A micromechanical model of cyclic deformation and fatigue-crack nucleation in f.c.c. single crystals

We have developed a micromechanical finite-element model of fatigue-crack initiation in nominally defect-free pure f.c.c. metals. The scale of observation envisioned is that of a single persistent slip band (PSB) intersecting the free surface of a single crystal. The nucleation event is identified with the formation of a sharp surface crack, whose subsequent growth obeys the laws of fracture mechanics. Basic building blocks of the theory are: a model of cyclic plasticity tailored to PSBs which accounts for the Bauschinger effect, PSB elongation due to pair annihilation, and vacancy generation; and a model of vacancy diffusion which accounts for pipe diffusion and the surface motion resulting from the outward flux of vacancies. Our numerical simulations show that this flux causes the surface to recede, which contributes to the formation of grooves at the PSB/matrix interface. Eventually, those grooves sharpen to form a mathematically sharp crack. The model thus provides a quantitative prediction of the number of cycles required for the nucleation of a fatigue crack.

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