Stochastic Fatigue Damage in Viscoelastic Materials using Probabilistic Pseudo J-Integral Paris' Law

Fatigue damage of engineering materials severely affects the serviceability of their structures. It is impracticable to accurately predict fatigue damage process of engineering materials due to the variability of material properties, microstructure heterogeneity and others. This study aims to track the entire fatigue damage process of viscoelastic materials by coupling the variability with the fatigue damage mechanism. A typical viscoelastic material, asphalt binder, widely used in pavement engineering is selected for investigation in this study. A pseudo J-integral Paris' law model and probability theory are combined to establish a stochastic fatigue damage model for viscoelastic materials. Results show that the damage density can be determined by the apparent shear modulus and true shear modulus. The damage evolution rate is a function of material parameters (Paris’ law coefficients), apparent shear modulus, apparent shear strain amplitude and apparent phase angle. Then, a cumulative distribution function of loading time (TCDF) and damage density exceedance probability (DDEP) are derived and experimentally verified. Next, the stochastic fatigue damage model is proposed, which can track the entire fatigue damage process for viscoelastic materials, and it depends on the damage density, material parameters and variability parameters. The variability of minor damage can be used to predict the variability of severe damage based on the stochastic fatigue damage model.