PSI - Issue 23

A.A. Shanyavskiy et al. / Procedia Structural Integrity 23 (2019) 63–68 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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3. Scale changing and scale levels of transition from VHCF to HCF regime

As already mentioned above, the development of evolutionary processes in synergetic systems including metals under cyclic loading takes place in the direction of increasing scale levels. Moreover, as it was shown by Shanyavskiy (2018) to build a universal relation between stress and durability, that regardless of the crack origin location the limiting state associated with its formation is determined by the strain energy density. The external loading generates the localization of plastic strain combined with elastic lattice distortions that eventually leads to the formation of material discontinuity and nucleation of a fatigue crack. The more localized the stored energy, the longer the initiation of subsurface or surface crack, depending on the level of applied energy. Therefore, as shown by Shanyavskiy (2010), a complete description of the metal fracture evolution process at the three scale levels under consideration is provided by the bifurcation diagram that presents a cascade of fatigue S - N curves in terms of changing scales and bifurcation regions for which bimodal fatigue life distribution is assumed (Fig. 1). The diagram does not show bimodal fatigue life distribution. This is due to the fact that the general attention of fatigue process in this diagram is paid to the hierarchy of the scale level sequence for the processes of evolution from VHCF to HCF and, further, to LCF.

Fig. 1. Bifurcation diagram of metal fatigue ( N f – σ e ) combined with the stress-strain diagram ( σ e – ε ) in terms of equivalent stress, σ e , or strain energy density, d W /d V . The width of bifurcation regions, Δ q wi , are indicated for transitions to micro- or nano- (σ w 1 – σ w 2 ), meso- (σ w 2 – σ w 3 ), and macro- (σ w 3 – σ w 4 ) scale levels of fracture [Shanyavskiy (2010)]. The nucleation of subsurface cracks is first and the least energy-dissipating process of damage accumulation when a metal is a partially closed system. There are no exchanges with the environment because of subsurface nature of crack origination, however, the energy introduction results from the loading process. The next transition with increasing stress is determined by the growth of stress concentration on the surface, where, in particular, local deformations rise, that contributes to heat release and activation of metal oxidation processes. The higher the stress level, the more possible these processes. The surface is appeared to be damaged intensively in local zones, and, as the stress increases already in all cases, cracks are nucleated in the surface layer. Finally, the approach to the yield stress is accompanied by the damage accumulation at the macroscopic scale level followed by the creation of many zones with residual strains resulting in the multi-origin nucleation of fatigue cracks. The multi-scale approach to the analysis of metal behavior under cyclic loading differs from the one-scale approach and even from the two-scale approach without taking into account the existence of a mesoscale level. One of the most well-known works in a two-scale approach to the analysis of metal fatigue refers to the research by Mughrabi (2002). In the two-scale approach to the analysis of the transition to VHCF regime based on the Wöhler’s paradigm, it is shown that the transition to LCF regime occurs, in fact, bypassing HCF regime. One of the reasons for such an approach is due to the fact that in a one-scale approach and in standardized tests for determination of the