  We study the non-linear dynamics and failure statistics of a coupled-field
fatigue damage evolution model. We develop a methodology to derive averaged
damage evolution rate laws from such models. We show that such rate laws reduce
life-cycle simulation times by orders of magnitude and permit dynamical systems
analysis of long-time behavior, including failure time statistics. We use the
averaged damage rate laws to study 1 DOF and 2 DOF damage evolution models. We
identify parameter regimes in which the systems behave like a brittle material
and show that the relative variability for failure times is high for such
cases. We also use the averaged rate laws to construct damage evolution phase
portraits for the 2 DOF system and use insights derived from them to understand
failure time and location statistics. We show that, for brittle materials, as
the relative variability in failure time increases, the variability in failure
location decreases.
