A fundamental theory for slow crack growth in polyethylene

The following theoretical equation has been obtained for measuring the rate of slow crack growth in polyethylene in terms of the crack opening displacement rate δ: δ̇=αy(1−y2)2ηdoE2α2cK4 Here δy is the yield point, K is the stress intensity, η is the intrinsic viscosity of the fibrils in the craze, E is Young's modulus, δc is the stress to produce a craze, d0 is the primordial thickness from which the craze originates and γ is Poisson's ratio. The theoretical equation agrees with the experimental observation: δCK4e-−Q/RT Thus, for the first time, the dependence of δ on stress and notch depth have been derived in fundamental terms and the physical parameters that constitute the factor C have been identified. The intrinsic viscosity η can be calculated from the theory using specific experimental data. For example at 42°C, the fibrils in a craze in a homopolymer have an intrinsic viscosity of 3 × 1011 Pas. This is much larger than the melt viscosity of the amorphous region, which is about 105–106 Pas. Thus, the resistance of polyethylene to slow crack growth is governed by the crystals and not by the amorphous region.