| Abstract: | A fiber composite model of highly drawn polyethylene is presented. Quantitative predictions and calculations are made using shear-lag theory. The drawing process is shown to occur in two stages, a neck and a postneck taper. It is shown that there is an empirical linear relationship, with a high correlation, between the parameter x in shear-lag theory (which involves the aspect ratio of the reinforcing elements and the square root of the ratio of matrix shear modulus to the Young's modulus of the reinforcing elements) and the 3/2 power of the taper draw ratio. It is concluded that crystalline fibrils (the reinforcing elements) deform homogeneously during the secondary, taper drawing process. The increase in aspect ratio resulting from this homogeneous deformation is held to be responsible for the increase in tensile modulus owing to the increased efficiency of the fibrils as reinforcing elements. The model is also used to explain the self-hardening process exhibited by these fibers and, using measurements of density of hardened fibers, to predict that immediately after the neck the aspect (length to diameter) ratio of the crystalline reinforcing elements is ca. 2 and that the shear modulus of the matrix material in as-drawn fibers is ～103N/m2 and does not change significantly during the taper-drawing process. |
