TATB基PBX双曲Drucker-Prager强度准则适用性分析
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摘要
为准确建立三氨基三硝基苯(TATB)基高聚物粘接炸药(PBX)材料的强度准则,通过自主研制的主动围压试验机获取了不同温度(22.5,35,50℃),不同围压(0～10 MPa)下材料的强度;根据单轴拉伸、单轴压缩以及围压压缩实验数据,采用传统Drucker-Prager(D-P)以及双曲D-P强度准则分别建立了不同温度下TATB基PBX材料的强度模型,并分析了其对于强度实验数据的预测精度。结果表明,双曲D-P强度准则对于22.5,35,50℃下强度实验数据的预测相对误差最大分别为2.41%,3.46%,5.22%,均方根误差分别为0.42,0.38,0.44 MPa,优于传统D-P强度准则结果;对于间接三轴拉伸和压缩破坏应力状态的预测,其相对误差分别为4.93%和12.14%,总体上均优于传统D-P、Mohr-Column、双剪以及单轴强度准则。考虑中主应力影响且处处正则的双曲D-P强度准则能准确预测不同温度下TATB基PBX材料的强度特性。
To accurately establish the strength criterion of TATB-based PBX materials,the strength data under different confining pressures(0-10 MPa)and different temperatures(22.5,35,50 ℃)were obtained through the self-developed active confining pressure tester. Based on the experimental data of uniaxial tension,uniaxial compression and confining pressure compression,traditional Drucker-Prager(D-P)and hyperbolic D-P strength criteria were used to establish the strength model of TATB-based PBX at different temperatures,and the prediction accuracy for experimental strength data was analyzed. Results show that the maximum relative errors of the hyperbolic D-P strength criterion at 22.5,35 ℃ and 50 ℃ are 2.41%,3.46% and 5.22%,respec-tively,and the root mean square errors are 0.42,0.38 MPa,and 0.44 MPa,respectively,which are better than those of the tra-ditional D-P strength criterion. The relative errors for the prediction of indirect triaxial tensile and compressive failure stress are 4.93% and 12.14% respectively and they are superior to the traditional D-P,Mohr-Column,twin shear and uniaxial strength cri-teria. The hyperbolic D-P strength criterion of considering the influence of middle principal stress and being everywhere regular,can accurately predict the strength characteristics of TATB-based PBX materials at different temperatures.
To accurately establish the strength criterion of TATB-based PBX materials,the strength data under different confining pressures(0-10 MPa)and different temperatures(22.5,35,50 ℃)were obtained through the self-developed active confining pressure tester. Based on the experimental data of uniaxial tension,uniaxial compression and confining pressure compression,traditional Drucker-Prager(D-P)and hyperbolic D-P strength criteria were used to establish the strength model of TATB-based PBX at different temperatures,and the prediction accuracy for experimental strength data was analyzed. Results show that the maximum relative errors of the hyperbolic D-P strength criterion at 22.5,35 ℃ and 50 ℃ are 2.41%,3.46% and 5.22%,respec-tively,and the root mean square errors are 0.42,0.38 MPa,and 0.44 MPa,respectively,which are better than those of the tra-ditional D-P strength criterion. The relative errors for the prediction of indirect triaxial tensile and compressive failure stress are 4.93% and 12.14% respectively and they are superior to the traditional D-P,Mohr-Column,twin shear and uniaxial strength cri-teria. The hyperbolic D-P strength criterion of considering the influence of middle principal stress and being everywhere regular,can accurately predict the strength characteristics of TATB-based PBX materials at different temperatures.
引文
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[9]邓楚键,何国杰,郑颖人.基于M-C准则的D-P系列准则在岩土工程中的应用研究[J].岩土工程学报,2006,28(6):735-739.DENG Chu-jian,HE Guo-jie,ZHENG Ying-ren.Studies on Drucker-Prager yield criterions based on M-C yield criterion and application in geotechnical engineering[J].Chinese Journal of Geotechnical Engineering,2006,28(6):735-739.
[10]周永强,盛谦,刘芳欣,等.一种修正的Drucker-Prager屈服准则[J].岩土力学,2016,37(6):1657-1664.ZHOU Yong-qiang,SHENG Qian,LIU Fang-xin,et al.Astudy of modified Drucker-Prager yield criterion[J].Rock and Soil Mechanics,2016,37(6):1657-1664.
[11]李平恩,殷有泉.Drucker-Prager准则在拉剪区的修正[J].岩石力学与工程学报,2010,29(增刊):3029-3033.LI Ping-en,YIN You-quan.Modification of Drucker-Prager cri-terion in tensile shear region[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Suppl.):3029-3033.
[2]俞茂宏.强度理论百年总结[J].力学进展,2004,34(4):529-560.YU Mao-hong.Advances in strength theories for materials un-der complex stress state in the 20th century[J].Advances in Mechanics,2004,34(4):529-560.
[3]俞茂宏,昝月稳,范文,等.20世纪岩石强度理论的发展-纪念Mohr-Coulomb强度理论100周年[J].岩石力学与工程学报,2000,19(5):545-550.YU Mao-hong,ZAN Yue-wen,FAN Wen,et al.Advances in strength theory of rock in 20 century[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(5):545-550.
[4]俞茂宏.双剪理论及其应用[M].北京:科学出版社,1998:199-217.YU Mao-hong.Twin shear theory and its application[M].Bei-jing:Science Press,1998:199-217.
[5]Drucker D C,Prager W.Solid mechanics and plastic analysis or limit design[J].Quarterly of Applied Mathematics,1952,10(2):157-165.
[6]Ralph Robert Stevens.A strength model and service envelope for PBX 9501[R].LA-UR-14-20696,2014.
[7]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.
[8]唐维,李明,温茂萍,等.四种强度准则在高聚物粘结炸药强度分析中的适应性[J].固体力学学报,2013,34(6):56-61.TANG Wei,LI Ming,WEN Mao-ping,et al.Adaptability of four strength criterions in polymer bonded explosives strength analysis[J].Chinese Journal of Solid Mechanics,2013,34(6):56-61.
[9]邓楚键,何国杰,郑颖人.基于M-C准则的D-P系列准则在岩土工程中的应用研究[J].岩土工程学报,2006,28(6):735-739.DENG Chu-jian,HE Guo-jie,ZHENG Ying-ren.Studies on Drucker-Prager yield criterions based on M-C yield criterion and application in geotechnical engineering[J].Chinese Journal of Geotechnical Engineering,2006,28(6):735-739.
[10]周永强,盛谦,刘芳欣,等.一种修正的Drucker-Prager屈服准则[J].岩土力学,2016,37(6):1657-1664.ZHOU Yong-qiang,SHENG Qian,LIU Fang-xin,et al.Astudy of modified Drucker-Prager yield criterion[J].Rock and Soil Mechanics,2016,37(6):1657-1664.
[11]李平恩,殷有泉.Drucker-Prager准则在拉剪区的修正[J].岩石力学与工程学报,2010,29(增刊):3029-3033.LI Ping-en,YIN You-quan.Modification of Drucker-Prager cri-terion in tensile shear region[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Suppl.):3029-3033.