Relation between Fractal Dimension of Damage Morphology and Fatigue Limit by a Micormechanic Statistic Model

摘要

Statistical micromechanic fatigue model, developed for a set of ID elements on a ID row, is generalized to an ensemble of elements on a plane. The aim is to find relations between micro statistical damage parameters (probability of failure of neighbor elements etc.) and macro behavior (cyclic stress, fatigue life). Fractal damage geometry is found, with an exponential relation between its dimension and a microstatistic probability of local interaction (G). Since G is also related to the fatigue life (controls fatigue macro strength), a direct relation between damage morphology and fatigue stress is predicted. In addition, all basic micro-macro relations of the ID model, especially the stress-life power law, are found to be valid (although in a modified form) for the more general 2D case.