A random distribution (spectrum) of mechanical relaxation/retardation rateconstants and its influence on tensile strength of imperfect (real, visco-elastic) polymer fibers in constant strain-rate extension

A random distribution of relaxation/retardation rate constants is derived a nd incorporated into the thermodynamic theory of strength of imperfect (rea l) polymer fibers, which is used to analyze empirical polyethylene (fiber) strength data. The results, weighted equally with previous results, give fo r the perfect polyethylene fiber - the only unique reference state - at 25 degreesC: sigma (c)(strength) approximate to 7.5 GPa, K-c(modulus) approxim ate to 325 GPa, epsilon (c)(strain) approximate to 0.023, and W-c(failure w ork) approximate to 0.087 GPa. These numbers represent the best currently a vailable for the characterization constants of a perfect fibrilliform singl e crystal of finite molecular weight polyethylene. The widths of uncertaint y are ca. 15%. Also, these numbers are exactly those calculated with the th ermodynamic theory of failure based on stress-induced fusion with a constan t heat of fusion. Such figures indicate the general strength of the fusion theory. (C) 2001 Elsevier Science Ltd. All rights reserved.