ABSTRACT
The fatigue failure of a machine part under loading is contingent first and foremost on the stresses and strains within. The theoretical foundation used for fatigue analysis involves two attributes created by stresses: an elastic state exist the yield point of the material and a plastic state existing it. For fatigue analysis the isotropic hardening presents the most practical application. The use of kinematic hardening is impractical because the Bauschinger effect tends to disappear after a large number of fluctuations. The chapter deals with investigation of an elemental cube. It describes the following assumptions: the material is homogeneous and isotropic; the deformations are small so that the body dimensions are substantially unchanged; the body regains its original form when the applied load is removed; and the strains are infinitesimal, permitting an assumption of linear elasticity. Consider a body subject to an applied load in a Cartesian coordinate system within elastic domain.
