Constitutive Relation Of Polymer With Effects Of Molecule Chain's Orientation And Crystallite's Orientation

By the regularity of molecules' arrangement in space, polymer can be divided into three classes: crystalline, amorphous and semi-crystalline polymer. In the thesis, we study the mechanics properties of the polymers with effects of molecule chain's orientation and tetragonal crystallite's orientation, in which we employ the microstructure theory of polycrystals. The mechanics properties of polymers depend on their chemical compositions and microstructures. The microstructures include the orientation distribution of crystallites, the orientation distribution of molecule chains, the volume ratio of the crystalline state and the amorphous state, and crystallite's boundary structure. Studying on the microstrucures of polymers can be used to design mechanicas properties and instruct material processing of polymers. In the thesis, our studying includes four aspects:1) Herein we take a polymer to be an orthorhombic aggregate of many tiny tetragonal crystallites. Using theory of microstructures and group and considering the symmetry of tetragonal crystals, we deduce the elastic constitutive form of single tetragonal crystal and the relations of the orientation coefficients. Using the orientation distribution function w(R) to describe the probability density of finding a crystal with orientation R, by means of Maple program, we present elastic constitutive relation of tetragonal crystal, and get the effective elastic stiffness tensor and the effective softness tensor for an orthorhombic aggregate of tetragonal crystallites based on Voigt's model and Reuss's model. Finally, we give an example whose computational result coincides with the Hill's theory well.2) Mechanics properties of amorphous polymers are described in differential equations in this paper. We use the function q(ψ,θ) to describe the orientation distribution of molecule chains. By Maxwell model and Kelvin model, we get three-dimensional viscoelastic constitutive relation of amorphous polymers with the orientation coefficients of molecule chains. In this process, we make use of Laplace's transformation and Laplace's inverse transformation.3) With the method of deducing the constitutive relation of an orthorhombic polycrystal with the shape coefficients in Mojia Huang's paper (2005), we obtain the constitutive form of semi-crystalline polymer's viscoelasticity. The constitutive form contains the effects of orientation distribution of crystals and molecule chains, and their chemical properties.4) Herein we deduce the relation of wave velocity and elastic constitutive form of single tetragonal crystal. Moreover, for an isotropic aggregate of elastic tetragonal crystals, we use an integral method to obtain the dynamic surface impedance tensor by the Stroh's theory. Using the dynamic surface impedance tensor, we obtain the propagation velocity of Rayleigh wave.