A high-cycle fatigue criterion with internal variables

A multiaxial fatigue criterion is derived from a model to high-cycle fatigue. The model is motivated by the description of fatigue endurance as relying upon elastic shakedown in the material representative volume. By analogy, a simplified formal framework for identifying stress ranges which are feasible with respect to fatigue endurance is proposed at the usual macroscopic level of stress analysis, in the setting of continuum mechanics assumptions. There, the modifications of the characteristic volume, which are responsible for the elastic shakedown of the material, are represented by internal tensorial variables. Thus, the resulting fatigue criterion also indicates the directions of induced anisotropy. The model shows good adequacy to experimental data when applied to nine different materials.