考虑应变率和温度响应的少烟NEPE推进剂粘弹性本构模型
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摘要
为研究少烟NEPE推进剂力学性能的应变率及温度相关性,使用万能材料试验机分别在不同应变率(4.17×10-4～4.17×10-1s-1)和温度(-40～50℃)下测试了推进剂的力学性能,建立了考虑应变率和温度响应的本构模型。结果表明,少烟NEPE推进剂具有应变率硬化特性,其拉伸应力与对数应变率呈线性关系;降低温度使推进剂的定伸应力和模量增大,升温则相反。结合少烟NEPE推进剂的线性对数应变率效应和温度变化特性,建立了粘弹性本构模型,该模型用多蠕变模式与非线性弹簧的组合来反映力学性能的率相关性,用率相关模型与温度函数的乘积形式来描述力学性能的温度相关性。模型预测与实验曲线对比表明,所建模型在实验温度、应变率、0.1～1.0应变范围内预测的准确性较好,其百分误差小于24%。
In order to study the strain rate and temperature dependence of mechanical performance of low smoke NEPE propellant,the universal testing machine was utilized to investigate the mechanical properties of low smoke NEPE propellant under various strain rates( 4.17×10~(-4)～ 4.17×10~(-1)s~(-1)) and temperatures(-40～50 ℃),moreover,a constitutive model considering strain rate and temperature was built.Results show that the low smoke NEPE propellant has strain rate hardening characteristics,there exists linear relation between tensile stress and the logarithm of strain rate; tensile stress and modulus of the propellant increase with the dropping of temperature,however,rising temperature may lead to opposite results.The viscoelastic constitutive model is established by considering the relationship between tensile stress and the logarithm of the strain rate( ·ε),as well as relationship between tensile stress and temperature. Combination of the multi creep modes and nonlinear spring element is put forward to describe the rate dependence mechanical behavior,moreover,the product form of rate related model and the temperature function is employed to reflect the temperature dependence. By comparisons,the calculated results agree well with the experimental results in the scope of the test temperatures,strain rates and strains( 0.1 ～ 1.0),the percentage error is within 24%.
In order to study the strain rate and temperature dependence of mechanical performance of low smoke NEPE propellant,the universal testing machine was utilized to investigate the mechanical properties of low smoke NEPE propellant under various strain rates( 4.17×10~(-4)～ 4.17×10~(-1)s~(-1)) and temperatures(-40～50 ℃),moreover,a constitutive model considering strain rate and temperature was built.Results show that the low smoke NEPE propellant has strain rate hardening characteristics,there exists linear relation between tensile stress and the logarithm of strain rate; tensile stress and modulus of the propellant increase with the dropping of temperature,however,rising temperature may lead to opposite results.The viscoelastic constitutive model is established by considering the relationship between tensile stress and the logarithm of the strain rate( ·ε),as well as relationship between tensile stress and temperature. Combination of the multi creep modes and nonlinear spring element is put forward to describe the rate dependence mechanical behavior,moreover,the product form of rate related model and the temperature function is employed to reflect the temperature dependence. By comparisons,the calculated results agree well with the experimental results in the scope of the test temperatures,strain rates and strains( 0.1 ～ 1.0),the percentage error is within 24%.
引文
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[12]胡少青.NEPE推进剂的粘-超弹本构模型及其应用研究[D].南京:南京理工大学,2015.HU Shaoqing.A visco-hyperelastic constitutive model for NEPE propellant and its application[D].Nanjing:Nanjing University of Science and Technology,2015.
[13]Schapery R A.On the characterization of nonlinear viscoelastic materials[J].Polymer Engineering&Science,1969,9(4):295-310.
[14]朱兆祥,徐大本,王立礼.环氧树脂在高应变率下的热粘弹性本构方程和时温等效性[J].宁波大学学报,1988,1(1):58-68.ZHU Zhaoxiang,XU Daben,WANG Lili.Thermo-viscoelastic constitutive equation and time-temperature equivalence relation of epoxy resin under high strain rate[J].Journal of Ningbo University,1988,1(1):58-68.
[15]Fukuhara M,Sampei A.Low-temperature elastic moduli and internal dilational and shear friction of polymethyl methacrylate[J].Journal of Polymer Science Part B:Polymer Physics,1995,33(12):1847-1850.
[16]Feng G,Ngan A H W.Effects of creep and thermal drift on modulus measurement using depth-sensing indentation[J].Journal of Materials Research,2002,17(3):660-668.
[17]Ngan A H W,Tang B.Viscoelastic effects during unloading in depth-sensing indentation[J].Journal of Materials Research,2002,17(10):2604-2610.
[18]常新龙,赖建伟,张晓军,等.HTPB推进剂高应变率粘弹性本构模型研究[J].推进技术,2014,35(1):123-127.CHANG Xinlong,LAI Jianwei,ZHANG Xiaojun,et al.High strain-rate viscoelastic constitutive model for HTPB propellant[J].Journal of Propulsion Technology,2014,35(1):123-127.
[19]张君发.宽泛应变率下NEPE推进剂热粘超弹性本构模型研究[D].南京:南京理工大学,2014.ZHANG Junfa.Research on the thermo-visco-hyperelastic constitutive model of NEPE propellant over a large range of strain rates[D].Nanjing:Nanjing University of Science and Technology,2014.
[2]张伟,谢五喜,樊学忠,等.纳米铝粉对少烟NEPE推进剂燃烧性能的影响[J].固体火箭技术,2014,37(4):516-520.ZHANG Wei,XIE Wuxi,FAN Xuezhong,et al.Effects of nano-aluminum on combustion characteristic of low smoke NEPE propellants[J].Journal of Solid Rocket Technology,2014,37(4):516-520.
[3]Mooney R.A theory of large elastic deformation[J].Journal of applied physics,1940,240:582-592.
[4]Rivlin R S.Large elastic deformation of isotropic materials:Ⅰ.Fundation concepts,Ⅱ.Some uniqueness theories for pure homogeneous deformations[J].Philosophical Transactions of the Royal Society of London.Series A,1948,240:459-508.
[5]Yeoh O H.Some forms of the strain energy function for rubber[J].Rubber Chemistry and Technology,1993,66(5):754-771.
[6]Renaud C,Cros J M,Feng Z Q,et al.The Yeoh model applied to the modeling of large deformation contact/impact problems[J].International Journal of Impact Engineering,2009,36(5):659-666.
[7]Gajewski M,Szczerba R,Jemioo S.Modelling of elastomeric bearings with application of Yeoh hyperelastic material model[J].Procedia Engineering,2015,111:220-227.
[8]Ogden R W.Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids[J].Proceedings of the Royal Society of London,1972,326(1567):565-584.
[9]封涛,许进升,范兴贵,等.考虑初始缺陷的HTPB推进剂粘超弹本构模型[J].含能材料,2018,26(4):316-322.FENG Tao,XU Jinsheng,FAN Xinggui,et al.Visco-hyperelastic constitutive model of HTPB propellant considering initial defects[J].Chinese Journal of Energetic Materials,2018,26(4):316-322.
[10]Villar L D,Rezende L C.Time-temperature superposition principle applied to thermally aged composite propellant[C]//AIAA/SEA/ASEE Joint Propulsion Conference.Orlando,FL,2013.
[11]石增强,刘朝丰,阳建红.一种改进的R-L分数阶导数定义在固体推进剂粘弹性本构模型中的应用[J].应用力学学报,2009,26(1):168-171.SHI Zengqiang,LIU Chaofeng,YANG Jianhong.Modified Riemann-Liouville fractional order derivative definition in solid propellant viscoelasticity constitutive model[J].Chinese Journal of Applied Mechanics,2009,26(1):168-171.
[12]胡少青.NEPE推进剂的粘-超弹本构模型及其应用研究[D].南京:南京理工大学,2015.HU Shaoqing.A visco-hyperelastic constitutive model for NEPE propellant and its application[D].Nanjing:Nanjing University of Science and Technology,2015.
[13]Schapery R A.On the characterization of nonlinear viscoelastic materials[J].Polymer Engineering&Science,1969,9(4):295-310.
[14]朱兆祥,徐大本,王立礼.环氧树脂在高应变率下的热粘弹性本构方程和时温等效性[J].宁波大学学报,1988,1(1):58-68.ZHU Zhaoxiang,XU Daben,WANG Lili.Thermo-viscoelastic constitutive equation and time-temperature equivalence relation of epoxy resin under high strain rate[J].Journal of Ningbo University,1988,1(1):58-68.
[15]Fukuhara M,Sampei A.Low-temperature elastic moduli and internal dilational and shear friction of polymethyl methacrylate[J].Journal of Polymer Science Part B:Polymer Physics,1995,33(12):1847-1850.
[16]Feng G,Ngan A H W.Effects of creep and thermal drift on modulus measurement using depth-sensing indentation[J].Journal of Materials Research,2002,17(3):660-668.
[17]Ngan A H W,Tang B.Viscoelastic effects during unloading in depth-sensing indentation[J].Journal of Materials Research,2002,17(10):2604-2610.
[18]常新龙,赖建伟,张晓军,等.HTPB推进剂高应变率粘弹性本构模型研究[J].推进技术,2014,35(1):123-127.CHANG Xinlong,LAI Jianwei,ZHANG Xiaojun,et al.High strain-rate viscoelastic constitutive model for HTPB propellant[J].Journal of Propulsion Technology,2014,35(1):123-127.
[19]张君发.宽泛应变率下NEPE推进剂热粘超弹性本构模型研究[D].南京:南京理工大学,2014.ZHANG Junfa.Research on the thermo-visco-hyperelastic constitutive model of NEPE propellant over a large range of strain rates[D].Nanjing:Nanjing University of Science and Technology,2014.