Stress Intensity Controlled Kinetic Crack Growth and Stress History Dependent Life Prediction with Statistical Variability

Consistent with viscoelastic behavior, a power law form in terms of the stress intensity factor is used to specify crack kinetics (growth rate) in the central crack problem under Mode I conditions. The crack growth rate is integrated to obtain the crack size and thereby the stress intensity factor as a function of time. The crack is allowed to grow in a controlled, load dependent manner until it reaches the size at which it becomes unstable. The corresponding time at which this occurs is taken as the lifetime of the material under the specified load history. The special cases of constant load (creep rupture) and constant strain rate to failure are found to have a very simple relationship with each other. This lifetime relationship is verified through the comparison with corresponding data upon a polymeric composite. Finally the creep rupture case is generalized to a probabilistic formalism. The theoretically predicted lifetime distribution functions are verified with data, also upon a polymeric composite. Possible extension of the entire formalism to cyclic fatigue in metals is discussed. Dedicated to Professor Z.P. Bažant for his many contributions.