Fatigue, Fractals, and a Modified Miner’s Rule

A Mechano Chemical Fatigue Model (MCFM) was recently developed. Two basic features of the model are studied here: (a) the fractal (self-similarity under magnification) property of the damage function, which is predicted by the model and (b) how it leads to a “Modified Miner’s Rule” (MMR), where the fatigue response is dependent on the loading order. Based on the simplest (basic) case of the model, the damage function is dependent on a single parameter when a Weibull strength distribution for the microscale elements (chains) is used. the MCFM proposes a rational explanation to a linear fatigue failure envelope for a two level (High-Low, Low-High) stress loading while the damage law is nonlinear. This is in contrast to the regular Miner Rule, where the damage progression is assumed linear. Applying multilevel cyclic loading the model shows a “fading memory“ response for a monotonically increasing stress. While for a decreasing stress steps there is an intermediate delay stage for which a constant damage rate is found. The microscopic basis of the MCFM enables a clear and direct physical interpretation of the macro behavior as related to the microscale damage mechanisms.