CDM analysis of fatigue crack initiation under random loading

Fatigue crack initiation is a random phenomenon due to: (i) microstructural variations and micro-defect interactions, (ii) randomness in loading, and, (iii) environmental fluctuations. Current fatigue crack initiation models tend to be empirical in nature. Continuum damage mechanics (CDM) defines damage as the aggregate effect of micro-defects present within a material. The critical damage corresponds to the formation of a macrocrack (i.e. localization). Damage growth is a dissipative process, and the current state of damage can be assumed to encapsulate the history of the process. Starting from first principles of thermodynamics, and assuming isotropic damage growth occurring close to equilibrium in the pre-localization stage, stochastic differential equations for incremental damage growth in successive load cycles are developed. Probabilistic estimates of fatigue crack initiation period are obtained that include (i) randomness in material properties, (ii) intrinsic noise in the damage growth process, and (iii) randomness in the stress (or strain) amplitude in each cycle.