Hyperelastic Modeling And Analysis Of Multiscale Carbon Nanotubes-Reinforced Resin-Matrix Nanocomposites

As the reinforcement phase of polymer,nano materials have great potential of mechanical and physical properties.In order to promote the development of nano reinforced polymer composites,proper constitutive relations must be established to predict the change of the overall mechanical properties of the composite with the molecular structure of polymer and nano materials.Based on the understanding of the mechanism of molecular level enhancement,a multi-scale super elastic constitutive equation is established to reflect the relationship between the nano structure and macro response of the composite.The unknown parameters in constitutive equation are identified by molecular dynamics method.The correctness of the multi-scale super elastic constitutive model is verified by comparing the experimental and theoretical calculation.Firstly,based on the basic form of the super elastic constitutive equation of fiber reinforced composites,the hyperelasticity of epoxy resin and carbon nanotubes is characterized by eight chain model and pipeline model respectively.The relationship between micro deformation and macro deformation of CNTs is determined.The transverse isotropic super elastic constitutive model of CNT epoxy resin is established which can characterize the influence of CNT mass fraction and ratio of length to diameter Type.The constitutive equation is extended from transverse isotropy to macro isotropy by the theory of molecular chain average distribution,and five parameters to be measured in the constitutive equation are determined.In order to verify the applicability of the constitutive equation,the effects of the parameters of epoxy resin and carbon nanotubes on mechanical response were analyzed under uniaxial tensile load,and compared with the theoretical and experimental data.Secondly,based on the molecular dynamics simulation,the measurement method of the micro unknown parameters in the super elastic constitutive equation of carbon nanotubes epoxy resin is established.The relationship between the average number of Kuhn segments and the degree of polymerization of the monomer between the crosslinking points of epoxy resin was established by molecular chain statistical method.In order to obtain the quasi-static response of epoxy resin under plane shear load,the model was transformed from high energy state to low energy state by artificial aging method,and the time independent shear modulus of epoxy resin was calculated.Based on the relationship between the length of Kuhn chain segment and the length of the continuous length,the micro length of the CNTs is measured by bending simulation.The relationship formula between the length and the diameter,length and wall number of the CNTs is given.The youngs modulus of ep oxy resin and carbon nanotubes was measured,and the relationship between Youngs modulus and diameter and wall number was established.Finally,the carbon nanotubes epoxy resin specimens were prepared,and the effects of the mass fraction and length diameter ratio of carbon nanotubes on the mechanical response of the composites were investigated under uniaxial tensile load.According to the materials and data used in the experiment,the accuracy of the constitutive model is verified based on the parameter identification method established in Chapter 3.The applicable range of the constitutive model is determined under different crosslinking degree and carbon nanotubes mass fraction.