Constitutive Relation Of Anisotropic Polymers

By the regularity of molecules' arrangement in space, polymer can be divided into three classes: crystalline, amorphous and semi-crystalline polymer. Here we research the high polymer with hexagonal crystals, assume that the mechanical properties of macromolecule material depend on the chemical composition and microstructure (include the orientation distribution of crystallites and orientation distribution of molecule chains, the boundary constitute of crystallites etc.) of the crystal and non-crystal. We try to find the relationship of mechanic properties and microstructure of high polymer by the method of metal poly-crystal material, find out the constitute relation function of high polymer material consider the crystal orientation distribution, molecule chains orientation distribution, and chemical effects of crystal and non-crystal. The works include three facets hereinafter:1) In this paper, we use the molecular chain orientation distribution function q(ψ,θ) to describe the amorphous molecular chain orientation, give the description method of polymer chain orientation distribution, and research the constitutive relationship with orientation coefficient effect, which focused on freedom connecting chain and the freedom rotary chain of these two important chain model.2) Based on the work of Wu and Giessen, we studied the deformation of polymer and the evolution of its molecular chains under triaxial tensions, and give the constitutive relation of polymer with the orientation coefficients of molecular chains, study the orientation evolution of molecular chains under complicated stress states, and derive an explicit expression of anisotropic polymer.3) Herein we give the six-party crystal elastic stiffness matrix, and use Taylor formula obtain the elastic constitutive relation, which included the crystal orientation distribution, molecular chain orientation distribution, crystalline and amorphous nature of the chemical effect of crystalline polymer, and use polymer crystallinity to get the macro constitutive relationship.