A probabilistic treatment of creep rupture behavior for polymers and other materials

A recent deterministic derivation for the creep rupture behavior of polymers is taken as the basis for the present work. The formulation is that for the prediction of the lifetime of viscoelastic materials under constant load, based upon kinetic crack growth from initial flaws. The statistical generalization involves using a Weibull type distribution for the instantaneous static strengths. Then the resulting full statistical character for the lifetimes as a function of stress level is found. The lifetime distributions are determined to be much broader than are the static strength distributions. An unusual statistical characteristic emerges from the derivation. When the lifetimes are viewed on log stress versus log lifetime scales the envelopes for the various probability levels of failure are found to have a common shape, as in a single master curve, but they are shifted relative to each other along the log stress axis. This shifting property could have considerable utility in reducing the number of tests required to obtain a complete, statistical database. Finally, similar implications for fatigue characterization are considered.