FORMULATION OF A STOCHASTIC-MODEL OF FATIGUE-CRACK GROWTH

Based on a global/local energy balance a deterministic model of fatigue crack growth under constant amplitude loading is derived. The energy terms resulting from the continuous plasticity and localized fracture around the crack tip are determined for small scale yielding leading to the fatigue crack growth equation involving the stress intensity factor and its amplitude. Four material parameters which should be identified from experimental data have a physical interpretation; these are eventually assumed to be random variables and model the statistical scatter of the crack growth versus N curves observed in experiments. A Gaussian white noise random field is additionally assumed to describe the stochastic material non-homogeneity within a specimen. Its effect on the crack growth is derived and results in a positive non-stationary random function depending on the crack length. Statistical parameters of the random fields are identified. Verification of the model by comparison with experimental results is undertaken in a subsequent paper.