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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1. Introduction The methodology for the determination of fatigue curves proposed by Wöhler (1863) was subsequently used not only as a method of plotting fatigue S - N curves but also as a one-scale level methodology or paradigm for describing and studying the metal behavior under cyclic loading. The range of low durability at high-stress levels was studied intensively, leading to the conclusion that the total stress range for metal fatigue cannot be described by a single fatigue S - N curve. The low cycle fatigue (LCF) regime was considered when a nonlinear relationship between stress and strain is realized, that corresponds to the occurrence of residual strains in a smooth specimen. The region of macroscopically elastic metal behavior is related to the high cycle fatigue (HCF) regime.

Nomenclature C i , m i

material constants for S - N curve

d W /d V strain energy density N f durability Δ q wi

width of bifurcation region in terms of stress material factors in the relation between σ – 1 and σ 0.2 material factors in the relation between σ – 1 and σ U

A , α B , β σ – 1 σ 0.2

fatigue limit yield stress

σ U σ e σ wi

ultimate strength

equivalent uniaxial cyclic tensile stress

stress for boundaries of a transition region between scale levels

The standards created in different countries of the world imply the definition of the “fatigue limit” when 10 7 cycles are reached without failure, regardless of the ratio of the yield stress, σ 0.2 , to the determined stress leve l σ – 1 , which is a characteristic of the material in the form of “fatigue limit” . Thus, even in the most simplified form, the problem of metal fatigue under consideration is characterized by two scale levels, corresponding to either LCF or HCF regime. In 1998, Claude Bathias organized a workshop on the problems of metal fatigue in the field of durability more than 10 8 loading cycles, which he called the field of Gigacycle fatigue and discussed this problem in Bathias and Paris (2005). The workshop gave a start to a new scientific field, on which international conferences were held regularly. The region of a new concept of metal fatigue was referred to as the very high cycle fatigue (VHCF). In fact, a microscopic or nanoscale level in the metal behavior was revealed, which is characterized by the subsurface origin of fatigue cracks in a specimen. Thus, firstly, from the detection of the VHCF regime, it follows that the “fatigue limit” of metals in accordance with the one-scale level approach does not exist as discussed in Sakai and Ochi (2004), Bathias and Paris (2005). Secondly, the scale hierarchy implies the introduction of scale level boundaries when considering models for fatigue life prediction. Thirdly, the linear damage summation rule proposed by Miner (1945), being the main method for determining the life of structural elements, can be valid only within the range for each scale level. Therefore, the parameters of the fatigue S - N curve must be different when summarizing damage for different scale levels. It is worth noting that a change in scale levels does not exist at only one stress level. There should be a certain range of stress levels, within which, according to the principles of synergetics, the violation of the unambiguous correspondence principle is realized, i.e. two different fracture mechanisms can exist simultaneously, with different probabilities, demonstrated in Shanyavskiy (2007). Two modes of fatigue life distribution correspond to the mechanisms.