Polycrystalline microstructure, cubic elasticity, and nucleation of high-cycle fatigue cracks

Abstract

It is well-known that high-cycle fatigue cracks usually nucleate in surface well-oriented grains with a high Schmid factor. A numerical evaluation of the effect of crystalline elasticity anisotropy (which is often neglected) on the stress state in well-oriented grains is presented. Each of these grains is located at the free surface of an aggregate. The other crystallographic orientations are random. Numerous finite element computations are carried out for evaluating the effect of the neighboring grain orientations. Resolved shear stress and normal stress averages are given, as well as scatter parameters and histograms. Several metals, orientations, and loading conditions are considered. For common (anisotropic) metals/alloys such as copper and austenitic steels, the local average resolved shear stress is about 18% smaller than the macroscopic value which induces a Schmid factor value with respect to the macroscopic tensile stress of 0.41 instead of the classical 0.5 value. Relative scatters in resolved shear stress and corresponding normal stress are high (respectively ±  22% and ±  38%). These high scatter values computed for small applied loads can explain many observations taken from the literature showing a large scatter in the plastic slip line feature, dislocation microstructure, microstructurally short crack nucleation, and propagation rate among well-oriented surface grains. Finally, the effects of some geometrical parameters are evaluated (2D/3D effects, subsurface grains....).