Non-commutative fatigue damage evolution by material heterogeneity

Fatigue life tests under varying stress levels have revealed deviations from the linear Palmgren–Miner (PM) rule. The non-commutative damage accumulation has been demonstrated in two-level fatigue tests: longer life under low-to-high (L-H) loading order and shorter life for H-L loading order. Tests under random loading were also far from the PM predictions. We present a consistent Fiber Bundle Model (FBM) which follows microcrack initiation, growth and coalescence. Using a commutative microcrack initiation law, we improve our earlier work, and obtain the damage evolution and Basquin’s power law analytically. We show that the macro non-commutative behavior is dominated by material heterogeneity, which controls the microcrack initiation morphology. Fatigue life under two-level loading and under random loading is found analytically and relations between micro-parameters and macro stress-life results are revealed.