A micromechanical fatigue model with damage morphology

Abstract

A stochastic two-parameter Micromechanical Fatigue Model (MFM), which considers morphological aspects of microcrack coalescence and arrest, is proposed. The material is modeled as an ensemble of elements with a stochastic failure strain distribution. By using set theory tools, equilibrium and material strength partitioning, an analytical fatigue life relation is obtained. The cycle-by-cycle damage evolution is transformed into a continuous form, leading to a non-linear separable differential equation. An exact solution of this equation yields the familiar stress-life power-law ( σ = AN b ) and endurance limit. These are directly related to two characteristic micromechanical parameters of material heterogeneity: the strength distribution shape factor of the ensemble and the microcrack arrest probability. The model proposes a new generic relation between the damage evolution function and the S–N power-law, which is validated by recent experiments for three different steels studied elsewhere. The damage evolution morphology includes the full microcrack size distribution. Good prediction capabilities are obtained for high-to-low two-level fatigue loading based on single-level data only.