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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2. Bimodal fatigue life distribution For the first time, Shabalin (1967) studied the regularity of occurrence of the transition region from one to another type of metal fracture with regard to the boundary between the LCF and HCF regimes. The idea of the S - N curve discontinuity was introduced, which does not reflect the physics of the phenomenon of changing the scale of damage accumulation in metals, since each of the fatigue regimes has its own relationship between the equivalent uniaxial cyclic tensile stress, σ e , and durability, N f , in the following form proposed by Shanyavskiy (2010): (1) In Eq. (1), the subscript “ i ” denotes to the scale level, where “ 1 ” is for the micro- (or nanoscale) level corresponding to VHCF; “ 2 ” is for mesoscale (HCF); “ 3 ” is for the macroscale level (LCF). A detailed study of this phenomenon by Ivanova and Terentiev (1975) showed that, depending on the type of material, the transition region has a certain width Δ q wi , and the relative position of the fatigue S - N curves is determined by the type of metal: - for cyclically strain-hardening metals, the transition from the HCF regime to the LCF regime (according to the increasing scale hierarchy) occurs with increasing durability; - for cyclically softening metals, a transition to lower durability occurs; - for cyclically stable metals, there is a change in the fatigue S - N curve inclination angle. From the synergetic s’ point of view, the emergence of a bimodal fatigue life distribution means that the metal behavior is unstable during the transition from one to another leading mechanism of evolution as shown by Shanyavskiy (2007). The occurrence of this transition is due to self-organization in the behavior of the metal and the choice of the evolution path that allows maintaining the stability of the system (metal) under the external influence at the lowest energy dissipation. Since in LCF and HCF regimes cracks in metals originate from the surface or in the surface layer, the surface state has a significant influence on the durability of materials. The regularity of surface layer behavior was studied systematically in the framework of physical mesomechanics by Panin (2000, 2015) that allowed considering the surface layer as a specific medium through which the metal exchanges energy with the environment. The existence of the meso-to-macroscale transition region is well known and studied but was unrelated to the natural evolutionary process, which is typical for the self-organized behavior of a synergetic system undergoing a cascade of unstable states. These transitions correspond to the bifurcation region and scale hierarchy from VHCF to HCF should be considered for metal behavior in the region. In the second half of the 20th century, a great number of experiments were conducted on a large number of specimens from the same alloy to obtain a conception of the statistical nature of metal fatigue (for example, Stulen (1951), Bastenair (1973), Zakharova (1974, 1981)). An increase in the scatter of durability by more than two orders of magnitude in the stress region in the vicinity of the so- called “fatigue limit” was evident. For the first time, Zakharova (1974, 1981) carried out a detailed analysis of the phenomenon under consideration in the form of a bimodal fatigue life distribution for durability range of 10 6 -5 ∙ 10 8 cycles. Fatigue tests of a large number of smooth and notched specimens from alloys based on Fe, Ni, Cu and Ti under rotating bending loading conditions were performed. Moreover, published in literature results of fatigue tests achieved on specimens from steel by Bastener et al. (1961) were analyzed. Test frequency was 200 Hz, and a predetermined number of cycles sustained by a specimen without failure was set as 5∙10 8 cycles. Analysis of the test results was carried out on the assumption that at a fixed stress level, fatigue life scatter is determined by both dispersion of material characteristics and the difference in the nature of metal fatigue behavior characterizing by two rather than one life distribution law described by Eq. (1) with different factors. The fatigue behavior of titanium alloy VT9 studied by Shanyavskiy et al. (2007) showed that crack initiation occurred from the specimen surface for both branches of the bimodal fatigue life distribution. This means that on the mesoscale level in the vicinity of the so-called “ fatigue limit ” a bimodal fatigue life distribution is revealed while maintaining the surface crack initiation. Thus, it can be concluded that for the stress level of the so-called “ fatigue limit ” a multimodal fatigue life distribution is realized, i.e. surface crack is possible to initiate by different mechanisms with different probabilities and a subsurface crack may originate with a low probability. i f e N C i   m