The assessment of fatigue durability and critical plane determination for multiaxial cyclic loading at an arbitrary shift of phases

The real experience of different structural elements shows that cyclic loading conditions and stress strain state are often quite different from laboratory test conditions such as axial tension-compression, bending or pure torsion. As a rule, the structural elements are subjected to complex (multiaxial) loading conditions during service, that is why multiaxial fatigue criteria should be used for durability estimation of such elements. A present multiaxial criterion allows us to estimate the number of cycles to fracture for specimens or structural element (fatigue life) with an influence of the orientation of the so-call critical plane of fatigue damage accumulation. Analytical solutions were obtained for the present fatigue criterion to determine the orientation of the critical plane of the fatigue damage development under cyclic loading for multiaxial stress states. Cyclic loading with arbitrary shifts of phases for the classical fatigue range (low-cycle and high-cycle fatigue) was considered. Several common cases of the three dimensional cyclic loading, i.e. tension-compression and bending-torsion, are studied. It is shown that at certain values of phase shifts the fatigue durability can be very low even under stress amplitudes that do not lead to fracture in the case of sine phase loading. The comparison with the experimental data and numerical calculations based on the other criterion is made. A disc of a low-pressure stage of a gas-turbine engine subjected to cyclic loading due to centrifugal forces was considered. By using a simplified stress distribution, as well as a stress distribution calculated by the finite element method, the areas of stress concentration and orientation of the critical plane in these zones are determine and the durability of the disk operating was estimated.