Issue 49

M. Bannikov et alii, Frattura ed Integrità Strutturale, 49 (2019) 383-395; DOI: 10.3221/IGF-ESIS.49.38 388 reversible. The defects weakly correlate with each other, and the amplitude of the second harmonic is small and varies little. However, in the process of cyclic loading, irreversible microdamages are appeared, which begin to interact with each other, which subsequently leads to the formation of a fatigue crack. In one of the samples, which were destroyed with the formation of a surface crack, a monotonic decrease in the amplitude of the second harmonic uncharacteristic for others was found during the testing process (Fig. 4.b). This is supposed to be due to the fact that the initial structure of the material was saturated with defects, since the samples were pre-deformed. During cyclic loading, a small amplitude in the material resulted in relaxation of internal stresses [20], which reduced the nonlinearity of the signal. When a stress relaxation resource is depleted, an avalanche-like growth of the second harmonic amplitude is observed, which indicates a high correlation of defects and their interaction on a large scale compared with the internal nucleation of a fatigue crack. In the fig. 5 the growth of the amplitude of the second harmonic is shown. At the time point of 5.415 * 10 ^ 4, the software stopped the experiment on the basis of a significant increase in the amplitude of the second harmonic (6 times), which indicated the formation of a fatigue crack. Later, the experiment was started again, which allowed us to observe how the amplitude of the second harmonic increases with increasing crack length. Thus, the βrelative parameter can be used not only as an indicator of the appearance of a fatigue crack, but also to determine its size, as it was done in [21]. Figure 5. The amplitude of the second harmonic of prestrained sample AMG-6. The difference in the number of cycles between the moment of detection of the nucleation of a fatigue crack and its exit to macroscopic destruction (the output of the system from resonance) was more than 2 • 10 6 cycles. M ATHEMATICAL MODEL he wide-range constitutive equations [22-24], describing the relationship between the kinetics of damage caused by defects and the relaxation properties of materials, were used to construct a mathematical model that is capable of describing the deformation behavior of metals and alloys under fatigue loading. To describe the evolution of the structure of the material, two parameters are introduced: tensor: ( ) 2 s   s lb bl and scalar: 3 0 ( ) R δ r  where: s - tensor of microshears [23]; s - shear intensity; l - unit normal vector to the shear plane; b - unit vector in the direction of shear; δ - scale-invariant, structural parameter; R - the distance between defects, 0 r - the characteristic size of the nuclei of defects.