PBX炸药的应力应变曲线近似呈现为S型,应力应变关系表现出明显的非线性;拉伸强度与压缩强度相比,数值较低,材料非对称性显著。

    图3
                            拉伸与压缩载荷下的应力应变曲线构建流程

    图3 拉伸与压缩载荷下的应力应变曲线构建流程

    Fig.3 Construction process of stress‑strain curves under tension and compression load

    4为17个温度点下的拉伸压缩应力应变曲线。由图4可知,随温度的升高,压缩强度由-40 ℃时42.41 MPa降至75 ℃时12.64 MPa,拉伸强度由-40 ℃时11.55 MPa降低至75 ℃时2.69 MPa,劣化明显,曲线的非线性特征和拉压非对称性特征也随之改变。

    图4
                            17个温度点下的拉伸压缩应力应变曲线

    图4 17个温度点下的拉伸压缩应力应变曲线

    Fig.4 Tension‑compression stress‑strain curves at 17 temperature points

  • 3 基于SVM算法构建应力应变关系式

    应力应变关系的描述问题,本质上为一个多元非线性回归问题。应力应变关系的描述首先需构建训练集,为SVM算法提供基础输入样本,其中Tεσ分别代表温度、应变与应力,[T,ε]i,σi,i=1,2,...,n,[T,ε]iRn,σiR;之后,利用拉格朗日乘子法将样本映射至更高维度的特征空间并利用核函数求解,最终得对应的应力应变关系[21]

  • 3.1 训练集构建

    利用SVM算法描述材料的应力应变关系,首先需建立训练数据集。数据集由所有待测温度下的数据组成,含有温度、应变、应力3个指标。将温度、应变的数据点作为输入数据,将应力的数据点作为输出数据,构建训练数据集。由于所采集的3个指标间数值差距较大且量纲不同,在对应力应变关系描述前需对样本进行归一化处理,本研究中分别将温度T、应变ε与应力σ归一化至区间[1,2]。三者所用归一化公式相同,仅以T为例:

    Tn=T-TminTmax-Tmin+1
    (1)

    式中,Tn代表归一化后的数值,为无量纲数。Tmax代表温度与应变中的最大值,Tmin代表温度最小值,T代表本次所选数值,单位均为℃。

  • 3.2 应力应变关系式的理论推导

    SVM作为一种监督学习模型,其对于应力应变关系描述问题的认知实质上是结构风险函数的最优化。在数据集导入后,引入Hinge Loss损失函数,惩罚因子C,不敏感损失函数ω和松弛变量ξiξi*,可得优化目标,如式(2[22]

    min12w2+Ci=1lξi+i=1lξi*
    (2)

    式(2)得到的目标函数实质上为一凸二次规划(convex quadratic programming)问[23]。对于此问题,可利用拉格朗日对偶性(给每一个约束加上一个拉格朗日乘子的方式,定义拉格朗日函数),通过求解与原问题等价的对偶问题得到原始问题的最优解。

    引入拉格朗日乘子αi≥0,α*i≥0,μi≥0,μ*i≥0,由拉格朗日乘子法[24]

    Lw,b,α,α*,ξ,ξ*,μ,μ*=12w2+Ci=1nξi+ξ*-i=1nμiξi-i=1nμ*ξ*+i=1nαifxi-yi-ω-ξi+i=1nα*yi-fxi-ω-ξ*
    (3)

    带入式(2),令wbξξ*偏导为零,将结果带回,在满足KKT条[25]后,便可得出所需的wb,进而得最优解α*=α1,α2,,αlT。此时所建立的模型已可解决线性样本的分类求解问题,但对于应力应变关系描述这一非线性回归问题,仍需引入核函数Kxi,xj,将所构建模型推广到非线性层面,并得最终决策函数,如式(4):

    fx=i=1nαi*-αiKxi,xj+b
    (4)

    在本研究中,考虑到应力应变曲线明显的非线性特征以及多个自变量的存在,选用了如式(5)所示的径向基(RBF)核函数。

    Kxi,xj=exp-xi-xj2/γ2
    (5)

    式中,γ为核参数。

  • 3.3 应力应变关系式的参数寻优

    确定核函数后,关键问题在于如何确定最佳的(Cγ)组合。对于这一问题,本研究采用较为常用的方法——网格搜索[26](grid search)进行选点,K‑CV(K‑fold cross validation)方[27]对选出点的进行验证,判断其是不是最优点。

    参数搜寻进行两次。第一次寻优的特点是范围广但精度低,目的是初略确定最优参数组合可能出现的范围;第二次寻优则在第一次寻优结果的基础上,在缩小搜索范围的同时增加精度,目的是尽可能精确的寻到最优参数。

    首先定义两参数的初始搜索范围[2,3,4,5,6,7,8,9,10,210],步长为1,交叉验证的初始化分组数K为3。第二次寻优中C搜索范围取[26,210],γ搜索范围取[22,26],搜索步长为0.5,交叉验证初始化分组数K为3。得(Cγ)的最佳寻优结果为(724.0773,16)。

  • 3.4 SVM应力应变关系式

    确定参数,训练模型,得到如式(6)所示的非线性应力应变关系式。

    σ=((i1635wie-γ[T,ε]-[T,ε]i2+b)-1)×(σmax+σmin)-σmin
    (6)

    式中,1635为支持向量总数。γ为核参数,值为16。b为偏置,取值为-0.9437。σ为应力值。wi为支持向量在本构方程中的系数,取值如表1所示。[Tε]i为支持向量,为1635×2的矩阵,两列分别代表温度与应变的特征值,取值如表2所示。后一部分用来实现反归一化功能,其中σmax为拉伸应力数值的最大值,其值为11.55 MPa。σmin为压缩应力数值的最小值,其值为-42.41 MPa。另外,计算中无需考虑量纲,可直接计算。

    表1 应力应变关系式参数取值表

    Table 1 The Table for selection value of parameter for stress‑strain relationship

    no.wino.wino.wi
    1-724.0773546-724.07731091724.0773
    2724.0773547-724.07731092724.0773
    3705.6254548-724.07731093724.0773
    4-724.0773549-724.07731094724.0773
    5-724.0773550-724.07731095724.0773
    543-139.14911088724.0773163351.0194
    544-724.07731089724.07731634724.0773
    545-724.07731090724.07731635-141.4290

    表2 应力应变关系式支持向量xi取值

    Table 2 Selection value for support vector xi of stress‑strain relationship

    no.temperature /oC

    strain

    /%

    no.

    temperature

    /℃

    strain /%
    111.3878191.52171.8276
    211.83298201.52171.8381
    311.83958211.52171.8475
    8151.52171.7731163321.6554
    8161.52171.7885163421.6604
    8171.52171.8037163521.9101
    8181.52171.8164---
  • 4 结果与讨论

  • 4.1 测试集构建

    为对SVM关系式的误差进行量化表达,进而判断其是否满足工程实践的需求,首先需利用测试集将SVM关系式在对应温度、应变下的应力值以数值方式输出。测试集样本的构建方法为:以各个温度下的应变数值最小值作为首点,以步长0.005依次递增,直至覆盖此温度下的应变数值最大值;应力为模型输出值,在测试集中可任意指定。

  • 4.2 误差分析

    为量化误差,将SVM关系式预测值与实验数据置于同一坐标系中,依次在相同应变位置进行等距取点。计算平均绝对百分比误差(MAPE)、平均绝对误差(MAD)、相关系数(R),之后更换同温度的另一实验曲线进行相同操作,最后以所求得的平均值作为最终误差。

    5为SVM应力应变关系式在-40,15,75 ℃处预测结果与实验结果之间的对比。可发现在所选出的温度点处,预测曲线与实验曲线之间吻合程度较好,可描述包括不均匀塑性变形(缩颈)段在内的全部应变范围,仅在75 ℃时,受高温影响,PBX材料的塑性增加使原始数据产生了明显波动。

    html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F002.jpg

    a. -40 ℃

    html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F003.jpg

    b. 15 ℃

    html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F004.jpg

    c. 75 ℃

    图5 SVM应力应变关系式预测结果与实验结果对比

    Fig.5 Comparison of the predictive results of SVM stress‑strain relationship and the experimental ones

    将SVM应力应变关系式预测结果与实验数据在MAPE、MAD与R三个指标上进行对比。相应计算公式如下:

    MAPE=1ninxi-yi/yi×100
    (7)
    MAD=1ninxi-yi
    (8)
    R=Covx,yDxDy
    (9)

    根据计算出的误差结果,可发现SVM描述的拉压非线性应力应变关系在17个温度点上均保持了令人满意的描述精度。其中,最大MAPE位于55 ℃,为7.768%;最大MAD出现在55 ℃时,为0.8476 MPa;最小R为0.9987,出现在40 ℃。

    SVM算法因为其便利的可展开性(如式(6)),为基于算法描述的应力应变关系式在诸如ANSYS等有限元软件中的二次开发应用带来了便利;而在更为复杂的实验数据的规律挖掘方面(如考虑围压影响的应力应变数据),仅需增加训练集的数据列,便可基于SVM算法描述更为复杂的应力应变关系。

  • 5 结 论

    通过对TATB基PBX进行单轴拉压测试,对所得数据利用SVM算法构建应力应变关系式,结合统计学指标对误差进行量化分析,得到以下结论:

    (1) -40~75 ℃内,随温度的升高,TATB基PBX炸药压缩强度与拉伸强度劣化明显,压缩强度由-40 ℃时42.41 MPa降至75 ℃时12.64 MPa,拉伸强度由-40 ℃时11.55 MPa降至75 ℃时2.69 MPa;随着材料强度的变化,应力应变曲线的非线性和拉压不对称性特征也随之改变。

    (2) 将温度和应变作为自变量指标,将应力作为应变量指标,利用RBF核函数,采用二维网格搜索与K‑CV方法,明确了本研究中的最佳参数组合为(724.0773,16),得到了宽温域下TATB基PBX炸药基于SVM算法的应力应变关系式,可对拉伸压缩应力应变曲线的规律进行描述。

    (3) 通过预测集,利用SVM关系式输出预测值与实测数据进行误差分析,发现在所有实验温度下,平均MAPE不超过7.77%,平均MAD均小于0.8476 MPa,相关系数(R)均大于0.998,普适性良好。从工程实用的角度为高精度描述宽温域下材料的应力应变关系提供了一种解决方案。

    (责编:高 毅)

  • 参考文献

    • 1

      Talawar M B, Agarwal A P,Anniyappan M, et al. Method for preparation of fine TATB (2-5 μm) and its evaluation in plastic bonded explosive (PBX) formulations[J]. Journal of Hazardous Materials,2006,B137: 1848-1852.

    • 2

      Skidmore C B,Idar D J,Buntain G A, et al. Aging and PBX 9502[R]. Los Alamos National Laboratory report LA‑UR‑98‑1206,1998.

    • 3

      唐明峰, 庞海燕, 蓝林钢, 等. RDX基PBX的本构行为与应变历史、应变率效应[J]. 含能材料, 2016, 24(9): 832-837.

      TANG Ming‑feng, PANG Hai‑yan, LAN Lin‑gang, et al. Constitutive behavior of RDX‑based PBX with loading‑history and loading‑rate effects[J]. Chinese Journal of Energetic Materials(Hanneng Cailiao), 2016, 24(9): 832-837.

    • 4

      唐维, 颜熹琳, 温茂萍, 等. 典型PBX基于Boltzmann函数的准静态单轴拉压非线性本构模型[J]. 含能材料, 2017, 25(8): 689-693.

      TANG Wei,YAN Xi‑lin,WEN Mao‑ping. A uniaxial nonlinear tension‑compression constitutive model based on boltzmannfunction for typical PBXs under quasi‑static loading[J]. Chinese Journal of Energetic Materials(Hanneng Cailiao),2017,25(8): 689-693.

    • 5

      Bennett J G,Haberman K S,et al. A constitutive model for the non‑shock ignition and mechanical response of high explosives[J].Journal of the Mechanics and Physics of Solids,1998,46 (12): 2303-2322.

    • 6

      Peeters R L, Hackett R M. Constitutive modeling of plastic‑bonded explosives[J].Experimental Mechanics, 1981:111-116.

    • 7

      R Browning, M Gurtin, W Williams. A one‑dimensional viscoplastic constitutive theory for filled polymers[J].InternationalJournal of Solids and Structures, 1984, 20: 921-934.

    • 8

      Ramberg W, Osgood W R. Description of stress‑strain curves by three parameters[J]. Technical Note,1943,902.

    • 9

      Browning R,Gurtin M,Williams W. A model for viscoplastic materials with temperature dependence[J].International Journalof Solids and Structures, 1989, 25: 441-457.

    • 10

      李尚昆,黄西城,王鹏飞. 高聚物粘结炸药的力学性能研究进展[J].火炸药学报, 2016, 39(8): 1-11.

      LI Shang‑kun, HUANG Xi‑cheng, WANG Peng‑fei. Recent advances in the investigation on mechanical properties of PBX[J]. Chinese Journal of Explosives & Propellants, 2016, 39(8): 1-11.

    • 11

      Timm K, Halim K, Alexandr K, et al. The lattice boltzmannmethod[M]. Berlin:Springer‑Verlag,2017.

    • 12

      Shunk Devin. PBX 9502 literature review: An engineering perspective[R]. Los Alamos National Laboratory report LA‑UR‑13‑21673, 2013.

    • 13

      Jiang N, Zhao Z, Ren L. Design of structural modular neural networks with genetic algorithm[J]. Advances in Engineer Software, 2003, 34(1): 17-24.

    • 14

      Asfaram A, Ghaedi M, AhmadiAzqhandi M H, et al. Statistical experimental design, least squaressupport vector machine (LS‑SVM) and artificialneural network (ANN) methods for modeling thefacilitated adsorption of methylene blue dye [J]. RSC Advances, 2016, 6: 40502-40516.

    • 15

      VAPNIK V N. The nature of statistical learning theory[M]. New York: Springer, 1995.

    • 16

      Farzad N, Faezeh J, Ehsan M, et al. Experimental observations and SVM‑based prediction of properties of polypropylene fibres reinforced self‑compacting composites incorporating nano‑CuO[J]. Construction and Building Materials, 2017, 143: 589-598.

    • 17

      Ramin G, Mohammad R G, Mohammad N. Comparative studies of metamodeling and AI‑Based techniques in damagedetection of structures[J]. Advances in Engineering Software, 2018, 115: 65-77.

    • 18

      Qasim A A, Zamri C, Mohammed F A, et al. Support vector regression‑based model for prediction of behaviorstone column parameters in soft clay under highway embankment[J]. Neural Computing and Applications, 2017, 30(8): 2459-2469.

    • 19

      魏小红,常双君,申孝立. 基于HLLE‑SVM预测混合炸药爆轰性能[J]. 含能材料, 2014, 22(2): 221-225.

      WEI Xiao‑hong, CHANG Shuang‑jun, SHEN Xiao‑li. Prediction of the Composite Explosion Parameters by HLLE‑SVM [J].Chinese journal of energetic materials(Hanneng Cailiao), 2014, 22(2): 221-225.

    • 20

      周红萍, 庞海燕, 温茂萍, 等. 3种粘结剂材料的力学性能对比研究[J]. 材料导报, 2009, 23(12): 34-36, 52.

      ZHOU Hong‑ping, PANG Hai‑yan, WEN Map‑ping, et al. Comparative studies on the mechanical properties of three kinds of binders[J].Materials Review, 2009, 23(12): 34-36, 52.

    • 21

      Ian G, Yoshua B, and AaronC. Deep Learning[M]. Massachusetts: Massachusetts Institute of Technology Press, 2016:88-90.

    • 22

      周志华. 机器学习[M]. 北京:清华大学出版社,2016: 121-139.

      ZHOU Zhi‑hua. Machine learning[M]. Beijing:Tsinghua University Press,2016: 121-139.

    • 23

      Goldfarb D, Idnani A. A numerically stable dual method for solving strictly convex quadratic programs[J]. Mathematical Programming, 1983, 27(1): 1-33.

    • 24

      Burachik R S,Rizvi M M. On weak and strong Kuhn‑Tucker conditions for smooth multi‑objective optimization [J]. Journal of Optimization Theory and Applications, 2012, 155: 477-491.

    • 25

      叶永伟,陆俊杰,钱志勤,等. 基于LS‑SVM的机械式温度仪表误差预测研究[J]. 仪器仪表学报, 2016, 37(1): 57-66.

      YE Yong‑wei, LU Jun‑jie, QIAN Zhi‑qin, et al. Study on the temperature error prediction of mechanical temperature instrument based on LS‑SVM[J]. Chinese Journal of Scientific Instrument, 2016, 37(1): 57-66.

    • 26

      叶永伟,陆俊杰,钱志勤,等. 基于LS‑SVM的机械式温度仪表误差预测研究[J]. 仪器仪表学报, 2016, 37(1): 57-66.

      YE Yong‑wei, LU Jun‑jie, QIAN Zhi‑qin, et al. Study on the temperature error prediction of mechanical temperature instrument based on LS‑SVM[J]. Chinese Journal of Scientific Instrument, 2016, 37(1): 57-66.

    • 27

      Reuter U, Sultana A, Reischl D S. A comparative study of machine learning approaches for modeling concrete failure Surfaces[J]. Advances in Engineering Software, 2018, 116: 67-79.

段晓畅

机 构:

1. 中北大学 环境与安全工程学院, 山西 太原 030051

2. 中国工程物理研究院 化工材料研究所, 四川 绵阳 621999

Affiliation:

1. School of Environment and Safety Engineering,North University of China,Taiyuan 030051,China

2. Institute of Chemical Materials,CAEP,Mianyang 621999,China

邮 箱:yzduanxc@126.com

作者简介:段晓畅(1994-),男,硕士研究生,主要从事智能算法在PBX炸药力学中的应用研究。e‑mail:yzduanxc@126.com

孙杰

机 构:中国工程物理研究院 化工材料研究所, 四川 绵阳 621999

Affiliation:Institute of Chemical Materials,CAEP,Mianyang 621999,China

刘迎彬

机 构:中北大学 环境与安全工程学院, 山西 太原 030051

Affiliation:School of Environment and Safety Engineering,North University of China,Taiyuan 030051,China

常双君

机 构:中北大学 环境与安全工程学院, 山西 太原 030051

Affiliation:School of Environment and Safety Engineering,North University of China,Taiyuan 030051,China

赵龙

机 构:中国工程物理研究院 化工材料研究所, 四川 绵阳 621999

Affiliation:Institute of Chemical Materials,CAEP,Mianyang 621999,China

袁洪魏

机 构:中国工程物理研究院 化工材料研究所, 四川 绵阳 621999

Affiliation:Institute of Chemical Materials,CAEP,Mianyang 621999,China

唐维

机 构:中国工程物理研究院 化工材料研究所, 四川 绵阳 621999

Affiliation:Institute of Chemical Materials,CAEP,Mianyang 621999,China

角 色:通讯作者

Role:Corresponding author

邮 箱:tangwei@caep.cn

作者简介:唐维(1981-),男,副研究员,主要从事PBX炸药的力学行为研究。e‑mail:tangwei@caep.cn

html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F005.jpg
html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F006.jpg
html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F007.jpg
html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F008.jpg
html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F009.jpg
html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F001.jpg
no.wino.wino.wi
1-724.0773546-724.07731091724.0773
2724.0773547-724.07731092724.0773
3705.6254548-724.07731093724.0773
4-724.0773549-724.07731094724.0773
5-724.0773550-724.07731095724.0773
543-139.14911088724.0773163351.0194
544-724.07731089724.07731634724.0773
545-724.07731090724.07731635-141.4290
no.temperature /oC

strain

/%

no.

temperature

/℃

strain /%
111.3878191.52171.8276
211.83298201.52171.8381
311.83958211.52171.8475
8151.52171.7731163321.6554
8161.52171.7885163421.6604
8171.52171.8037163521.9101
8181.52171.8164---
html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F002.jpg
html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F003.jpg
html/hncl/CJEM2018205/alternativeImage/485223af-3b4c-4ead-b425-ee881d3d3c7e-F004.jpg

图1 -20 ℃与20 ℃下单轴压缩应力应变曲线 -- a. -20 ℃

Fig.1 Uniaxial compressive stress‑strain curves at -20 ℃ and 20 ℃ -- a. -20 ℃

图1 -20 ℃与20 ℃下单轴压缩应力应变曲线 -- b. 20 ℃

Fig.1 Uniaxial compressive stress‑strain curves at -20 ℃ and 20 ℃ -- b. 20 ℃

图2 -20 ℃与20 ℃下单轴拉伸应力应变曲线 -- a. -20 ℃

Fig.2 Uniaxial tensile stress‑strain curves at -20 ℃ and 20 ℃ -- a. -20 ℃

图2 -20 ℃与20 ℃下单轴拉伸应力应变曲线 -- b. 20 ℃

Fig.2 Uniaxial tensile stress‑strain curves at -20 ℃ and 20 ℃ -- b. 20 ℃

图3 拉伸与压缩载荷下的应力应变曲线构建流程

Fig.3 Construction process of stress‑strain curves under tension and compression load

图4 17个温度点下的拉伸压缩应力应变曲线

Fig.4 Tension‑compression stress‑strain curves at 17 temperature points

表1 应力应变关系式参数取值表

Table 1 The Table for selection value of parameter for stress‑strain relationship

表2 应力应变关系式支持向量xi取值

Table 2 Selection value for support vector xi of stress‑strain relationship

图5 SVM应力应变关系式预测结果与实验结果对比 -- a. -40 ℃

Fig.5 Comparison of the predictive results of SVM stress‑strain relationship and the experimental ones -- a. -40 ℃

图5 SVM应力应变关系式预测结果与实验结果对比 -- b. 15 ℃

Fig.5 Comparison of the predictive results of SVM stress‑strain relationship and the experimental ones -- b. 15 ℃

图5 SVM应力应变关系式预测结果与实验结果对比 -- c. 75 ℃

Fig.5 Comparison of the predictive results of SVM stress‑strain relationship and the experimental ones -- c. 75 ℃

image /

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  • 参考文献

    • 1

      Talawar M B, Agarwal A P,Anniyappan M, et al. Method for preparation of fine TATB (2-5 μm) and its evaluation in plastic bonded explosive (PBX) formulations[J]. Journal of Hazardous Materials,2006,B137: 1848-1852.

    • 2

      Skidmore C B,Idar D J,Buntain G A, et al. Aging and PBX 9502[R]. Los Alamos National Laboratory report LA‑UR‑98‑1206,1998.

    • 3

      唐明峰, 庞海燕, 蓝林钢, 等. RDX基PBX的本构行为与应变历史、应变率效应[J]. 含能材料, 2016, 24(9): 832-837.

      TANG Ming‑feng, PANG Hai‑yan, LAN Lin‑gang, et al. Constitutive behavior of RDX‑based PBX with loading‑history and loading‑rate effects[J]. Chinese Journal of Energetic Materials(Hanneng Cailiao), 2016, 24(9): 832-837.

    • 4

      唐维, 颜熹琳, 温茂萍, 等. 典型PBX基于Boltzmann函数的准静态单轴拉压非线性本构模型[J]. 含能材料, 2017, 25(8): 689-693.

      TANG Wei,YAN Xi‑lin,WEN Mao‑ping. A uniaxial nonlinear tension‑compression constitutive model based on boltzmannfunction for typical PBXs under quasi‑static loading[J]. Chinese Journal of Energetic Materials(Hanneng Cailiao),2017,25(8): 689-693.

    • 5

      Bennett J G,Haberman K S,et al. A constitutive model for the non‑shock ignition and mechanical response of high explosives[J].Journal of the Mechanics and Physics of Solids,1998,46 (12): 2303-2322.

    • 6

      Peeters R L, Hackett R M. Constitutive modeling of plastic‑bonded explosives[J].Experimental Mechanics, 1981:111-116.

    • 7

      R Browning, M Gurtin, W Williams. A one‑dimensional viscoplastic constitutive theory for filled polymers[J].InternationalJournal of Solids and Structures, 1984, 20: 921-934.

    • 8

      Ramberg W, Osgood W R. Description of stress‑strain curves by three parameters[J]. Technical Note,1943,902.

    • 9

      Browning R,Gurtin M,Williams W. A model for viscoplastic materials with temperature dependence[J].International Journalof Solids and Structures, 1989, 25: 441-457.

    • 10

      李尚昆,黄西城,王鹏飞. 高聚物粘结炸药的力学性能研究进展[J].火炸药学报, 2016, 39(8): 1-11.

      LI Shang‑kun, HUANG Xi‑cheng, WANG Peng‑fei. Recent advances in the investigation on mechanical properties of PBX[J]. Chinese Journal of Explosives & Propellants, 2016, 39(8): 1-11.

    • 11

      Timm K, Halim K, Alexandr K, et al. The lattice boltzmannmethod[M]. Berlin:Springer‑Verlag,2017.

    • 12

      Shunk Devin. PBX 9502 literature review: An engineering perspective[R]. Los Alamos National Laboratory report LA‑UR‑13‑21673, 2013.

    • 13

      Jiang N, Zhao Z, Ren L. Design of structural modular neural networks with genetic algorithm[J]. Advances in Engineer Software, 2003, 34(1): 17-24.

    • 14

      Asfaram A, Ghaedi M, AhmadiAzqhandi M H, et al. Statistical experimental design, least squaressupport vector machine (LS‑SVM) and artificialneural network (ANN) methods for modeling thefacilitated adsorption of methylene blue dye [J]. RSC Advances, 2016, 6: 40502-40516.

    • 15

      VAPNIK V N. The nature of statistical learning theory[M]. New York: Springer, 1995.

    • 16

      Farzad N, Faezeh J, Ehsan M, et al. Experimental observations and SVM‑based prediction of properties of polypropylene fibres reinforced self‑compacting composites incorporating nano‑CuO[J]. Construction and Building Materials, 2017, 143: 589-598.

    • 17

      Ramin G, Mohammad R G, Mohammad N. Comparative studies of metamodeling and AI‑Based techniques in damagedetection of structures[J]. Advances in Engineering Software, 2018, 115: 65-77.

    • 18

      Qasim A A, Zamri C, Mohammed F A, et al. Support vector regression‑based model for prediction of behaviorstone column parameters in soft clay under highway embankment[J]. Neural Computing and Applications, 2017, 30(8): 2459-2469.

    • 19

      魏小红,常双君,申孝立. 基于HLLE‑SVM预测混合炸药爆轰性能[J]. 含能材料, 2014, 22(2): 221-225.

      WEI Xiao‑hong, CHANG Shuang‑jun, SHEN Xiao‑li. Prediction of the Composite Explosion Parameters by HLLE‑SVM [J].Chinese journal of energetic materials(Hanneng Cailiao), 2014, 22(2): 221-225.

    • 20

      周红萍, 庞海燕, 温茂萍, 等. 3种粘结剂材料的力学性能对比研究[J]. 材料导报, 2009, 23(12): 34-36, 52.

      ZHOU Hong‑ping, PANG Hai‑yan, WEN Map‑ping, et al. Comparative studies on the mechanical properties of three kinds of binders[J].Materials Review, 2009, 23(12): 34-36, 52.

    • 21

      Ian G, Yoshua B, and AaronC. Deep Learning[M]. Massachusetts: Massachusetts Institute of Technology Press, 2016:88-90.

    • 22

      周志华. 机器学习[M]. 北京:清华大学出版社,2016: 121-139.

      ZHOU Zhi‑hua. Machine learning[M]. Beijing:Tsinghua University Press,2016: 121-139.

    • 23

      Goldfarb D, Idnani A. A numerically stable dual method for solving strictly convex quadratic programs[J]. Mathematical Programming, 1983, 27(1): 1-33.

    • 24

      Burachik R S,Rizvi M M. On weak and strong Kuhn‑Tucker conditions for smooth multi‑objective optimization [J]. Journal of Optimization Theory and Applications, 2012, 155: 477-491.

    • 25

      叶永伟,陆俊杰,钱志勤,等. 基于LS‑SVM的机械式温度仪表误差预测研究[J]. 仪器仪表学报, 2016, 37(1): 57-66.

      YE Yong‑wei, LU Jun‑jie, QIAN Zhi‑qin, et al. Study on the temperature error prediction of mechanical temperature instrument based on LS‑SVM[J]. Chinese Journal of Scientific Instrument, 2016, 37(1): 57-66.

    • 26

      叶永伟,陆俊杰,钱志勤,等. 基于LS‑SVM的机械式温度仪表误差预测研究[J]. 仪器仪表学报, 2016, 37(1): 57-66.

      YE Yong‑wei, LU Jun‑jie, QIAN Zhi‑qin, et al. Study on the temperature error prediction of mechanical temperature instrument based on LS‑SVM[J]. Chinese Journal of Scientific Instrument, 2016, 37(1): 57-66.

    • 27

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