Predictions of limiting mechanical performance for anisotropic crystalline polymers

A four-stage synthesis of molecular, micromechanical, and macromechanical models is used to predict the dependence of the longitudinal and transverse Young's moduli and the axial and transverse shear moduli of anisotropic polyethylene on percent crystallinity and the state of molecular orientation. Variational methods are employed to establish the upper and lower limits for anisotropic elastic response. The difference between lower and upper bound limits is interpreted as the potential for improving mechanical performance. A modified form of the Tsai-Halpin equation is used to examine parametric ranging (via a contiguity factor, ξ) between the lower and Tupper bound limits. In this application, the contiguity factor is interpreted as a characteristic of the internal stress-strain distribution which is dependent upon the size, shape, packing geometry, and elastic properties of the crystalline and amorphous regions. The potential for achieving high modulus polymeric materials is illustrated by treating percent crystallinity, molecular orientation, and contiguity as materials design variables subject to control by processing conditions. Optimum property trade-offs, necessary for balancing the over all mechanical behavior of anisotropic materials, are illustrated through the control of orientation and contiguity, The theoretical predictions for the moduli of anisotropic polyethylene are in good agreement with values reported for material processed by traditional procedures as well as ultra-oriented polyethylene.