TATB基PBX在不同围压下的Boltzmann-P本构模型及其数值计算方法
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摘要
围压对于PBX材料的力学性能影响显著,围压影响的实质为静水压力的影响。该文基于Boltzmann本构模型,建立了考虑静水压力影响的TATB基PBX准静态Boltzmann-P非线性弹性本构模型,提出了针对该本构模型的非线性计算方法,采用Mises等效应力-应变并引入泊松比提出了一维本构模型转化为三维模型的数值方法,然后通过二次开发实现了本构模型以及相应算法的实际应用。通过对单位体积单元进行计算,在无围压条件以及围压两种条件下Boltzmann-P模型描述精度均高于Boltzmann模型,验证了Boltzmann-P本构模型及相应算法与所开发程序的正确性。
Aiming at the characteristic that confining pressure has a significant influence on the mechanical properties of Polymer bonded explosive(PBX), a quasi-static constitutive model considering the effect of hydrostatic pressure called the Boltzmann-P model was proposed on the basis of the existing Boltzmann model. A nonlinear calculation method for the constitutive model and a numerical method of transforming the one-dimensional constitutive model into the three-dimensional model by using Mises equivalent stress strain and introducing Poisson's ratio are developed. Through secondary development, the constitutive model and the practical application of the corresponding algorithm were realized. Through the calculation of unit elements, it is shown that the description accuracy of the Boltzmann-P model is better than that of the Boltzmann model without and with confining pressure. The rationality and accuracy of the Boltzmann-P constitutive model, the corresponding algorithm and the developed subroutine are verified.
Aiming at the characteristic that confining pressure has a significant influence on the mechanical properties of Polymer bonded explosive(PBX), a quasi-static constitutive model considering the effect of hydrostatic pressure called the Boltzmann-P model was proposed on the basis of the existing Boltzmann model. A nonlinear calculation method for the constitutive model and a numerical method of transforming the one-dimensional constitutive model into the three-dimensional model by using Mises equivalent stress strain and introducing Poisson's ratio are developed. Through secondary development, the constitutive model and the practical application of the corresponding algorithm were realized. Through the calculation of unit elements, it is shown that the description accuracy of the Boltzmann-P model is better than that of the Boltzmann model without and with confining pressure. The rationality and accuracy of the Boltzmann-P constitutive model, the corresponding algorithm and the developed subroutine are verified.
引文
[1]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 Mingfeng,Pang Haiyan,Lan Lingang,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.(in Chinese)
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[3]Boddy R L,Gould P J,Jardine A P,et al.Damage in Polymer Bonded Energetic Composites:Effect of Loading Rate[J].Journal of Dynamic Behavior of Materials,2016,2(1):157―165.
[4]Xiao Y C,Sun Y,Wang Z J.Investigating the static and dynamic tensile mechanical behaviour of polymer‐bonded explosives[J].Strain,2018,54(2):e12262.
[5]Xiao Y C,Sun Y,Li X,et al.Dynamic mechanical behavior of PBX[J].Propellants Explosives Pyrotechnics,2016,41(4):629―636.
[6]陈蓉,卢芳云,林玉亮,等.一种含铝炸药压缩力学性能和本构关系研究[J].含能材料,2007,15(5):460―463.Chen Rong,Lu Fangyun,Lin Yuliang,et al.Mechanical behavior and constitutive model of pressed aluminized explosive[J].Chinese Journal of Energetic Materials(Hanneng Cailiao),2007,15(5):460―463.(in Chinese)
[7]王礼立,施绍裘.ZWT非线性热粘弹性本构关系的研究与应用[J].宁波大学学报:理工版,2000(B12):141―149.Wang Lili,Shi Shaoqiu.Research and application of ZWT nonlinear thermo-viscoelastic constitutive model[J].Journal of Ningbo University(Natural Science&Engineering Edition),2000(B12):141―149.(in Chinese)
[8]卢强,王占江,王礼立,等.基于ZWT方程的线黏弹性球面波分析[J].爆炸与冲击,2013,33(5):463―470.Lu Qiang,Wang Zhanjiang,Wang Lili,et al.Analysis of linear visco-elastic spherical waves based on ZWTconstitutive equation[J].Explosion and Shock Waves,2013,33(5):463―470.(in Chinese)
[9]Feng Zhenzhou,Wang Xinjun,Wang Fusheng,et al.Implementation and its application in finite element analysis of constitutive model for ZWT nonlinear viscoelastic material[J].Journal of Materials Science and Engineering,2007,25(2):269―272.
[10]Clements B.ViscoSCRAM:past,present and future[P].LANL,LA-UR-11-1245,2011.
[11]罗景润.PBX的损伤、断裂及本构关系研究[D].绵阳:中国工程物理研究院,2001.Luo Jingrun.Study on damage,fracture and constitutive relation of PBX[D].Mianyang:China Academy of Engineering Physics,2001.(in Chinese)
[12]郭虎.高聚物粘结炸药微裂纹统计本构模型研究[D].绵阳:中国工程物理研究院,2012.Guo Hu.Study on the visco statistical crack mechanics for PBXs[D].Mianyang:China Academy of Engineering Physics,2012.(in Chinese)
[13]张延耿,楼建锋,周婷婷,等.PBX炸药含各向异性损伤的黏弹性统计微裂纹本构模型初步研究[J].高压物理学报,2016,30(4):301―310.Zhang Yangeng,Lou Jianfeng,Zhou Tingting,et al.Initial study on constitutive model of PBXs via viscoelastic statistical crack mechanics including anisotropic damage[J].Chinese Journal of High Pressure Physics,2016,30(4):301―310.(in Chinese)
[14]高军,黄再兴.PBX炸药粘弹性损伤本构模型参数敏感度分析[J].工程力学,2015,32(2):201―206.Gao Jun,Huang Zaixing.Parameter sensitivity analysis for viscoelastic damage constitutive model for PBXmaterials[J].Engineering Mechanics,2015,32(2):201―206.(in Chinese)
[15]高军,黄再兴.PBX炸药粘弹性损伤本构模型的参数识别[J].工程力学,2013,30(7):299―304.Gao Jun,Huang Zaixing.Parameter identification for viscoelastic damage constitutive of PBX[J].Engineering Mechanics,2013,30(7):299―304.(in Chinese)
[16]成丽蓉,施惠基.PBX炸药含裂纹扩展损伤的粘塑性本构关系[J].含能材料,2015,23(10):999―1003.Cheng Lirong,Shi Huiji.Elastic-viscoplastic constitutive coupled micro-cracks propagation damage of PBX[J].Chinese Journal of Energetic Materials(Hanneng Cailiao),2015,23(10):999―1003.(in Chinese)
[17]周栋,黄风雷,姚惠生.PBX炸药粘弹性损伤本构关系研究[J].北京理工大学学报,2007,27(11):945―947.Zhou Dong,Huang Fenglei,Yao Huisheng.Study on the visco-Elastic constitutive model of PBX[J].Transactions of Beijing Institute of Technology,2007,27(11):945―947.(in Chinese)
[18]冯希金,危银涛,李志超,等.未硫化橡胶非线性粘弹性本构模型研究[J].工程力学,2016,33(7):212―219.Feng Xijin,Wei Yintao,Li Zhichao,et al.Research on nonlinear viscoelastic constitutive model for uncured rubber[J].Engineering Mechanics,2016,33(7):212―219.(in Chinese)
[19]董满生,鹿婧,凌天清,等.考虑温度效应的沥青混合料参数模型[J].工程力学,2016,33(6):180―185.Dong Mansheng,Lu Jin,Ling Tianqing,et al.Parametric model for asphalt mixtures considering temperature effect[J].Engineering Mechanics,2016,33(6):180―185.(in Chinese)
[20]Donald A Wiegand,Brett Reddingius.Mechanical properties of confined explosives[J].Journal of Energetic Materials,2005,23(2):75―98.
[21]Wiegand D A,Pinto J,Nicolaides S.The mechanical response to TNT and a composite,composition B,of TNT and RDX to compressive stress:I.Uniaxial stress and fracture[J].Journal of Energetic Materials,1991,9(1/2):19―80.
[22]Pinto J,Wiegand D A.The mechanical response of TNTand A composite,composition B,of TNT and RDX to compressive stress:II Triaxial stress and yield[J].Journal of Energetic Materials,1991,9(3):205―263.
[23]Wiegand D A,Pinto J.The mechanical response of TNTand A composite,composition B,of TNT and RDX to compressive stress:III Dependence on processing and composition[J].Journal of Energetic Materials,1991,9(5):349―413.
[24]唐维.TATB基PBX炸药的准静态本构模型与强度准则[D].南京:南京理工大学,2016.Tang Wei.Constitutive models and strength criterions of a TATB-based PBX under quasi-static loading[D].Nanjing:Nanjing University of Science&Technology,2016.(in Chinese)
[25]Tang Wei,Yan Xilin,Wen Maoping,et al.Boltzmann function based nonlinear tension-compression constitutive model for typical polymer bonded explosives under quasi-static loading[J].Chinese Journal of Energetic Materials(English Version),2017,25(8):689―693.
[26]温茂萍,李明,庞海燕,等.炸药件力学性能各向同异性试验研究[J].含能材料,2006,14(4):286―289.Wen Maoping,Li Ming,Pang Haiyan,et al.Study on mechanical isotropic of PBX[J].Chinese Journal of Energetic Materials(Hanneng Cailiao),2006,14(4):286―289.(in Chinese)
[27]温茂萍,庞海燕,敬仕明,等.等静压与模压JOB-9003炸药力学性能比较研究[J].含能材料,2004,12(6):338―341.Wen Maoping,Pang Haiyan,Jing Shiming,et al.Comparative study on mechanical properties of two kinds of JOB-9003 shaped separately by isostatic liquid pressing and mould pressing[J].Chinese Journal of Energetic Materials(Hanneng Cailiao),2004,12(6):338―341.(in Chinese)
[2]Kakavas P A.Mechanical properties of propellant composite materials reinforced with ammonium perchlorate particles[J].International Journal of Solids&Structures,2014,51(10):2019―2026.
[3]Boddy R L,Gould P J,Jardine A P,et al.Damage in Polymer Bonded Energetic Composites:Effect of Loading Rate[J].Journal of Dynamic Behavior of Materials,2016,2(1):157―165.
[4]Xiao Y C,Sun Y,Wang Z J.Investigating the static and dynamic tensile mechanical behaviour of polymer‐bonded explosives[J].Strain,2018,54(2):e12262.
[5]Xiao Y C,Sun Y,Li X,et al.Dynamic mechanical behavior of PBX[J].Propellants Explosives Pyrotechnics,2016,41(4):629―636.
[6]陈蓉,卢芳云,林玉亮,等.一种含铝炸药压缩力学性能和本构关系研究[J].含能材料,2007,15(5):460―463.Chen Rong,Lu Fangyun,Lin Yuliang,et al.Mechanical behavior and constitutive model of pressed aluminized explosive[J].Chinese Journal of Energetic Materials(Hanneng Cailiao),2007,15(5):460―463.(in Chinese)
[7]王礼立,施绍裘.ZWT非线性热粘弹性本构关系的研究与应用[J].宁波大学学报:理工版,2000(B12):141―149.Wang Lili,Shi Shaoqiu.Research and application of ZWT nonlinear thermo-viscoelastic constitutive model[J].Journal of Ningbo University(Natural Science&Engineering Edition),2000(B12):141―149.(in Chinese)
[8]卢强,王占江,王礼立,等.基于ZWT方程的线黏弹性球面波分析[J].爆炸与冲击,2013,33(5):463―470.Lu Qiang,Wang Zhanjiang,Wang Lili,et al.Analysis of linear visco-elastic spherical waves based on ZWTconstitutive equation[J].Explosion and Shock Waves,2013,33(5):463―470.(in Chinese)
[9]Feng Zhenzhou,Wang Xinjun,Wang Fusheng,et al.Implementation and its application in finite element analysis of constitutive model for ZWT nonlinear viscoelastic material[J].Journal of Materials Science and Engineering,2007,25(2):269―272.
[10]Clements B.ViscoSCRAM:past,present and future[P].LANL,LA-UR-11-1245,2011.
[11]罗景润.PBX的损伤、断裂及本构关系研究[D].绵阳:中国工程物理研究院,2001.Luo Jingrun.Study on damage,fracture and constitutive relation of PBX[D].Mianyang:China Academy of Engineering Physics,2001.(in Chinese)
[12]郭虎.高聚物粘结炸药微裂纹统计本构模型研究[D].绵阳:中国工程物理研究院,2012.Guo Hu.Study on the visco statistical crack mechanics for PBXs[D].Mianyang:China Academy of Engineering Physics,2012.(in Chinese)
[13]张延耿,楼建锋,周婷婷,等.PBX炸药含各向异性损伤的黏弹性统计微裂纹本构模型初步研究[J].高压物理学报,2016,30(4):301―310.Zhang Yangeng,Lou Jianfeng,Zhou Tingting,et al.Initial study on constitutive model of PBXs via viscoelastic statistical crack mechanics including anisotropic damage[J].Chinese Journal of High Pressure Physics,2016,30(4):301―310.(in Chinese)
[14]高军,黄再兴.PBX炸药粘弹性损伤本构模型参数敏感度分析[J].工程力学,2015,32(2):201―206.Gao Jun,Huang Zaixing.Parameter sensitivity analysis for viscoelastic damage constitutive model for PBXmaterials[J].Engineering Mechanics,2015,32(2):201―206.(in Chinese)
[15]高军,黄再兴.PBX炸药粘弹性损伤本构模型的参数识别[J].工程力学,2013,30(7):299―304.Gao Jun,Huang Zaixing.Parameter identification for viscoelastic damage constitutive of PBX[J].Engineering Mechanics,2013,30(7):299―304.(in Chinese)
[16]成丽蓉,施惠基.PBX炸药含裂纹扩展损伤的粘塑性本构关系[J].含能材料,2015,23(10):999―1003.Cheng Lirong,Shi Huiji.Elastic-viscoplastic constitutive coupled micro-cracks propagation damage of PBX[J].Chinese Journal of Energetic Materials(Hanneng Cailiao),2015,23(10):999―1003.(in Chinese)
[17]周栋,黄风雷,姚惠生.PBX炸药粘弹性损伤本构关系研究[J].北京理工大学学报,2007,27(11):945―947.Zhou Dong,Huang Fenglei,Yao Huisheng.Study on the visco-Elastic constitutive model of PBX[J].Transactions of Beijing Institute of Technology,2007,27(11):945―947.(in Chinese)
[18]冯希金,危银涛,李志超,等.未硫化橡胶非线性粘弹性本构模型研究[J].工程力学,2016,33(7):212―219.Feng Xijin,Wei Yintao,Li Zhichao,et al.Research on nonlinear viscoelastic constitutive model for uncured rubber[J].Engineering Mechanics,2016,33(7):212―219.(in Chinese)
[19]董满生,鹿婧,凌天清,等.考虑温度效应的沥青混合料参数模型[J].工程力学,2016,33(6):180―185.Dong Mansheng,Lu Jin,Ling Tianqing,et al.Parametric model for asphalt mixtures considering temperature effect[J].Engineering Mechanics,2016,33(6):180―185.(in Chinese)
[20]Donald A Wiegand,Brett Reddingius.Mechanical properties of confined explosives[J].Journal of Energetic Materials,2005,23(2):75―98.
[21]Wiegand D A,Pinto J,Nicolaides S.The mechanical response to TNT and a composite,composition B,of TNT and RDX to compressive stress:I.Uniaxial stress and fracture[J].Journal of Energetic Materials,1991,9(1/2):19―80.
[22]Pinto J,Wiegand D A.The mechanical response of TNTand A composite,composition B,of TNT and RDX to compressive stress:II Triaxial stress and yield[J].Journal of Energetic Materials,1991,9(3):205―263.
[23]Wiegand D A,Pinto J.The mechanical response of TNTand A composite,composition B,of TNT and RDX to compressive stress:III Dependence on processing and composition[J].Journal of Energetic Materials,1991,9(5):349―413.
[24]唐维.TATB基PBX炸药的准静态本构模型与强度准则[D].南京:南京理工大学,2016.Tang Wei.Constitutive models and strength criterions of a TATB-based PBX under quasi-static loading[D].Nanjing:Nanjing University of Science&Technology,2016.(in Chinese)
[25]Tang Wei,Yan Xilin,Wen Maoping,et al.Boltzmann function based nonlinear tension-compression constitutive model for typical polymer bonded explosives under quasi-static loading[J].Chinese Journal of Energetic Materials(English Version),2017,25(8):689―693.
[26]温茂萍,李明,庞海燕,等.炸药件力学性能各向同异性试验研究[J].含能材料,2006,14(4):286―289.Wen Maoping,Li Ming,Pang Haiyan,et al.Study on mechanical isotropic of PBX[J].Chinese Journal of Energetic Materials(Hanneng Cailiao),2006,14(4):286―289.(in Chinese)
[27]温茂萍,庞海燕,敬仕明,等.等静压与模压JOB-9003炸药力学性能比较研究[J].含能材料,2004,12(6):338―341.Wen Maoping,Pang Haiyan,Jing Shiming,et al.Comparative study on mechanical properties of two kinds of JOB-9003 shaped separately by isostatic liquid pressing and mould pressing[J].Chinese Journal of Energetic Materials(Hanneng Cailiao),2004,12(6):338―341.(in Chinese)
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