Probabilistic approach in high cycle multiaxial fatigue:: volume and surface effect

In high cycle fatigue, it has been experimentally proved that the stress distribution as well as the size of the loaded sample can change the fatigue strength. The specimen free surface is also known to have an influence. When dealing with multiaxial load conditions those effects still act. In this paper, a multiaxial endurance criterion combined with the weakest link theory is modified to describe the fatigue limit distribution under several load conditions (tension, torsion, rotating bending and plane bending). With this model, all the known effects on fatigue strength can be reflected and the probability for endurance can be adequately predicted for any complex loading. The weakest link theory can also account for the decrease of multiaxial fatigue limit with the stressed volume. A second model, based only on the damage developed at the surface, is then proposed. While the original Weibull theory makes no distinction between potential initiation sites at the free surface and in the volume and can lead to unsatisfactory predictions when applied to materials containing defects like nodular cast iron, the new surface approach distinguishes surface effect and volume effect.