PBX炸药装药的力学性能及损伤破坏研究
摘要
随着现代高性能武器系统的飞速发展，弹药的安全性问题日益突出，新型常规武器对炸药装药的起爆性能提出了更高的要求。高聚物粘结炸药（PBX）是一类具有较高能量密度、优良机械性能和较高安全性能等的高能复合材料，在国防和国民经济等领域广为使用。然而，即便是PBX这类钝感炸药，意外爆炸事件也时有发生。为适应高性能武器装备发展的需要，研究钝感高能炸药的各项性能就显得尤为重要。PBX炸药本身结构复杂，加之其在发挥效能前的服役过程中所受力学环境复杂，研究PBX炸药的力学性能，特别是动态力学性能是目前研究炸药安全性的一个重要课题。本文旨在研究PBX炸药的动态力学响应和损伤的产生和发展规律。采用霍普金森压杆（SHPB）作为主要的实验平台，研究PBX炸药的动态压缩和拉伸力学特性，并观察PBX炸药受动态加载后的细观损伤形貌，最终建立含细观损伤的本构关系，为研究含能材料的安全性提供一定的理论支撑。
本文主要有三个部分，第一部分为PBX炸药力学性能的基础研究，从宏观层次观察了损伤的发展及其在应力应变曲线上的反映。从实验结果看PBX炸药这类材料具有典型的力学脆性，脆性材料的损伤模式一般以微裂纹的产生和发展为主，要研究其损伤特性就需要观察内部细观裂纹的发展变化。因此，第二部分采用巴西实验为主要加载方式对PBX炸药的细观损伤演化过程进行了实验和数值模拟研究。在获得了PBX炸药的损伤特性之后，需要对其发展规律进行数学描述。在本文的最后一部分，采用微裂纹扩展区损伤本构模型来描述PBX炸药内部微裂纹演化发展对宏观应力应变曲线的影响。详细的研究内容如下：
第一部分的内容主要为PBX炸药的宏观动态力学响应研究。首先针对PBX炸药这类破坏应变很小的脆性材料，改进传统的SHPB测试方法以获得更为准确的实验结果。采用半导体和石英晶体联合测试技术提高实验信号的信噪比；采用不同脉冲和不同波形整形器进行加载研究PBX炸药的宏观损伤力学特性，发现PBX炸药的损伤发展对冲击加载比较敏感，且极限加载应变率很低。根据PBX炸药的一维压缩应力应变曲线特点，建立了对PBX炸药单轴压缩下的唯象本构描述，能较好地反映PBX炸药从加载到破坏后卸载过程中的应力应变关系。为精确标定半导体的灵敏度系数和石英晶体的压电系数，将改进的激光微位移速度干涉系统用于SHPB系统杆中质点速度的测试。结果表明，激光干涉方法标定的系数比传统方法标定的系数要小10%左右。由于激光微位移速度干涉仪可采用多点同时测量，本文尝试直接测量SHPB实验中试样两端的速度历史，获得材料的应力应变响应并拓展到中应变率实验的测试。
为研究PBX炸药的组成结构对其力学性能的影响，对三种PBX炸药的力学性能进行了对比研究，获得了三种炸药各力学参数随温度的变化情况，分析了PBX炸药中各成分对力学量的贡献。结果表明，各材料的动态模量、强度随温度的升高而减小，而破坏应变基本保持不变。三种PBX炸药中，PBX3具有较特殊的破坏模式，力学性能相对稳定。TATB的加入对HMX有很明显的钝感作用，对PBX炸药的整体宏观力学性能有很大的改善。
第二部分的主要内容为PBX炸药的细观损伤发展的实验研究和数值模拟研究。采用准静态和动态巴西实验对磨抛后的PBX炸药进行加载，回收试样观测PBX炸药的细观损伤发展情况。结果表明，PBX炸药中裂纹是主要的损伤形式。静态加载时，微观裂纹主要为界面脱粘裂纹，宏观裂纹主要为穿晶断裂裂纹；界面脱粘裂纹在加载早期即可形成，但不影响材料对外界的承载能力；穿晶断裂可能是试样破坏的主要原因。动态加载时，观察到的微裂纹和宏观裂纹均为穿晶断裂。
采用离散元数值方法模拟PBX炸药在巴西实验过程中的裂纹扩展过程。为验证该方法的有效性，用HMX炸药晶体的参数作为均匀材料的基本参数，模拟均匀材料在巴西实验过程中的应变场分布，符合巴西实验的理论分析结果。建立能反映PBX炸药细观结构的模型，并模拟了PBX炸药圆盘试样受巴西实验加载后的响应情况。模拟结果表明：沿晶断裂先于穿晶断裂出现；带有沿晶裂纹的试样依然能承受加载；晶体出现断裂后试样内部结构失稳，表现为宏观失效；颗粒尺寸小的试样抗拉性能增强，在微裂纹形成后的很长一段时间还能承受加载，直到穿晶裂纹出现。
第三部分为PBX炸药的含细观损伤本构关系研究。采用裂纹的张开，闭合裂纹的摩擦滑移以及翼型裂纹的弯折扩展等机制来描述PBX炸药的本构行为。考虑单轴压缩加载的计算结果表明，采用裂纹扩展区概念发展的含细观损伤本构关系能反映PBX炸药的应力应变曲线的基本形状。最后，对该模型进行了理论改进以用于描述动态加载时材料的响应。在今后的工作中将发展该模型用于LS-DYNA模拟中，为武器效应评估提供理论支撑。
As modern high-powered weapon systems develop so fast, the safety problem ofthe explosive gradually becomes more and more spiculate. New-style normal weapongives higher requirement of explosives’ detonation initiation behavior. Polymer-bondedexplosive (PBX) is a kind of high energetic composite, having higher energy density,better mechanical behavior and higher safety property. Therefore, they are widely usedin many areas like national defense and civil economy. However, unexpectedexplosions occur sometimes even if the insensitive explosives were used. To satisfy therequirement of high property weapon equipments, it is crucial to investigate eachproperty of the insensitive explosives. Because PBX has complicate structure and itusually undergoes very complex mechanical state before explosion, to study PBX’smechanical behavior, especially the dynamic mechanical behavior is an important taskfor researching the safety behavior of PBX. This thesis aims at the research on thedynamic response and damage evolution. Using Split Hopkinson Pressure Bar (SHPB),we studied the dynamic compressive and tensile behavior of PBX, obtained the damagefeature at meso-scale of recovered specimen, and finally constructed the constitutiverelation involving the meso-damage evolution.
There are three parts in the thesis. The basic mechanical researches of PBX wereperformed firstly. Damage developments and its influences on stress-strain curves wereexperimentally observed. From the experimental results, it can be inferred that PBX istypically brittle. The according damage modes are mainly micro-cracks’ initiation andspreading, and development of PBX’s inner micro-cracks needs to be experimentallyobtained for the investigation of damage evolution of PBX. Hence, in the second part,the experimental and numerical studies of PBX’s meso-damage evolution were carriedout by way of Brazilian test. After the obtainment of the damage feature of PBX, themathematical description of the evolution law is necessary to be founded. Therefore, atthe last part, the micro-crack development region constitutive model was adopted todescribe the influence of inner micro-cracks’ evolution on the macro stress-strain curve.Follows are the details.
The first part mainly works on the macro dynamic response of PBX. Themeasurement of the SHPB tests was improved to obtain more accurate data, because thefailure strain of PBX was quite small. Using quartz crystal as stress gauge andsemiconductor strain gauge together, high Signal-to-Noise signals were obtained. Usingdifferent wave length and pulse shaper, it was found that the damage evolution wassensitive to impact loading, and the range of the loading strain rate was small due to thelow strain rate limit. According to the feature of the stress-strain curve, constitutive equations were developed and they could describe the stress-strain relation including theunloading stage after failure. Laser micro-displacement velocity interferometer wasdeveloped to accurately calibrate the coefficients of semiconductor and quartz crystalslices, by measuring the particle velocity of the bars directly. Results show thecoefficients obtained by laser interferometer are smaller by10%than that obtained bytraditional methods. Because the laser interferometer system can realize multi-pointmeasurement, the velocity history of specimen’s two ends can be obtained directly.Moreover, it is still can be developed to measure the signals of long pulse at middlestrain rate loading cases.
Mechanical behaviors of three PBXs are compared by taking high temperatureSHPB tests to investigate the influence of the components on the whole mechanicalresponses. Several mechanical parameters’ variations with temperature were obtainedand the contributions of PBXs’ each component to mechanical parameters wereanalyzed also. Results show the dynamic modulus and the failure strength decreases asthe temperature rises, but the failure strain changes little. Among the three PBXs, PBX3has unique failure mode and most stable mechanical behavior. The addition of TATBcan insentisize HMX obviously and improve the macro mechanical properties of PBXgreatly.
The second part concerns about experimental and simulative investigation of themeso-damage evolution. At first, the quasi-static and dynamic Brazilian tests wereperformed on polished PBX and the meso-damage features of recovered specimen wereobserved using optical microscope. It is found that cracks are the main damage mode inPBX, like many brittle materials. In case of quasi-static loading, most microcracks areinterface debonding cracks, and macrocracks are mainly transgranular fracture cracks.The interface cracks may initiate at early stage of loading and they have little influenceon specimen’s sustainability. Transgranular cracks may be the primary cause ofspecimen’s macro-failure. In case of dynamic loading, the observed macro-cracks andmicro-cracks both exhibit transgranular fracture.
Discrete element method was adopted to simulate the cracking process of PBXduring Brazilian tests. To prove the validity of this method, homogenous material modelwas built using HMX’s parameters. The strain distributions of the disk specimen duringBrazilian test were obtained and they were similar to the theoretic analysis of Braziliantests. Meso-structure of PBX was presented. Specimens with different particle size weremodeled under the loading of Brazilian test. Simulation results show that interfacecracks occur before transgranular cracks, and specimen with interface debonding crackscan sustain the applied loading, also. The specimen fails at macro-scale after the crystalfractures. Specimen with smaller particle size can sustain for a long time withmicrocracks before transgranular cracks occur.
The third part focuses on the constitutive relation concerning the meso-damage evolution. The damage evolution contains the cracks’ splaying, the friction and slidingof closed cracks and the bending spread of wing cracks. Computing results in case ofuniaxial compression loading show that this constitutive model can describe themechanical behavior. At last, the model was developed for the use in dynamic loadingcase theoretically. In further work, the model will be developed for the use inLS-DYNA.
本文主要有三个部分，第一部分为PBX炸药力学性能的基础研究，从宏观层次观察了损伤的发展及其在应力应变曲线上的反映。从实验结果看PBX炸药这类材料具有典型的力学脆性，脆性材料的损伤模式一般以微裂纹的产生和发展为主，要研究其损伤特性就需要观察内部细观裂纹的发展变化。因此，第二部分采用巴西实验为主要加载方式对PBX炸药的细观损伤演化过程进行了实验和数值模拟研究。在获得了PBX炸药的损伤特性之后，需要对其发展规律进行数学描述。在本文的最后一部分，采用微裂纹扩展区损伤本构模型来描述PBX炸药内部微裂纹演化发展对宏观应力应变曲线的影响。详细的研究内容如下：
第一部分的内容主要为PBX炸药的宏观动态力学响应研究。首先针对PBX炸药这类破坏应变很小的脆性材料，改进传统的SHPB测试方法以获得更为准确的实验结果。采用半导体和石英晶体联合测试技术提高实验信号的信噪比；采用不同脉冲和不同波形整形器进行加载研究PBX炸药的宏观损伤力学特性，发现PBX炸药的损伤发展对冲击加载比较敏感，且极限加载应变率很低。根据PBX炸药的一维压缩应力应变曲线特点，建立了对PBX炸药单轴压缩下的唯象本构描述，能较好地反映PBX炸药从加载到破坏后卸载过程中的应力应变关系。为精确标定半导体的灵敏度系数和石英晶体的压电系数，将改进的激光微位移速度干涉系统用于SHPB系统杆中质点速度的测试。结果表明，激光干涉方法标定的系数比传统方法标定的系数要小10%左右。由于激光微位移速度干涉仪可采用多点同时测量，本文尝试直接测量SHPB实验中试样两端的速度历史，获得材料的应力应变响应并拓展到中应变率实验的测试。
为研究PBX炸药的组成结构对其力学性能的影响，对三种PBX炸药的力学性能进行了对比研究，获得了三种炸药各力学参数随温度的变化情况，分析了PBX炸药中各成分对力学量的贡献。结果表明，各材料的动态模量、强度随温度的升高而减小，而破坏应变基本保持不变。三种PBX炸药中，PBX3具有较特殊的破坏模式，力学性能相对稳定。TATB的加入对HMX有很明显的钝感作用，对PBX炸药的整体宏观力学性能有很大的改善。
第二部分的主要内容为PBX炸药的细观损伤发展的实验研究和数值模拟研究。采用准静态和动态巴西实验对磨抛后的PBX炸药进行加载，回收试样观测PBX炸药的细观损伤发展情况。结果表明，PBX炸药中裂纹是主要的损伤形式。静态加载时，微观裂纹主要为界面脱粘裂纹，宏观裂纹主要为穿晶断裂裂纹；界面脱粘裂纹在加载早期即可形成，但不影响材料对外界的承载能力；穿晶断裂可能是试样破坏的主要原因。动态加载时，观察到的微裂纹和宏观裂纹均为穿晶断裂。
采用离散元数值方法模拟PBX炸药在巴西实验过程中的裂纹扩展过程。为验证该方法的有效性，用HMX炸药晶体的参数作为均匀材料的基本参数，模拟均匀材料在巴西实验过程中的应变场分布，符合巴西实验的理论分析结果。建立能反映PBX炸药细观结构的模型，并模拟了PBX炸药圆盘试样受巴西实验加载后的响应情况。模拟结果表明：沿晶断裂先于穿晶断裂出现；带有沿晶裂纹的试样依然能承受加载；晶体出现断裂后试样内部结构失稳，表现为宏观失效；颗粒尺寸小的试样抗拉性能增强，在微裂纹形成后的很长一段时间还能承受加载，直到穿晶裂纹出现。
第三部分为PBX炸药的含细观损伤本构关系研究。采用裂纹的张开，闭合裂纹的摩擦滑移以及翼型裂纹的弯折扩展等机制来描述PBX炸药的本构行为。考虑单轴压缩加载的计算结果表明，采用裂纹扩展区概念发展的含细观损伤本构关系能反映PBX炸药的应力应变曲线的基本形状。最后，对该模型进行了理论改进以用于描述动态加载时材料的响应。在今后的工作中将发展该模型用于LS-DYNA模拟中，为武器效应评估提供理论支撑。
As modern high-powered weapon systems develop so fast, the safety problem ofthe explosive gradually becomes more and more spiculate. New-style normal weapongives higher requirement of explosives’ detonation initiation behavior. Polymer-bondedexplosive (PBX) is a kind of high energetic composite, having higher energy density,better mechanical behavior and higher safety property. Therefore, they are widely usedin many areas like national defense and civil economy. However, unexpectedexplosions occur sometimes even if the insensitive explosives were used. To satisfy therequirement of high property weapon equipments, it is crucial to investigate eachproperty of the insensitive explosives. Because PBX has complicate structure and itusually undergoes very complex mechanical state before explosion, to study PBX’smechanical behavior, especially the dynamic mechanical behavior is an important taskfor researching the safety behavior of PBX. This thesis aims at the research on thedynamic response and damage evolution. Using Split Hopkinson Pressure Bar (SHPB),we studied the dynamic compressive and tensile behavior of PBX, obtained the damagefeature at meso-scale of recovered specimen, and finally constructed the constitutiverelation involving the meso-damage evolution.
There are three parts in the thesis. The basic mechanical researches of PBX wereperformed firstly. Damage developments and its influences on stress-strain curves wereexperimentally observed. From the experimental results, it can be inferred that PBX istypically brittle. The according damage modes are mainly micro-cracks’ initiation andspreading, and development of PBX’s inner micro-cracks needs to be experimentallyobtained for the investigation of damage evolution of PBX. Hence, in the second part,the experimental and numerical studies of PBX’s meso-damage evolution were carriedout by way of Brazilian test. After the obtainment of the damage feature of PBX, themathematical description of the evolution law is necessary to be founded. Therefore, atthe last part, the micro-crack development region constitutive model was adopted todescribe the influence of inner micro-cracks’ evolution on the macro stress-strain curve.Follows are the details.
The first part mainly works on the macro dynamic response of PBX. Themeasurement of the SHPB tests was improved to obtain more accurate data, because thefailure strain of PBX was quite small. Using quartz crystal as stress gauge andsemiconductor strain gauge together, high Signal-to-Noise signals were obtained. Usingdifferent wave length and pulse shaper, it was found that the damage evolution wassensitive to impact loading, and the range of the loading strain rate was small due to thelow strain rate limit. According to the feature of the stress-strain curve, constitutive equations were developed and they could describe the stress-strain relation including theunloading stage after failure. Laser micro-displacement velocity interferometer wasdeveloped to accurately calibrate the coefficients of semiconductor and quartz crystalslices, by measuring the particle velocity of the bars directly. Results show thecoefficients obtained by laser interferometer are smaller by10%than that obtained bytraditional methods. Because the laser interferometer system can realize multi-pointmeasurement, the velocity history of specimen’s two ends can be obtained directly.Moreover, it is still can be developed to measure the signals of long pulse at middlestrain rate loading cases.
Mechanical behaviors of three PBXs are compared by taking high temperatureSHPB tests to investigate the influence of the components on the whole mechanicalresponses. Several mechanical parameters’ variations with temperature were obtainedand the contributions of PBXs’ each component to mechanical parameters wereanalyzed also. Results show the dynamic modulus and the failure strength decreases asthe temperature rises, but the failure strain changes little. Among the three PBXs, PBX3has unique failure mode and most stable mechanical behavior. The addition of TATBcan insentisize HMX obviously and improve the macro mechanical properties of PBXgreatly.
The second part concerns about experimental and simulative investigation of themeso-damage evolution. At first, the quasi-static and dynamic Brazilian tests wereperformed on polished PBX and the meso-damage features of recovered specimen wereobserved using optical microscope. It is found that cracks are the main damage mode inPBX, like many brittle materials. In case of quasi-static loading, most microcracks areinterface debonding cracks, and macrocracks are mainly transgranular fracture cracks.The interface cracks may initiate at early stage of loading and they have little influenceon specimen’s sustainability. Transgranular cracks may be the primary cause ofspecimen’s macro-failure. In case of dynamic loading, the observed macro-cracks andmicro-cracks both exhibit transgranular fracture.
Discrete element method was adopted to simulate the cracking process of PBXduring Brazilian tests. To prove the validity of this method, homogenous material modelwas built using HMX’s parameters. The strain distributions of the disk specimen duringBrazilian test were obtained and they were similar to the theoretic analysis of Braziliantests. Meso-structure of PBX was presented. Specimens with different particle size weremodeled under the loading of Brazilian test. Simulation results show that interfacecracks occur before transgranular cracks, and specimen with interface debonding crackscan sustain the applied loading, also. The specimen fails at macro-scale after the crystalfractures. Specimen with smaller particle size can sustain for a long time withmicrocracks before transgranular cracks occur.
The third part focuses on the constitutive relation concerning the meso-damage evolution. The damage evolution contains the cracks’ splaying, the friction and slidingof closed cracks and the bending spread of wing cracks. Computing results in case ofuniaxial compression loading show that this constitutive model can describe themechanical behavior. At last, the model was developed for the use in dynamic loadingcase theoretically. In further work, the model will be developed for the use inLS-DYNA.
引文
[1] Sandusky H W. Influence of fresh damage on the shock reactivity and sensitivityof several energetic materials[C]. Proceedings10th International DetonationSymposium. Boston, Massachusetts,1993:490-498.
[2] Liu C,Browning R. Fracture in PBX9501at low rates[C]. Proceedings12thInternational Detonation Symposium. San Diego, California,2002:121-126.
[3] G. Goudrean. Evaluation of mechanical properties of PBXW-113explosive.1985.
[4] Hoffman H J. High-strain rate testing of gun propellants.1989.
[5] Blumenthal W R, Thompson D G, Cady C D, et al. Compressive properties ofPBXN-110and Its HTPB-based binder as a function of temperature and strainrate, in12th International Detonation Conference.2002: California.
[6]罗景润. PBX的损伤、断裂及本构关系[D].绵阳:2001.
[7]李英雷,李大红,胡时胜. TATB钝感炸药本构的实验研究[J].爆炸与冲击,1999,19(4):355-359.
[8]吴会民,卢芳云.三种含能材料力学行为应变率效应的实验研究[J].含能材料,2004,12(4):227-230.
[9]陈荣,卢芳云,林玉亮,等.一种含铝炸药的本构关系研究[J].含能材料,2007,10(5):460-463.
[10] Palmer S, Field J, Huntley J. Deformation, strengths and strains to failure ofpolymer bonded explosives[J]. Proceedings of the Royal Society of London.Series A: Mathematical and Physical Sciences,1993,440(1909):399-419.
[11]陈鹏万.高聚物粘结炸药的细观结构及力学性能[D].北京:中国科学院力学研究所,2001.
[12] Pinto J,Wiegand D. The mechanical response of TNT and A composite,composition B, of TNT and RDX to compressive stress: II triaxial stress andyield[J]. Journal of Energetic Materials,1991,9(3):205-263.
[13]韩小平,张元冲.高能材料动态力学性能实验研究[J].爆炸与冲击,1995,15(1):20-27.
[14] Wiegand D A, Pinto J, Nicolaides S. The mechanical response of TNT and acomposite, composition B, of TNT and RDX to compressive stress: I uniaxialstress and fracture[J]. Journal of Energetic Materials,1991,9(1-2):19-80.
[15] Wiegand D, Nicolaides S, Pinto J. Mechanical and thermomechanical propertiesof NC base propellants[J]. Journal of Energetic Materials,1990,8(5):442-461.
[16]韩小平,张元冲.冲击载荷下炸药装药动态响应的有限元分析及热点形成机理的数值模拟研究[J].爆炸与冲击,1997,17(2):143-152.
[17] Kachanov L M. Introduction to continuum damage mechanics[M]. TheNetherlands: Martinus Nijhoff1986.
[18] Krajcinovic D. Damage mechanics: accomplishments, trends and needs[J].International Journal of Solids and Structures,2000,37(1):267-277.
[19] Martin J B,Leckie F A. On the creep rupture of structure[J]. J. Mech. Phys.Solids,1972,20:223-228.
[20] Hayhurst D R,Leckie F A. The effect of creep constitutive and damagerelationships upon the rupture time of a solid circular torsion bar[J]. J. Mech.Phys. Solids,1972,21:431-448.
[21] Lee C,Cozzarelli F A. Strain-dependent creep damage in random inhomogeneousmaterials, in DTIC.1980, State University of New York: Buffalo. p.1-60.
[22] Wong F C,Ait-Kadi A. Predictive capability of a new Mori-Tanakamicromechanical model for particulate composites.1998, American Institute ofAeronautics and Astronautics. p.1394-1404.
[23] Okada H. Numerical investigation for microstructure effects on the crack growthbehavior of particulate composite materials, in AD.2006. p.1-62.
[24] Schapery R A. Application of thermodynamics to thermomechanics, fracture andbirefringent phenomena in viscoelastic media[J]. Journal of Applied Physics,1964,33(5):1451-1465.
[25] Schapery R A. Nonlinear viscoelastic and viscoplastic constitutive equations withgrowing damage[J]. International Journal of Fracture,1999,97:33-66.
[26] Tan H, Liu C, Huang Y, et al. The cohesive law for the particle/matrix interfacesin high explosives[J]. Journal of the Mechanics and Physics of Solids,2005,53:1892-1917.
[27] Wu Y, Ling Z, Dong Z. Stress-strain fields and the effectiveness shear propertiesfor three-phase composites with imperfect interface[J]. Int. J. Solids Struct,1999,37:1275-1292.
[28] Tan H, Huang Y, Liu C, et al. The Mori-Tanaka method for composite materialswith nonlinear interface debonding[J]. Int. J. Plasticity,2005.
[29] Ha K,Schapery R A. A three-dimensional viscoelastic constitutive model forparticulate composites with growing damage and its experimental validation[J].Internat. J. Solids Struct,1998,35:3497-3517.
[30] Hinterhoelzl R M,Schapery R A. FEM implementation of a three-dimensionalviscoelastic constitutive model for particulate composites with damage growth[J].Mechanics of Time-Dependent Materials,2004,8:65-94.
[31] Schapery R A. Simplification in the viscoelastic behavior of composites withgrowing damage[C]//Dvorak G J,(ed.). IUTAM Symposium in InelasticDeformation of Composite Materials. Berlin,1990:193-214.
[32] Park S W,Schapery R A. A viscoelastic constitutive model for particulatecomposites with growing damage[J]. Internat. J. Solids. Struct.,1997,32:931-947.
[33]陈鹏万,黄风雷.含能材料损伤理论及应用[M].北京:北京理工大学出版社2006.
[34] Rice J R,Tracery D M. On the ductile enlargement of voids in triaxial stressfields[J]. J. Mech. Phys. Solids,1969,17(3):201-217.
[35] Johnson J N. Dynamic fracture and spallation[J]. J. Appl. Phys.,1981,52(4):2812-2825.
[36] Carroll M M,Holt A C. Void nucleation effects in biaxially stretched sheets[J]. J.Eng. Mater. Technol.,1972,102:247-256.
[37] Seaman L, Curran D R, Shockey D A. Compitational models for ductile andbrittle fracture[J]. J. Appl. Phys.,1976,47(11):4814-4824.
[38] Curran D R, Seaman L, Shockey D A. Dyanmic failure of solids[J]. Phys. Rep.,1987,147:254-388.
[39] Seaman L, Curran D R, Shockey D A. Computational models for ductile andbrittle fracture[J]. Jounal of Applied Phsyics,1976,47(11):4814-4826.
[40] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth-ⅠYield criteria and flow rules for porous ductile media[J]. Eng. Mater. Technol.,1977,99:2-15.
[41] Gurson A L. Porus rigid-plastic materials containing rigid inclusions-yieldfunction, plastic potential and void nucleation[C]//Taplin D M,(ed.). Proc. Int.Conf. Fracture. Oxford: Pergamon Press,1977:357-364.
[42] Tvergaard V. Ductile fracture by cavity nucleation between larger voids[J]. J.Mech. Phys. Solids,1982,30:265-286.
[43] Chu C C,Needleman A. Void nucleation effects in biaxially streched sheets[J]. J.Engng Mater Technol,1980,102:249-256.
[44] Tvergaard V,Needleman A. Analysis of the cup-cone fracture in a round tensilebar[J]. Acta Met.,1984,32:157-169.
[45]白以龙,柯孚久,夏蒙焚.固体中微裂纹系统统计演化的基本描述[J].力学进展,1991,23(3):290-298.
[46] Bai Y L, Xia M F, Ke F J, et al. Statistical microdamage mechanics and damagefield evolution[J]. Thero. Appl. Fract. Mech.,2001,37:1-10.
[47] Bai Y L, Xia M F, Ke F J, et al. Closed trans-scale statistical microdamagemechanics[J]. Acta Mechanica Sinica,2002,18(1):1-17.
[48] Feng J, Jing F, Zhang G. Dynamic ductile fragmentation and the damagefunction model[J]. J. Appl. Phys.,1997,81(6):4.
[49] Zhang C, Zou S, Zhang B. Damage evolution of ductile materials under impactloading[J]. Mechanics research Communication,2006,33:26-34.
[50] Bondonaff J L. Probabilistic Models of Cumulative Damage[M]. New York:Wiley and Sons1985.
[51]邢修三.脆性断裂的微观机理和非平衡统计特性[J].力学进展,1986,16:495-510.
[52] Dienes J K. Frictional Hot-spots and Propellant Sensitivity[C]. Mat. Res. Soc.Symp. Proc.,1984,24:373-381.
[53] Dienes J K. A unified theory of flow, hot spot, and fragmentation with anapplication to explosive sensitivity[M]. Lee D (ed.). In high-pressure shockcompression of solids Ⅱ.1996.
[54] Bennett J G, Haberman K S, Johnson J N, et al. A constitutive model for thenon-shock ignition and mechanical response of high explosives[J]. J. Mech. Phys.Solids,1998,46(12):2303-2322.
[55] Frank-Kamenetakii A A. On the mathematical theory of thermal explosions[M].Acta Physicochimica URSS.1942,Vol. XVI:357-361.
[56] Cook M D, Haskins P J, Stennett C, et al. Cumulative damage hotspot model foruse with arrhenius based ignition and growth model[C].12th internationaldetonation symposium. California,2002.
[57] Salvetat B,Gueryj F. Visulizaition and modeling of delayed detonation in thecard cap test[C].10th International Symposium on Detonation,1993:7.
[58] Perzyna P. Constitutive modeling for brittle dynamic fracture in dissipativesolids[J]. Ach. Mech.,1986,138(5~6).
[59] Matheson E R,Rosenberg J T. A mechanistic study of delayed detonation inimpact damaged solid rocket propellant[J]. Shock Compression of CondensedMatter,2001:464-467.
[60] Matheson E R, Drumheller D S, Baer M R. A coupled damage and reactionmodel for simulating ernergetic material response to impact hazards[J]. ShockCompression of Condensed Matter,1999:651-654.
[61] Baer M R, Hertel E S, Bell R L. Multidimensional DDT modeling of ernergeticmaterials[J]. Shock Compression of Condensed Matter,1995:433-436.
[62] Drumheller D S. The role of distention in reacting porous solids[J]. ShockCompression of Condensed Matter,1999:133-136.
[63] Demol G, Goutelle J G, Mazel P. CHARME：a reactive model for pressedexplosives using pore and gain size distribution as parameters[J]. ShockCompression of Condensed Matter,1997:353-356.
[64] Reaugh J E. Multi-scale Computer Simulations to Study the Reaction Zone ofSolid Explosives[C].13th International Detonation Symposium. Norfolk, VA,United States,2006.
[65] Conley P A,Benson D J. Microstructural effets in shock initiation[C].11thInternational Detonation Symposium. Snowmass, CO, United States,1998:768-780.
[66]于继东.炸药冲击响应的二维细观离散元模拟[D].绵阳:中国工程物理研究院,2007.
[67]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].绵阳:中国工程物理研究院,2006.
[68]尚海林.非均质炸药冲击载荷作用下热点形成的离散元模拟研究[D].绵阳:中国工程物理研究院,2009.
[69] Xu A G, Pan X F, Zhang G C. Material-point simulation of cavity collapse undershock[J]. Journal of Physics: Condensed Matter,2007,19:1-11.
[70] Chen W, Zhang B, Forrestal M J. A split Hopkinson bar technique forlow-impedance materials[J]. Experimental Mechanics,1999,39(2):81-85.
[71] Zhao H, Gary G, Klepaczko J R. On the use of a viscoelastic split Hopkinsonpressure bar[J]. International Journal of Impact Engineering,1997,19(4):319-330.
[72] Chen W, Lu F, Zhou B. A quartz-crystal-embedded split Hopkinson pressure barfor soft materials[J]. Experimental Mechanics,2000,40(1):1-6.
[73]林玉亮,卢芳云,卢力.石英压电晶体在霍普金森压杆实验中的应用[J].高压物理学报,2005,19(4):299-304.
[74] Chen W, Lu F, Frew D J, et al. Dynamic compression testing of soft materials[J].Journal of Applied Mechanics-Transactions of the Asme,2002,69(3):214-223.
[75] Pan Y, Chen W, Song B. Upper limit of constant strain rates in a split Hopkinsonpressure bar experiment with elastic specimens[J]. Experimental Mechanics,2005,45(5):440-446.
[76] Ottosen N S,Ristinmaa M. The mechanics of constitutive modeling[M]. Oxford,UK: Elsevier Science2005.
[77] Sargin M. Stress-strain relationships for concrete and the analysis of structuralconcrete sections[M]: Solid Mechanics Division, University of Waterloo1971.
[78] Nemat-Nasser S, Isaacs J B, Starrett J E. Hopkinson techniques for dynamicrecovery experiments[J]. Proceedings of the Royal Society of London. Series A:Mathematical and Physical Sciences,1991,435(1894):371-391.
[79] Song B,Chen W. Loading and unloading split Hopkinson pressure barpulse-shaping techniques for dynamic hysteretic loops[J]. ExperimentalMechanics,2004,44(6):622-627.
[80]林玉亮.软材料高应变率测试试验技术及本构行为研究[D].长沙:国防科学技术大学,2005.
[81]刘鸿文.材料力学[M].北京:高等教育出版社1992.
[82] Ma Z,Ravi-Chandar K. Confined compression: A stable homogeneousdeformation for constitutive characterization[J]. Experimental Mechanics,2000,40(1):38-45.
[83]施绍裘,王礼立.材料在准一维应变下被动围压的SHPB试验方法[J].实验力学,2000,15(4):377-384.
[84]胡绍楼.激光干涉测速技术[M].北京:国防工业出版社,2001.
[85] Barker L M. Behavior of Dense Media Under High Pressures[J]. New York:Gordon and Breach,1968:483-505.
[86]杨成龙.激光干涉测速技术[J].爆炸与冲击,1989,9(4):363-373.
[87] Hemsing W, Mathews A, Warnes R, et al. VISAR (Velocity InterferometerSystem for Any Reflector): Line-imaging interferometer.1990, Los AlamosNational Lab., NM (USA).
[88]李泽仁,李幼平.光纤传输速度干涉仪[J].爆炸与冲击,1994,14(2):175-181.
[89] Zhang R, Li M, Wang J, et al. Experimental research on an arbitrary pulsegeneration system for imaging VISAR[J]. Optics&Laser Technology,2011,43(1):179-182.
[90] Boehly T, Munro D, Celliers P, et al. Demonstration of the shock-timingtechnique for ignition targets on the National Ignition Facility[J]. Physics ofPlasmas,2009,16(5):056302.
[91] Levin L, Tzach D, Shamir J. Fiber optic velocity interferometer with very shortcoherence length light source[J]. Review of Scientific Instruments,1996,67(4):1434-1437.
[92] Chen R, Huang S, Xia K, et al. A modified Hopkinson bar system for testingultra-soft materials under intermediate strain rates[C],2009:389-394.
[93] Liu Z Y, Kubota S, Nagano S, et al. High-speed photographic study onoverdriven detonation of high explosive[C].24th international congress onhigh-speed phtotgraphy and photonics: proceedings of SPIE,2001:731.
[94] Linder K D, DeRego P, Gomez A, et al. Autonomous characterization ofplastic-bonded explosives[C]. Proceedings of SPIE application of digital imageprocessing XXIX. San Diego, USA,2006:631215.
[95] Gruau C, Picart D, Belmas R, et al. Ignition of a confined high explosive underlow velocity impact[J]. International Journal of Impact Engineering,2009,36(4):537-550.
[96] Drodge D, Williamson D, Palmer S, et al. The mechanical response of a PBX andbinder: combining results across the strain-rate and frequency domains[J].Journal of Physics D: Applied Physics,2010,43(33):335403.
[97] Siviour C, Laity P, Proud W, et al. High strain rate properties of apolymer-bonded sugar: their dependence on applied and internal constraints[J].Proceedings of the Royal Society A: Mathematical, Physical and EngineeringScience,2008,464(2093):1229-1255.
[98] Bourne N,Gray III G. Dynamic response of binders; teflon, estane andKel-F-800[J]. Journal of Applied Physics,2005,98(12):123503.
[99] Drodge D R,Proud W G. The effects of particle size and separation on PBXdeformation[C]. Shock Compression of Condensed Matter,2009.
[100] Yeager J, Dattelbaum A, Orler E, et al. Adhesive properties of somefluoropolymer binders with the insensitive explosive1,3,5-triamino-2,4,6-trinitrobenzene (TATB)[J]. Journal of colloid and interface science,2010,352(2):535-541.
[101] Salazar M R, Kress J D, Lightfoot J M, et al. Low-temperature oxidativedegradation of PBX9501and its components determined via molecular weightanalysis of the Poly [ester urethane] binder[J]. Polymer Degradation and Stability,2009,94(12):2231-2240.
[102] Idar D, Thompson D, Gray Iii G, et al. Influence of polymer molecular weight,temperature, and strain rate on the mechanical properties of PBX9501[C]. ShockCompression of Condensed Matter2001.
[103] Proud W G, Gould D P P J, Williamson D M, et al. The Mechanical Performanceof Polymers and Polymer Composites at High Strain-Rates[C]. Proceedings ofIMPLAST2010conference. Rhode Island USA: SEM Inc,2010.
[104] Singh G, Prem Felix S, Pandey D, et al. Studies on energetic compounds PartXXXIX: Thermal analysis of a plastic bonded explosive containing RDX andHTPB[J]. Journal of thermal analysis and calorimetry,2005,79(3):631-635.
[105] Xu X, Xiao J, Huang H, et al. Molecular dynamic simulations on the structuresand properties of-CL-20(001)/F2314PBX[J]. Journal of hazardous materials,2010,175(1-3):423-428.
[106] Gray III G, Idar D, Blumenthal W, et al. High-and low-strain rate compressionproperties of several energetic material composites as a function of strain rate andtemperature[C]. Proceedings of11th international detonation symposium: LosAlamos National Lab., NM (United States),1998.
[107] Gray III G, Blumenthal W, Cady C, et al. Influence of Temperature on theHigh-Strain-Rate Mechanical Behavior of PBX9501and PBXN-9[C]. Shockcompression of condensed matter,1997.
[108] Lee J S,Jaw K S. Thermal decomposition properties and compatibility of CL-20,NTO with silicone rubber[J]. Journal of thermal analysis and calorimetry,2006,85(2):463-467.
[109] Jaw K S,Lee J S. Thermal behaviors of petn base polymer bonded explosives[J].Journal of thermal analysis and calorimetry,2008,93(3):953-957.
[110] Drodge D R, Addiss J W, Williamson D M, et al. Hopkinson Bar Studies of aPBX Simulant[C]. Shock Compression of Condensed Matter. Melville, NY,11747-4502, USA: American Institute of Physics,2007:513-516.
[111]朱伟.高能体系结构和性能的分子动力学研究[D].南京:南京理工大学,2008.
[112]马秀芳.高聚物粘结炸药结构与性能的计算模拟研究[D].南京:南京理工大学,2006.
[113] Ma X F, Xiao J J, Huang H, et al. Simulative Calculation of Mechanical Property,Binding Energy and Detonation Property of TATB/Fluorine‐polymer PBX[J].Chinese Journal of Chemistry,2006,24(4):473-477.
[114] Ravichandran G,Subhash G. Critical-appraisal of limiting strain rates forcompression testing of ceramics in a split Hopkinson pressure bar[J]. Journal ofthe American Ceramic Society,1994,77(1):263-267.
[115] Walley S M, Field J E, Greenaway M W. Crystal sensitivities of energeticmaterials[J]. Materials Science and Technology,2006,22(4):402-413.
[116] Johnson H,Wilson A. Mechanical properties of high explosives, inMHSMP-73-5B.1972, Mason and Hanger-Silas Mason Co.: USA. p.11.
[117] Skidmore C, Phillips D, Howe P, et al. The evolution of microstructural changesin pressed HMX explosives[C].11th detonation symposium. Colorado,1998:556-564.
[118] Rae P J, Palmer S J P, Goldrein H T. Quasi-static studies of the deformation andfailure of PBX9501[J]. Proceedings of the Royal Society A: Mathematical,Physical and Engineering Science,2002,458(2025):2227-2242.
[119] Proud W, Palmer S, Field J, et al. AFM studies of PBX systems[J].Thermochimica acta,2002,384(1-2):245-251.
[120] Goldrein H, Palmer S, Field J. Construction of a high-resolution moiréinterferometer for investigating microstructural displacement fields inmaterials[J]. Philosophical Transactions of the Royal Society of London. SeriesA: Mathematical, Physical and Engineering Sciences,2002,360(1794):939-952.
[121] Lewis A,Goldrein H. Strain measurement techniques in explosives[J]. Strain,2004,40(1):33-37.
[122] Rae P, Goldrein H, Palmer S, et al. Studies of the failure mechanisms ofpolymer-bonded explosives by high resolution moiré interferometry andenvironmental scanning electron microscopy[C],1998:31.
[123] Grantham S G, Siviour C R, Proud W G, et al. High-strain rate Brazilian testingof an explosive simulant using speckle metrology[J]. Measurement Science&Technology,2004,15(9):1867-1870.
[124] Siviour C R, Grantham S G, Williamson D M, et al. Novel measurements ofmaterial properties at high rates of strain using speckle metrology[J]. ImageScience Journal,2009,57(6):326-332.
[125] Liu Z W, Xie H M, Li K X, et al. Fracturebehavior of PBXsimulationsubject tocombinedthermal and mechanicalloads[J]. Polymer Testing,2009,28(6):627-635.
[126] Yamaguchi I. A laser-speckle strain gauge[J]. Journal of Physics E: ScientificInstruments,1981,14:1270.
[127] Peters W,Ranson W. Digital imaging techniques in experimental stressanalysis[J]. Optical Engineering,1982,21(3).
[128] Sutton M A, McNeill S R, Jang J, et al. Effects of subpixel image restoration ondigital correlation error estimates[J]. Optical Engineering,1988,27:870-877.
[129] Sutton M, Bruck H, McNeill S. Determination of deformations using digitalcorrelation with the Newton-Raphson method for partial differentialcorrections[J]. Experimental Mechanics,1989,29(3):261-267.
[130]孟立波.数字散斑相关方法的应用和研究[D].北京:清华大学,2005.
[131]李喜德.数字散斑强度相关计量理论和应用[D].西安:西安交通大学,1992.
[132] Ji H W, Qin Y, Lu H. Initial estimates in digital image correlation method by anew displacement mode[J]. Journal of Experimental Methmatics,2001,46(1):49-52.
[133]金观昌.计算机辅助光学测量[M].北京:清华大学出版社2007.
[134]李旭东.多点爆炸效应及其防护问题的实验与计算研究[D].北京:北京大学,2008.
[135]陈俊达.数字散斑相关方法理论和应用研究[D].北京:清华大学,2007.
[136]陈荣.一种PBX炸药试样在复杂应力动态加载下的力学响应[D].长沙:国防科学技术大学,2010.
[137] Awaji H,Sato S. Diametral compressive testing method[J]. Journal ofEngineering Materials and Technology,1979,101(2):139-147.
[138] Wang Q Z, Jia X M, Kou S Q, et al. The flattened Brazilian disc specimen usedfor testing elastic modulus, tensile strength and fracture toughness of brittle rocks:analytical and numerical results[J]. International Journal of Rock Mechanics andMining Sciences,2004,41(2):245-253.
[139] Dai F, Huang S, Xia K, et al. Some Fundamental Issues in DynamicCompression and Tension Tests of Rocks Using Split Hopkinson Pressure Bar[J].Rock Mechanics and Rock Engineering,2010,43(6):657-666.
[140] Tan H, Liu C, Huang Y, et al. The cohesive law for the particle/matrix interfacesin high explosives[J]. Journal of the Mechanics and Physics of Solids,2005,53(8):1892-1917.
[141] Palmer S,Field J. The Deformation and Fracture of b-HMX[J]. Proceedings ofthe Royal Society of London-A. Mathematical and Physical Sciences,1982,383(1785):399-407.
[142] Nicholson D. On the detachment of a rigid inclusion from an elastic matrix[J].Journal of Adhesion,1979,10(3):255-260.
[143] Rivera T,Matuszak M L. Surface properties of potential plastic-bondedexplosives (PBX)[J]. Journal of colloid and interface science,1983,93(1):105-108.
[144]周红萍,庞海燕,温茂平,等.三种粘结剂的力学性能对比研究[J].材料导报,2009,23(12):34-36.
[145] Cundall P A. A computer model for simulating progressive, large-scalemovements in blocky rock systems, in Proceedings of International Symposiumof Rock Mchanics.1971: Nancy, France.
[146] Greenspan D. Quasimolecular modelling[M]. Singapore: World Scientific PubCo Inc1991.
[147] Kawai T. New discrete models and their application to seismic response analysisof structures[J]. Nuclear engineering and design,1978,48(1):207-229.
[148]王泳嘉.离散单元法及其在岩土力学中的应用[M].沈阳:东北工学院出版社1991.
[149] Tang Z, Horie Y, Psakhie S. Discrete meso-element modeling of shock processesin porous materials. Vol.1: Theory and model calculations.1995, TechnicalReport, North Carolina State University, Raleigh, NC.
[150]傅华.材料在冲击载荷下细观变形特征的数值模拟初步研究[D].绵阳:2006.
[151]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.
[152] Krajcinovic D. Continuum damage mechanics[J]. Applied Mechanics Review,1984,37:1-6.
[153] Kachanov M. Effective elastic properties of cracked solids: critial review of somebasic concepts[J]. Applied Mechanics Review,1992,45:304-335.
[154] Chow C L,Wang J. An anisotropic theory of elasticity for continuum damagemechanics[J]. International Journal of Fracture1987,33(1):3-16.
[155] Chow C L,Lu T J. A continuum damage mechanics approach to crack tipshielding in brittle solids[J]. International Journal of Fracture,1991,50(2):79-114.
[156]冯西桥.脆性材料的细观损伤理论和损伤结构的安定分析[D].北京:清华大学,1995.
[157] Mura T. Micromechanics of Defects in Solids[M]. The Netherlands: MartinusNijhoff Publishers1987.
[158] Ju J W,Lee X. Micromechanical damage models for brittle solids, I: tensileloadings[J]. Journal of Engineering Mechanics,1991,117:1495-1514.
[159] Fanella D,Krajcinovic D. A micromechanial model for concrete incompression[J]. Engineering Fracture Mechanics,1988,29(1):49-66.
[160] Horii H,Nemat-Nasser S. Compression-Induced Microcrack Growth in BrittleSolids: Axial Splitting and Shear Failure[J]. Journal of Geophysical Research,1985,90(B4):3105-3125.
[161] Freund L B. Dynamic fracture mechanics[M]. Cambridge: Cambridge UniversityPress1990.
[162] Kanninen M F,Poplar C H. Dynamic Fracture Mechanics[M]. Cambridge, UK:Cambridge University Press1985.
[163] Rose L R F. Recent Theoretical and Experimental Results on Fast BrittleFracture[J]. International Journal of Fracture,1976,12:799-813.
[164] Nakamura T, Shih C F, Freund L B. Analysis of a Dynamically LoadedThree-Point-Bend Ductile Fracture Specimen[J]. Engineering FractureMechanics,1986,25:323-399.
[165] Dulaney E N,Brace W F. Velocity Behavior of a Growing Crack[J]. Journal ofApplied Physics,1960,31:2233-2326.
[166] Mott N F. Fracture of Metals:Theoretical Considerations[J]. Engineering1948,165:16-18.
[167] Freund L B. Crack Propagation in an Elastic Solid Subjected to GeneralLoading-III. Stress Wave Loading[J]. Journal of the Mechanics and Physics ofSolids,1973,21:47-61.
[168] Atkinson C,Eshlby J D. The Flow of Energy into the Tip of a Moving Crack[J].International Journal of Fracture Mechanics,1968,4:3-8.
[169] Sih G C. Dynamic Aspects of Crack Propagation[M]. New York: McGraw-Hill1970.
[170] Rose L R F. An Approximate (Wiener-Hoof) Kernel for Dynamic Crack Problemin Linear Elasticity and Vicsoelasticity[J]. Proceedings, Royal Society of LondonA,1976,349:621-633.
[2] Liu C,Browning R. Fracture in PBX9501at low rates[C]. Proceedings12thInternational Detonation Symposium. San Diego, California,2002:121-126.
[3] G. Goudrean. Evaluation of mechanical properties of PBXW-113explosive.1985.
[4] Hoffman H J. High-strain rate testing of gun propellants.1989.
[5] Blumenthal W R, Thompson D G, Cady C D, et al. Compressive properties ofPBXN-110and Its HTPB-based binder as a function of temperature and strainrate, in12th International Detonation Conference.2002: California.
[6]罗景润. PBX的损伤、断裂及本构关系[D].绵阳:2001.
[7]李英雷,李大红,胡时胜. TATB钝感炸药本构的实验研究[J].爆炸与冲击,1999,19(4):355-359.
[8]吴会民,卢芳云.三种含能材料力学行为应变率效应的实验研究[J].含能材料,2004,12(4):227-230.
[9]陈荣,卢芳云,林玉亮,等.一种含铝炸药的本构关系研究[J].含能材料,2007,10(5):460-463.
[10] Palmer S, Field J, Huntley J. Deformation, strengths and strains to failure ofpolymer bonded explosives[J]. Proceedings of the Royal Society of London.Series A: Mathematical and Physical Sciences,1993,440(1909):399-419.
[11]陈鹏万.高聚物粘结炸药的细观结构及力学性能[D].北京:中国科学院力学研究所,2001.
[12] Pinto J,Wiegand D. The mechanical response of TNT and A composite,composition B, of TNT and RDX to compressive stress: II triaxial stress andyield[J]. Journal of Energetic Materials,1991,9(3):205-263.
[13]韩小平,张元冲.高能材料动态力学性能实验研究[J].爆炸与冲击,1995,15(1):20-27.
[14] Wiegand D A, Pinto J, Nicolaides S. The mechanical response of TNT and acomposite, composition B, of TNT and RDX to compressive stress: I uniaxialstress and fracture[J]. Journal of Energetic Materials,1991,9(1-2):19-80.
[15] Wiegand D, Nicolaides S, Pinto J. Mechanical and thermomechanical propertiesof NC base propellants[J]. Journal of Energetic Materials,1990,8(5):442-461.
[16]韩小平,张元冲.冲击载荷下炸药装药动态响应的有限元分析及热点形成机理的数值模拟研究[J].爆炸与冲击,1997,17(2):143-152.
[17] Kachanov L M. Introduction to continuum damage mechanics[M]. TheNetherlands: Martinus Nijhoff1986.
[18] Krajcinovic D. Damage mechanics: accomplishments, trends and needs[J].International Journal of Solids and Structures,2000,37(1):267-277.
[19] Martin J B,Leckie F A. On the creep rupture of structure[J]. J. Mech. Phys.Solids,1972,20:223-228.
[20] Hayhurst D R,Leckie F A. The effect of creep constitutive and damagerelationships upon the rupture time of a solid circular torsion bar[J]. J. Mech.Phys. Solids,1972,21:431-448.
[21] Lee C,Cozzarelli F A. Strain-dependent creep damage in random inhomogeneousmaterials, in DTIC.1980, State University of New York: Buffalo. p.1-60.
[22] Wong F C,Ait-Kadi A. Predictive capability of a new Mori-Tanakamicromechanical model for particulate composites.1998, American Institute ofAeronautics and Astronautics. p.1394-1404.
[23] Okada H. Numerical investigation for microstructure effects on the crack growthbehavior of particulate composite materials, in AD.2006. p.1-62.
[24] Schapery R A. Application of thermodynamics to thermomechanics, fracture andbirefringent phenomena in viscoelastic media[J]. Journal of Applied Physics,1964,33(5):1451-1465.
[25] Schapery R A. Nonlinear viscoelastic and viscoplastic constitutive equations withgrowing damage[J]. International Journal of Fracture,1999,97:33-66.
[26] Tan H, Liu C, Huang Y, et al. The cohesive law for the particle/matrix interfacesin high explosives[J]. Journal of the Mechanics and Physics of Solids,2005,53:1892-1917.
[27] Wu Y, Ling Z, Dong Z. Stress-strain fields and the effectiveness shear propertiesfor three-phase composites with imperfect interface[J]. Int. J. Solids Struct,1999,37:1275-1292.
[28] Tan H, Huang Y, Liu C, et al. The Mori-Tanaka method for composite materialswith nonlinear interface debonding[J]. Int. J. Plasticity,2005.
[29] Ha K,Schapery R A. A three-dimensional viscoelastic constitutive model forparticulate composites with growing damage and its experimental validation[J].Internat. J. Solids Struct,1998,35:3497-3517.
[30] Hinterhoelzl R M,Schapery R A. FEM implementation of a three-dimensionalviscoelastic constitutive model for particulate composites with damage growth[J].Mechanics of Time-Dependent Materials,2004,8:65-94.
[31] Schapery R A. Simplification in the viscoelastic behavior of composites withgrowing damage[C]//Dvorak G J,(ed.). IUTAM Symposium in InelasticDeformation of Composite Materials. Berlin,1990:193-214.
[32] Park S W,Schapery R A. A viscoelastic constitutive model for particulatecomposites with growing damage[J]. Internat. J. Solids. Struct.,1997,32:931-947.
[33]陈鹏万,黄风雷.含能材料损伤理论及应用[M].北京:北京理工大学出版社2006.
[34] Rice J R,Tracery D M. On the ductile enlargement of voids in triaxial stressfields[J]. J. Mech. Phys. Solids,1969,17(3):201-217.
[35] Johnson J N. Dynamic fracture and spallation[J]. J. Appl. Phys.,1981,52(4):2812-2825.
[36] Carroll M M,Holt A C. Void nucleation effects in biaxially stretched sheets[J]. J.Eng. Mater. Technol.,1972,102:247-256.
[37] Seaman L, Curran D R, Shockey D A. Compitational models for ductile andbrittle fracture[J]. J. Appl. Phys.,1976,47(11):4814-4824.
[38] Curran D R, Seaman L, Shockey D A. Dyanmic failure of solids[J]. Phys. Rep.,1987,147:254-388.
[39] Seaman L, Curran D R, Shockey D A. Computational models for ductile andbrittle fracture[J]. Jounal of Applied Phsyics,1976,47(11):4814-4826.
[40] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth-ⅠYield criteria and flow rules for porous ductile media[J]. Eng. Mater. Technol.,1977,99:2-15.
[41] Gurson A L. Porus rigid-plastic materials containing rigid inclusions-yieldfunction, plastic potential and void nucleation[C]//Taplin D M,(ed.). Proc. Int.Conf. Fracture. Oxford: Pergamon Press,1977:357-364.
[42] Tvergaard V. Ductile fracture by cavity nucleation between larger voids[J]. J.Mech. Phys. Solids,1982,30:265-286.
[43] Chu C C,Needleman A. Void nucleation effects in biaxially streched sheets[J]. J.Engng Mater Technol,1980,102:249-256.
[44] Tvergaard V,Needleman A. Analysis of the cup-cone fracture in a round tensilebar[J]. Acta Met.,1984,32:157-169.
[45]白以龙,柯孚久,夏蒙焚.固体中微裂纹系统统计演化的基本描述[J].力学进展,1991,23(3):290-298.
[46] Bai Y L, Xia M F, Ke F J, et al. Statistical microdamage mechanics and damagefield evolution[J]. Thero. Appl. Fract. Mech.,2001,37:1-10.
[47] Bai Y L, Xia M F, Ke F J, et al. Closed trans-scale statistical microdamagemechanics[J]. Acta Mechanica Sinica,2002,18(1):1-17.
[48] Feng J, Jing F, Zhang G. Dynamic ductile fragmentation and the damagefunction model[J]. J. Appl. Phys.,1997,81(6):4.
[49] Zhang C, Zou S, Zhang B. Damage evolution of ductile materials under impactloading[J]. Mechanics research Communication,2006,33:26-34.
[50] Bondonaff J L. Probabilistic Models of Cumulative Damage[M]. New York:Wiley and Sons1985.
[51]邢修三.脆性断裂的微观机理和非平衡统计特性[J].力学进展,1986,16:495-510.
[52] Dienes J K. Frictional Hot-spots and Propellant Sensitivity[C]. Mat. Res. Soc.Symp. Proc.,1984,24:373-381.
[53] Dienes J K. A unified theory of flow, hot spot, and fragmentation with anapplication to explosive sensitivity[M]. Lee D (ed.). In high-pressure shockcompression of solids Ⅱ.1996.
[54] Bennett J G, Haberman K S, Johnson J N, et al. A constitutive model for thenon-shock ignition and mechanical response of high explosives[J]. J. Mech. Phys.Solids,1998,46(12):2303-2322.
[55] Frank-Kamenetakii A A. On the mathematical theory of thermal explosions[M].Acta Physicochimica URSS.1942,Vol. XVI:357-361.
[56] Cook M D, Haskins P J, Stennett C, et al. Cumulative damage hotspot model foruse with arrhenius based ignition and growth model[C].12th internationaldetonation symposium. California,2002.
[57] Salvetat B,Gueryj F. Visulizaition and modeling of delayed detonation in thecard cap test[C].10th International Symposium on Detonation,1993:7.
[58] Perzyna P. Constitutive modeling for brittle dynamic fracture in dissipativesolids[J]. Ach. Mech.,1986,138(5~6).
[59] Matheson E R,Rosenberg J T. A mechanistic study of delayed detonation inimpact damaged solid rocket propellant[J]. Shock Compression of CondensedMatter,2001:464-467.
[60] Matheson E R, Drumheller D S, Baer M R. A coupled damage and reactionmodel for simulating ernergetic material response to impact hazards[J]. ShockCompression of Condensed Matter,1999:651-654.
[61] Baer M R, Hertel E S, Bell R L. Multidimensional DDT modeling of ernergeticmaterials[J]. Shock Compression of Condensed Matter,1995:433-436.
[62] Drumheller D S. The role of distention in reacting porous solids[J]. ShockCompression of Condensed Matter,1999:133-136.
[63] Demol G, Goutelle J G, Mazel P. CHARME：a reactive model for pressedexplosives using pore and gain size distribution as parameters[J]. ShockCompression of Condensed Matter,1997:353-356.
[64] Reaugh J E. Multi-scale Computer Simulations to Study the Reaction Zone ofSolid Explosives[C].13th International Detonation Symposium. Norfolk, VA,United States,2006.
[65] Conley P A,Benson D J. Microstructural effets in shock initiation[C].11thInternational Detonation Symposium. Snowmass, CO, United States,1998:768-780.
[66]于继东.炸药冲击响应的二维细观离散元模拟[D].绵阳:中国工程物理研究院,2007.
[67]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].绵阳:中国工程物理研究院,2006.
[68]尚海林.非均质炸药冲击载荷作用下热点形成的离散元模拟研究[D].绵阳:中国工程物理研究院,2009.
[69] Xu A G, Pan X F, Zhang G C. Material-point simulation of cavity collapse undershock[J]. Journal of Physics: Condensed Matter,2007,19:1-11.
[70] Chen W, Zhang B, Forrestal M J. A split Hopkinson bar technique forlow-impedance materials[J]. Experimental Mechanics,1999,39(2):81-85.
[71] Zhao H, Gary G, Klepaczko J R. On the use of a viscoelastic split Hopkinsonpressure bar[J]. International Journal of Impact Engineering,1997,19(4):319-330.
[72] Chen W, Lu F, Zhou B. A quartz-crystal-embedded split Hopkinson pressure barfor soft materials[J]. Experimental Mechanics,2000,40(1):1-6.
[73]林玉亮,卢芳云,卢力.石英压电晶体在霍普金森压杆实验中的应用[J].高压物理学报,2005,19(4):299-304.
[74] Chen W, Lu F, Frew D J, et al. Dynamic compression testing of soft materials[J].Journal of Applied Mechanics-Transactions of the Asme,2002,69(3):214-223.
[75] Pan Y, Chen W, Song B. Upper limit of constant strain rates in a split Hopkinsonpressure bar experiment with elastic specimens[J]. Experimental Mechanics,2005,45(5):440-446.
[76] Ottosen N S,Ristinmaa M. The mechanics of constitutive modeling[M]. Oxford,UK: Elsevier Science2005.
[77] Sargin M. Stress-strain relationships for concrete and the analysis of structuralconcrete sections[M]: Solid Mechanics Division, University of Waterloo1971.
[78] Nemat-Nasser S, Isaacs J B, Starrett J E. Hopkinson techniques for dynamicrecovery experiments[J]. Proceedings of the Royal Society of London. Series A:Mathematical and Physical Sciences,1991,435(1894):371-391.
[79] Song B,Chen W. Loading and unloading split Hopkinson pressure barpulse-shaping techniques for dynamic hysteretic loops[J]. ExperimentalMechanics,2004,44(6):622-627.
[80]林玉亮.软材料高应变率测试试验技术及本构行为研究[D].长沙:国防科学技术大学,2005.
[81]刘鸿文.材料力学[M].北京:高等教育出版社1992.
[82] Ma Z,Ravi-Chandar K. Confined compression: A stable homogeneousdeformation for constitutive characterization[J]. Experimental Mechanics,2000,40(1):38-45.
[83]施绍裘,王礼立.材料在准一维应变下被动围压的SHPB试验方法[J].实验力学,2000,15(4):377-384.
[84]胡绍楼.激光干涉测速技术[M].北京:国防工业出版社,2001.
[85] Barker L M. Behavior of Dense Media Under High Pressures[J]. New York:Gordon and Breach,1968:483-505.
[86]杨成龙.激光干涉测速技术[J].爆炸与冲击,1989,9(4):363-373.
[87] Hemsing W, Mathews A, Warnes R, et al. VISAR (Velocity InterferometerSystem for Any Reflector): Line-imaging interferometer.1990, Los AlamosNational Lab., NM (USA).
[88]李泽仁,李幼平.光纤传输速度干涉仪[J].爆炸与冲击,1994,14(2):175-181.
[89] Zhang R, Li M, Wang J, et al. Experimental research on an arbitrary pulsegeneration system for imaging VISAR[J]. Optics&Laser Technology,2011,43(1):179-182.
[90] Boehly T, Munro D, Celliers P, et al. Demonstration of the shock-timingtechnique for ignition targets on the National Ignition Facility[J]. Physics ofPlasmas,2009,16(5):056302.
[91] Levin L, Tzach D, Shamir J. Fiber optic velocity interferometer with very shortcoherence length light source[J]. Review of Scientific Instruments,1996,67(4):1434-1437.
[92] Chen R, Huang S, Xia K, et al. A modified Hopkinson bar system for testingultra-soft materials under intermediate strain rates[C],2009:389-394.
[93] Liu Z Y, Kubota S, Nagano S, et al. High-speed photographic study onoverdriven detonation of high explosive[C].24th international congress onhigh-speed phtotgraphy and photonics: proceedings of SPIE,2001:731.
[94] Linder K D, DeRego P, Gomez A, et al. Autonomous characterization ofplastic-bonded explosives[C]. Proceedings of SPIE application of digital imageprocessing XXIX. San Diego, USA,2006:631215.
[95] Gruau C, Picart D, Belmas R, et al. Ignition of a confined high explosive underlow velocity impact[J]. International Journal of Impact Engineering,2009,36(4):537-550.
[96] Drodge D, Williamson D, Palmer S, et al. The mechanical response of a PBX andbinder: combining results across the strain-rate and frequency domains[J].Journal of Physics D: Applied Physics,2010,43(33):335403.
[97] Siviour C, Laity P, Proud W, et al. High strain rate properties of apolymer-bonded sugar: their dependence on applied and internal constraints[J].Proceedings of the Royal Society A: Mathematical, Physical and EngineeringScience,2008,464(2093):1229-1255.
[98] Bourne N,Gray III G. Dynamic response of binders; teflon, estane andKel-F-800[J]. Journal of Applied Physics,2005,98(12):123503.
[99] Drodge D R,Proud W G. The effects of particle size and separation on PBXdeformation[C]. Shock Compression of Condensed Matter,2009.
[100] Yeager J, Dattelbaum A, Orler E, et al. Adhesive properties of somefluoropolymer binders with the insensitive explosive1,3,5-triamino-2,4,6-trinitrobenzene (TATB)[J]. Journal of colloid and interface science,2010,352(2):535-541.
[101] Salazar M R, Kress J D, Lightfoot J M, et al. Low-temperature oxidativedegradation of PBX9501and its components determined via molecular weightanalysis of the Poly [ester urethane] binder[J]. Polymer Degradation and Stability,2009,94(12):2231-2240.
[102] Idar D, Thompson D, Gray Iii G, et al. Influence of polymer molecular weight,temperature, and strain rate on the mechanical properties of PBX9501[C]. ShockCompression of Condensed Matter2001.
[103] Proud W G, Gould D P P J, Williamson D M, et al. The Mechanical Performanceof Polymers and Polymer Composites at High Strain-Rates[C]. Proceedings ofIMPLAST2010conference. Rhode Island USA: SEM Inc,2010.
[104] Singh G, Prem Felix S, Pandey D, et al. Studies on energetic compounds PartXXXIX: Thermal analysis of a plastic bonded explosive containing RDX andHTPB[J]. Journal of thermal analysis and calorimetry,2005,79(3):631-635.
[105] Xu X, Xiao J, Huang H, et al. Molecular dynamic simulations on the structuresand properties of-CL-20(001)/F2314PBX[J]. Journal of hazardous materials,2010,175(1-3):423-428.
[106] Gray III G, Idar D, Blumenthal W, et al. High-and low-strain rate compressionproperties of several energetic material composites as a function of strain rate andtemperature[C]. Proceedings of11th international detonation symposium: LosAlamos National Lab., NM (United States),1998.
[107] Gray III G, Blumenthal W, Cady C, et al. Influence of Temperature on theHigh-Strain-Rate Mechanical Behavior of PBX9501and PBXN-9[C]. Shockcompression of condensed matter,1997.
[108] Lee J S,Jaw K S. Thermal decomposition properties and compatibility of CL-20,NTO with silicone rubber[J]. Journal of thermal analysis and calorimetry,2006,85(2):463-467.
[109] Jaw K S,Lee J S. Thermal behaviors of petn base polymer bonded explosives[J].Journal of thermal analysis and calorimetry,2008,93(3):953-957.
[110] Drodge D R, Addiss J W, Williamson D M, et al. Hopkinson Bar Studies of aPBX Simulant[C]. Shock Compression of Condensed Matter. Melville, NY,11747-4502, USA: American Institute of Physics,2007:513-516.
[111]朱伟.高能体系结构和性能的分子动力学研究[D].南京:南京理工大学,2008.
[112]马秀芳.高聚物粘结炸药结构与性能的计算模拟研究[D].南京:南京理工大学,2006.
[113] Ma X F, Xiao J J, Huang H, et al. Simulative Calculation of Mechanical Property,Binding Energy and Detonation Property of TATB/Fluorine‐polymer PBX[J].Chinese Journal of Chemistry,2006,24(4):473-477.
[114] Ravichandran G,Subhash G. Critical-appraisal of limiting strain rates forcompression testing of ceramics in a split Hopkinson pressure bar[J]. Journal ofthe American Ceramic Society,1994,77(1):263-267.
[115] Walley S M, Field J E, Greenaway M W. Crystal sensitivities of energeticmaterials[J]. Materials Science and Technology,2006,22(4):402-413.
[116] Johnson H,Wilson A. Mechanical properties of high explosives, inMHSMP-73-5B.1972, Mason and Hanger-Silas Mason Co.: USA. p.11.
[117] Skidmore C, Phillips D, Howe P, et al. The evolution of microstructural changesin pressed HMX explosives[C].11th detonation symposium. Colorado,1998:556-564.
[118] Rae P J, Palmer S J P, Goldrein H T. Quasi-static studies of the deformation andfailure of PBX9501[J]. Proceedings of the Royal Society A: Mathematical,Physical and Engineering Science,2002,458(2025):2227-2242.
[119] Proud W, Palmer S, Field J, et al. AFM studies of PBX systems[J].Thermochimica acta,2002,384(1-2):245-251.
[120] Goldrein H, Palmer S, Field J. Construction of a high-resolution moiréinterferometer for investigating microstructural displacement fields inmaterials[J]. Philosophical Transactions of the Royal Society of London. SeriesA: Mathematical, Physical and Engineering Sciences,2002,360(1794):939-952.
[121] Lewis A,Goldrein H. Strain measurement techniques in explosives[J]. Strain,2004,40(1):33-37.
[122] Rae P, Goldrein H, Palmer S, et al. Studies of the failure mechanisms ofpolymer-bonded explosives by high resolution moiré interferometry andenvironmental scanning electron microscopy[C],1998:31.
[123] Grantham S G, Siviour C R, Proud W G, et al. High-strain rate Brazilian testingof an explosive simulant using speckle metrology[J]. Measurement Science&Technology,2004,15(9):1867-1870.
[124] Siviour C R, Grantham S G, Williamson D M, et al. Novel measurements ofmaterial properties at high rates of strain using speckle metrology[J]. ImageScience Journal,2009,57(6):326-332.
[125] Liu Z W, Xie H M, Li K X, et al. Fracturebehavior of PBXsimulationsubject tocombinedthermal and mechanicalloads[J]. Polymer Testing,2009,28(6):627-635.
[126] Yamaguchi I. A laser-speckle strain gauge[J]. Journal of Physics E: ScientificInstruments,1981,14:1270.
[127] Peters W,Ranson W. Digital imaging techniques in experimental stressanalysis[J]. Optical Engineering,1982,21(3).
[128] Sutton M A, McNeill S R, Jang J, et al. Effects of subpixel image restoration ondigital correlation error estimates[J]. Optical Engineering,1988,27:870-877.
[129] Sutton M, Bruck H, McNeill S. Determination of deformations using digitalcorrelation with the Newton-Raphson method for partial differentialcorrections[J]. Experimental Mechanics,1989,29(3):261-267.
[130]孟立波.数字散斑相关方法的应用和研究[D].北京:清华大学,2005.
[131]李喜德.数字散斑强度相关计量理论和应用[D].西安:西安交通大学,1992.
[132] Ji H W, Qin Y, Lu H. Initial estimates in digital image correlation method by anew displacement mode[J]. Journal of Experimental Methmatics,2001,46(1):49-52.
[133]金观昌.计算机辅助光学测量[M].北京:清华大学出版社2007.
[134]李旭东.多点爆炸效应及其防护问题的实验与计算研究[D].北京:北京大学,2008.
[135]陈俊达.数字散斑相关方法理论和应用研究[D].北京:清华大学,2007.
[136]陈荣.一种PBX炸药试样在复杂应力动态加载下的力学响应[D].长沙:国防科学技术大学,2010.
[137] Awaji H,Sato S. Diametral compressive testing method[J]. Journal ofEngineering Materials and Technology,1979,101(2):139-147.
[138] Wang Q Z, Jia X M, Kou S Q, et al. The flattened Brazilian disc specimen usedfor testing elastic modulus, tensile strength and fracture toughness of brittle rocks:analytical and numerical results[J]. International Journal of Rock Mechanics andMining Sciences,2004,41(2):245-253.
[139] Dai F, Huang S, Xia K, et al. Some Fundamental Issues in DynamicCompression and Tension Tests of Rocks Using Split Hopkinson Pressure Bar[J].Rock Mechanics and Rock Engineering,2010,43(6):657-666.
[140] Tan H, Liu C, Huang Y, et al. The cohesive law for the particle/matrix interfacesin high explosives[J]. Journal of the Mechanics and Physics of Solids,2005,53(8):1892-1917.
[141] Palmer S,Field J. The Deformation and Fracture of b-HMX[J]. Proceedings ofthe Royal Society of London-A. Mathematical and Physical Sciences,1982,383(1785):399-407.
[142] Nicholson D. On the detachment of a rigid inclusion from an elastic matrix[J].Journal of Adhesion,1979,10(3):255-260.
[143] Rivera T,Matuszak M L. Surface properties of potential plastic-bondedexplosives (PBX)[J]. Journal of colloid and interface science,1983,93(1):105-108.
[144]周红萍,庞海燕,温茂平,等.三种粘结剂的力学性能对比研究[J].材料导报,2009,23(12):34-36.
[145] Cundall P A. A computer model for simulating progressive, large-scalemovements in blocky rock systems, in Proceedings of International Symposiumof Rock Mchanics.1971: Nancy, France.
[146] Greenspan D. Quasimolecular modelling[M]. Singapore: World Scientific PubCo Inc1991.
[147] Kawai T. New discrete models and their application to seismic response analysisof structures[J]. Nuclear engineering and design,1978,48(1):207-229.
[148]王泳嘉.离散单元法及其在岩土力学中的应用[M].沈阳:东北工学院出版社1991.
[149] Tang Z, Horie Y, Psakhie S. Discrete meso-element modeling of shock processesin porous materials. Vol.1: Theory and model calculations.1995, TechnicalReport, North Carolina State University, Raleigh, NC.
[150]傅华.材料在冲击载荷下细观变形特征的数值模拟初步研究[D].绵阳:2006.
[151]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.
[152] Krajcinovic D. Continuum damage mechanics[J]. Applied Mechanics Review,1984,37:1-6.
[153] Kachanov M. Effective elastic properties of cracked solids: critial review of somebasic concepts[J]. Applied Mechanics Review,1992,45:304-335.
[154] Chow C L,Wang J. An anisotropic theory of elasticity for continuum damagemechanics[J]. International Journal of Fracture1987,33(1):3-16.
[155] Chow C L,Lu T J. A continuum damage mechanics approach to crack tipshielding in brittle solids[J]. International Journal of Fracture,1991,50(2):79-114.
[156]冯西桥.脆性材料的细观损伤理论和损伤结构的安定分析[D].北京:清华大学,1995.
[157] Mura T. Micromechanics of Defects in Solids[M]. The Netherlands: MartinusNijhoff Publishers1987.
[158] Ju J W,Lee X. Micromechanical damage models for brittle solids, I: tensileloadings[J]. Journal of Engineering Mechanics,1991,117:1495-1514.
[159] Fanella D,Krajcinovic D. A micromechanial model for concrete incompression[J]. Engineering Fracture Mechanics,1988,29(1):49-66.
[160] Horii H,Nemat-Nasser S. Compression-Induced Microcrack Growth in BrittleSolids: Axial Splitting and Shear Failure[J]. Journal of Geophysical Research,1985,90(B4):3105-3125.
[161] Freund L B. Dynamic fracture mechanics[M]. Cambridge: Cambridge UniversityPress1990.
[162] Kanninen M F,Poplar C H. Dynamic Fracture Mechanics[M]. Cambridge, UK:Cambridge University Press1985.
[163] Rose L R F. Recent Theoretical and Experimental Results on Fast BrittleFracture[J]. International Journal of Fracture,1976,12:799-813.
[164] Nakamura T, Shih C F, Freund L B. Analysis of a Dynamically LoadedThree-Point-Bend Ductile Fracture Specimen[J]. Engineering FractureMechanics,1986,25:323-399.
[165] Dulaney E N,Brace W F. Velocity Behavior of a Growing Crack[J]. Journal ofApplied Physics,1960,31:2233-2326.
[166] Mott N F. Fracture of Metals:Theoretical Considerations[J]. Engineering1948,165:16-18.
[167] Freund L B. Crack Propagation in an Elastic Solid Subjected to GeneralLoading-III. Stress Wave Loading[J]. Journal of the Mechanics and Physics ofSolids,1973,21:47-61.
[168] Atkinson C,Eshlby J D. The Flow of Energy into the Tip of a Moving Crack[J].International Journal of Fracture Mechanics,1968,4:3-8.
[169] Sih G C. Dynamic Aspects of Crack Propagation[M]. New York: McGraw-Hill1970.
[170] Rose L R F. An Approximate (Wiener-Hoof) Kernel for Dynamic Crack Problemin Linear Elasticity and Vicsoelasticity[J]. Proceedings, Royal Society of LondonA,1976,349:621-633.