The behavior of materials in different areas of cyclic loading is very different and can depend on both their state and the test conditions. As the criteria for damage during cyclic loading, width of the hysteresis loop, parameters of the dislocation theory, magnitude of the stresses and their intensity, relation with the grain size, etc. can serve. Meanwhile, there is still no general complex mathematical equation reflecting the effect on metal damage during fatigue of such important characteristics of polycrystals as the density or defectiveness, the stress relaxation rate, loading rate, structural and energy state of the material, namely, strength and hardness, and the applied emerging stress-strain state. In the present work, the influence of cyclic loading on failure from the point of view of competition of the loading and relaxation rates of internal stresses with allowance for the spectrum of plastic deformation waves is considered. Depending on the type and loading conditions, a different spectrum of the waves of plastic deformation and fracture is formed under different kinds and loading conditions. It is shown that as the frequency of cyclic loading (strain rate) increases, the voltage rise time decreases, and the voltage corresponding to a certain plastic deformation increases. The intensity of reducing the resistance to material destruction is related to the intensity of damage accumulation. General analytical equations for describing the behavior of the fatigue curves of polycrystalline metals and alloys are obtained, which allow one to represent the influence of the factors of their state in dependence on the influence of the external conditions of cyclic loading. The equation allows to simulate various situations of behavior of polycrystals with fatigue in metals, as well as to analyze the fatigue curves of materials in different states. Since the relaxation rate in polycrystals is the vectorial value = pl.d + p , representing the sum of the vectors of the plastic deformation rate ( pl.d ) and the actual fracture rate p is the nucleation and growth of cracks, then taking this into account, with increasing pl.d with constant total relaxation rate, the rate of destruction will decrease, the fatigue curve will go lower (position). Fatigue curves are constructed for various parameters of the structuralenergy state (Brinell hardness) and density-dependent coefficients.
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