丁羟包覆层的黏超弹本构模型
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摘要
为了准确地描述丁羟(HTPB)包覆层在有限变形下的拉伸力学特性,研究了HTPB包覆层的黏超弹本构模型。分别构建了含率相关函数的本构模型和并联式本构模型,前者由超弹模型与率相关项相乘得到,后者由超弹模型与含损伤因子的黏弹模型并联而成。进行了HTPB包覆层的单步松弛、多步松弛和不同速率的单轴拉伸试验,并将试验数据用于拟合模型参数。结果表明,HTPB包覆层对应变率极其敏感,且具有很大的延伸率,表现出明显的黏超弹特性;两种模型均能很好地预测HTPB包覆层较大形变范围内的拉伸力学性能,其中含率相关函数的模型的描述更加准确,其研究具有重要的军事意义。
The visco-hyperelastic constitutive models of hydroxyl-terminated polybutadiene(HTPB)inhibitor were studied to describe the tensile mechanical properties accurately under finite deformation.Visco-hyperelastic constitutive model with rate related function and parallel constitutive model were built respectively,and the first model was multiplicatively combined by hyper-elastic model and rate related function,while the latter model was parallelly formed by hyper-elastic model and viscoelastic model containing damage factor.In order to fit the model parameters by the test data,the single-step relaxation test,multi-step relaxation test and uniaxial tensile test at various rates of HTPB inhibitor were undertaken.The results show that HTPB inhibitor is extremely sensitive to strain rate and has agreat elongation,reflecting the obvious visco-hyperelasticity.Both of the models are able to predict the tensile mechanical properties of HTPB inhibitor in a large deformation range,meanwhile the model with rate related function can describe the mechanical properties more precisely,which is of great military significance.
The visco-hyperelastic constitutive models of hydroxyl-terminated polybutadiene(HTPB)inhibitor were studied to describe the tensile mechanical properties accurately under finite deformation.Visco-hyperelastic constitutive model with rate related function and parallel constitutive model were built respectively,and the first model was multiplicatively combined by hyper-elastic model and rate related function,while the latter model was parallelly formed by hyper-elastic model and viscoelastic model containing damage factor.In order to fit the model parameters by the test data,the single-step relaxation test,multi-step relaxation test and uniaxial tensile test at various rates of HTPB inhibitor were undertaken.The results show that HTPB inhibitor is extremely sensitive to strain rate and has agreat elongation,reflecting the obvious visco-hyperelasticity.Both of the models are able to predict the tensile mechanical properties of HTPB inhibitor in a large deformation range,meanwhile the model with rate related function can describe the mechanical properties more precisely,which is of great military significance.
引文
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[19] AKLONIS J J,MACNIGHT W J,沈明琦.聚合物黏弹性引论[M].北京:中国宇航出版社,2015.AKLONIS J J,MACNIGHT W J,SHEN M Q.Introduction to polymer viscoelasticity[M].Beijing:China Aerospace Publishing House,2015(in Chinese).
[20]杨光松.损伤力学与复合材料损伤[M].北京:国防工业出版社,1995.YANG Guangsong.Damage mechanics and composite material damage[M].Beijing:National Defence Industry Press,1995(in Chinese).
[21]顾志旭,郑坚,彭威,等.复合固体推进剂黏弹性微裂纹损伤本构模型[J].复合材料学报,2018,35(5):1203-1210.GU Zhixu,ZHENG Jian,PENG Wei,et al.A viscoelastic constitutive model of solid composite propellants with microcracking damage[J]. Acta Materiae Compositae Sinica,2018,35(5):1203-1210(in Chinese).
[22]蒙上阳,杨晓红,杨军辉.野战火箭发动机结构完整性评估数值方法[M].北京:国防工业出版社,2015.MENG Shangyang, YANG Xiaohong, YANG Junhui.Numerical method of structural integrity evaluation of field rocket mortor[M]. Beijing:National Defence Industry Press,2015(in Chinese).
[2]贾登.三元乙丙橡胶黏结界面变温力学特性及应用研究[D].南京:南京理工大学,2016.JIA Deng.Research of the temperature-dependent mechanical property of adhesive interface between EPDM films[D].Nanjing:Nanjing University of Science&Technology,2016(in Chinese).
[3]徐进升,鞠玉刚,周长省,等.模数对药柱热应力的影响[J].弹道学报,2011,32(3):74-78.XU Jinsheng,JU Yugang,ZHOU Changsheng,et al.Influence of model on thermal stress of grain[J].Journal of Ballistics,2011,32(3):74-78(in Chinese).
[4]张中水.EPDM绝热包覆层热解特性及本构模型研究[D].南京:南京理工大学,2016.ZHANG Zhongshui.Research on pyrolysis properties and constitutive model of EPDM insulation[D].Nanjing:Nanjing University of Science&Technology,2016(in Chinese).
[5] LEU L J,MUKHERJEE S.Sensivity analysis of hyperelastic-viscoplastic solids undergoing large deformations[J].Computational Mechanics,1994,15(2):101-116.
[6] SONG B,CHEN W,CHENG M.Novel model for uniaxial strain-rate-dependent stress-strain behavior of ethylene-propylene-dine monomer rubber in compression or tension[J].Journal of Applied Polymer Science,2004,92(3):1553-1558.
[7] CHAND S,SAHAY K,SAXENA R. Nonlinear viscohyperelastic constitutive relation for brain tissue with parametric sensitivity study[J].Engineering in Medicine ang Biology Society,1995,14(3):91-92.
[8] ANANI Y,ALIZADEH Y.Visco-hyperelastic constitutive law for modeling of foam’s behavior[J].Material&Design,2011,32(5):2940-2948.
[9] YANG L,SHIM V,LIM C.A visco-hyperelastic approach to modelling the constitutive behavior of rubber[J].International Journal of Impact Engineering,2000,24(6):545-560.
[10]谈炳东,许进升,贾云飞,等.短纤维增强EPDM包覆薄膜超弹性本构模型[J].力学学报,2017,49(2):317-323.TAN Bingdong,XU Jinsheng,JIA Yunfei,et al.Hyperelastic constitutive model for short fiber reinforced EPDM inhibitor film[J].Chinese Journal of Theoretical and Applied Mechanics,2017,49(2):317-323(in Chinese).
[11]杨晓红,许进升,孙俊丽,等.三元乙丙材料黏超弹本构模型研究[J].兵工学报,2014,35(8):1205-1209.YANG Xiaohong,XU Jinsheng,SUN Junli,et al.Research on visco-hyperelastic constitutive model of EPDM[J].Acta Armamentarii,2014,35(8):1205-1209(in Chinese).
[12]杨晓红,周长省,常武军,等.丁羟包覆层力学特性及本构模型研究[J].弹道学报,2014,26(4):94-97.YANG Xiaohong,ZHOU Changsheng,CHANG Wujun,et al.Research on mechanical properties and constitutive model of HTPB rubber inhibitor[J].Journal of Ballistics,2014,26(4):94-97(in Chinese).
[13]林适中.固体发动机燃烧室内绝热、衬层材料拉伸试验方法:QJ 916—85[S].北京:航天局708所,1985.LIN S Z.Tensile test of insulation and inhibitor materials of solid engine combustion chamber:QJ 916—85[S].Beijing:Space Agency 708,1985(in Chinese).
[14]张晓,郑坚,彭威,等.HTPB复合固体推进剂黏弹性应变能及非线性本构模型[J].固体火箭技术,2015,8(6):827-832.ZHANG Xiao,ZHENG Jian,PENG Wei,et al.Viscoelastic strain energy and nonlinear constitutive model for HTPB composite solid propellant[J].Journal of Solid Rocket Technology 2015,38(6):827-832(in Chinese).
[15]常武军,鞠玉涛,胡少青.HTPB固化胶片的超弹性本构模型[J].推进技术,2012,33(5):795-798.CHANG Wujun,JU Yutao,HU Shaoqing.Research on hyperelastic constitutive model for HTPB crosslinked specimen[J].Journal of Propulsion Technology,2012,33(5):795-798(in Chinese).
[16]黄克智,黄永刚.高等固体力学[M].北京:清华大学出版社,2013.HUANG Kezhi, HUANG Yonggang. Advanced solid mechanics[J].Beijing:Tsinghua University Press,2013(in Chinese).
[17]郑明军,王文静,陈政南,等.橡胶Mooney-Rivlin模型力学性能常数的确定[J].橡胶工业,2003,50(8):462-465.ZHENG Mingjun,WANG Wenjing,CHEN Zhengnan,et al.Determination for mechanical constants of rubber Mooney-Rivlin model[J].Rubber Industry,2003,50(8):462-465(in Chinese).
[18]余家泉,陈雄,周长省,等.EPDM薄膜橡胶包覆材料的黏-超弹本构模型研究[J].推进技术,2015,36(3):465-470.YU Jiaquan,CHEN Xiong,ZHOU Changsheng,et al.Visco-Hyperelastic constitutive model for filmy EPDM inhibitor[J].Journal of Propulsion Technology,2015,36(3):465-470(in Chinese).
[19] AKLONIS J J,MACNIGHT W J,沈明琦.聚合物黏弹性引论[M].北京:中国宇航出版社,2015.AKLONIS J J,MACNIGHT W J,SHEN M Q.Introduction to polymer viscoelasticity[M].Beijing:China Aerospace Publishing House,2015(in Chinese).
[20]杨光松.损伤力学与复合材料损伤[M].北京:国防工业出版社,1995.YANG Guangsong.Damage mechanics and composite material damage[M].Beijing:National Defence Industry Press,1995(in Chinese).
[21]顾志旭,郑坚,彭威,等.复合固体推进剂黏弹性微裂纹损伤本构模型[J].复合材料学报,2018,35(5):1203-1210.GU Zhixu,ZHENG Jian,PENG Wei,et al.A viscoelastic constitutive model of solid composite propellants with microcracking damage[J]. Acta Materiae Compositae Sinica,2018,35(5):1203-1210(in Chinese).
[22]蒙上阳,杨晓红,杨军辉.野战火箭发动机结构完整性评估数值方法[M].北京:国防工业出版社,2015.MENG Shangyang, YANG Xiaohong, YANG Junhui.Numerical method of structural integrity evaluation of field rocket mortor[M]. Beijing:National Defence Industry Press,2015(in Chinese).