Synergetic concept of metals fatigue

б.б.Shanyavskiy

State Center of Flight Safety

box 54, Sh.-1, Khimki, MO, 141426, Russia

A new concept of metals fatigue fracture description is discussed as a self-organized cascade of crack initiation processes changing one another with cyclic stress increase. A bifurcation diagram of metals fatigue fracture is plotted and described as a cascade of bifurcation transitions in damages accumulation from nano to macro scale levels. Basing on synergetic principles it is shown that minimal energy expenditure for metal fatigue fracture corresponds to the nano-scale level, when metal behaves as a partly closed system (PCS). The cracks are initiated under the surface of a sample or a detail, and metals durability does not depend on the surface state. Further, on meso and macro scale levels, the metal behaves as an open system (OS) and its durability depends entirely on the surface state. New ideology of estimation and control of metals fatigue durability is discussed both in the bifurcation area, and in the case when a metal behaves as a PCS or an OS.

At the end of the 19^th century Wöhler, studying high compressing loads effect on durability of railcar wheel pairs' shafts, showed experimentally that in conditions of shafts bending under rotation there was a stable relation between the level of bending stress, s_f, and a number of cycles, N_f, before the shaft fracture. Plotted dependence reflected the increase of number of cycles with decreasing stress amplitude in case of symmetrical cycle of tension - compression. The dependence was named as Wöhler curve or "S-N" curve. It can be described by a simple power law of stress level s_i and a number of cycles before the sample fracture.

These parameters are defined for all existing metals and are considered as material fatigue characteristics reflecting metal's ability to sustain cyclic loads before fracture.

Further researches showed that these parameters depend not only on metals structure, but also on external influence conditions: asymmetric loading, biaxial loading, alternate loading frequency, : Condition of metal surface turned out to be essential and even critical, because for example at high-temperature or corrosive influence of environment the metals deteriorate, which leads to fast crack initiation, reducing the number of cycles before fracture. The problem of metals surface state influence on durability has been investigated for over 20 years in the frame of new scientific branch called mesomechanics>.

Fatigue tests of metals were standardized allowing to receive comparable results for metals in different laboratories, particularly while creating new alloys.

Wöhler's essential achievement was that he demonstrated existence of a stress level s_f1, at which the average durability increases by several orders at decrease of stress level by several percents. Having introduced in calculation of durability a stress level which is 10-20% less than specified value of s_f1, one can expect that metal in construction will work so long that within the limits of reasonable operating time (e.g. within the limits of 100 years) there will be no fractures.

However, technical progress in fatigue tests allowed to proceed to cyclic loading frequencies for tested metals in hundreds and even thousands Hertz. This gave an opportunity in laboratory conditions to reach durability of 10⁹ cycles at stress level below s_f1 for a rather short period of time. It appeared that fractures in the field of durability over 10⁹ cycles not only existed but obeyed the similar dependence but with different factors. The revealed metals behavior was offered to be characterized with bimodal distribution of fatigue durability.

The further experiments showed that distribution of fatigue durability can be multimodal.

Thus, it appeared that simple dependence (Wöhler) did not allow describing uniformly the whole variety of the revealed experimental data on metals behavior accumulated for over 100 years. A new understanding of metals fatigue should be introduced as a cascade of interconnected processes running sequentially at different scale levels corresponding to behavior of open synergetic systems and partially closed thermodynamic systems.

The bifurcation diagram of sequence of damages accumulation processes for metals under multiparametric external cyclic loading is submitted. The cascade of changes of fatigue crack initiation mechanisms is explained basing on the diagram. It successively considers scale levels of discrete transitions in metals behavior because of bifurcation points passage:

-         instability I (nano-level), point s_w1, is associated with transition to material fracture by fatigue crack initiation from under the surface, as in a partly closed system;

-         instability II (meso-level I), point s_w2, is associated with transition to an open system whose fatigue crack nucleus is located on the sample surface;

-         instability III (meso-level II), point s_w3, is associated with transition of an open system to fatigue fracture with multiple nuclei when durability N_f is completely defined by the crack growth period N_p;

-         instability IV (macro-level), point s_w4, is associated with transition to repeated static fracture when the fracture nuclei are simultaneously located at the surface and inside the sample or dominate under the surface.

The hierarchy of scales in metals behavior replacing each other at transition through instability areas represents a metal as a synergetic system. The metal realizes one or another way of energy absorption and dissipation in a self-organizing kind of way under cyclic loading depending on its level, duration and conditions of the loading application to a sample or a construction element. Therefore in multiparametric case of external loading some of the abovementioned scale levels may be missed or are not achieved. However, at minimally possible level of loading intensiveness and the simplest way of regular cyclic loading of a material all listed above scale levels of self-organization processes can be realized at initiation, origination and development of metal fracture process.