The breaking strength of imperfect (real) polymer fibers

The thermodynamic fusion theory of strength of perfect polymer fibers of finite molecular weight is extended to include imperfect (i.e. real) fibers of incomplete crystallinity and orientation. Approximate equations for failure strength, strain, and work of failure are derived by extracting from the real visco-elastic fiber an equivalent reversible component suitable for thermodynamic analysis. This is facilitated by an explicit relationship between fiber breaking stress, sigma*, and breaking strain, epsilon*, which is shown to be sigma* = 0.632K epsilon* (K = modulus) for constant strain-rate deformations. It is shown that fiber breaking time is equivalent to the fiber visco-elastic mechanical relaxation time. Experimental data shows that the activation energy of rupture of polyethylene fibers is not the activation energy of covalent bond rupture. Instead it agrees with the activation energy expected of crystal melting in accordance with the fusion theory of rupture. The activation volume of the polyethylene fibers also agrees with the value expected from this theory. (C) 1999 Elsevier Science Ltd. All rights reserved.