Damage development under very-high-cycle fatigue regime

A method of testing metallic materials using piezoelectric elements under very-high-cycle fatigue (VHCF) regime is described in the paper. The scheme and structure of a high-frequency fatigue machine are discussed. For the experiments, the first mode of resonant longitudinal vibrations is calculated, corresponding to the natural frequency of the cylindrical corset sample. The results of some experiments on very-high-cycle fatigue fracture of VT3-1 titanium alloy samples at various stress ratio coefficients are presented. Mathematical modeling of the process of fatigue damages development in VHCF is carried out. For this, a bimodal representation of the fatigue curve is used. This bimodal representation contains two branches: the left branch corresponds to the classical low-cycle and high-cycle fatigue modes, and the right branch describes the very-high-cycle fatigue regime. On this basis, a kinetic model was built, associated with the known criterion of multiaxial fatigue fracture SWT, which contains a mechanism associated with the development of normal opening microcracks. This kinetic model of damage development can be used to calculate various modes of fatigue failure from low-cycle to very-high-cycle fatigue. On the basis of this model, a numerical method of solving the evolutionary equation for the damage function has been developed. The fatigue fracture of the material in this model corresponds to the degradation of its elastic moduli due to an increase of the damage function. Calculations of the crack-like zones development for fatigue fracture in the titanium corset specimens at different stress ratio coefficients for cyclic loading, used in the tests on a piezoelectric machine, was fulfilled. To test the performance of the model, a comparison between the experimental and calculated fatigue curves in the region of the VHCF was carried out.