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Structural-probabilistic modeling of fatigue failure under elastic-plastic deformation

Dmytro Babich (Department of Electroelastisity, S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv, Ukraine)
Volodymir Bastun (S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv, Ukraine)
Tatiana Dorodnykh (S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv, Ukraine)

International Journal of Structural Integrity

ISSN: 1757-9864

Article publication date: 14 March 2019

Issue publication date: 7 August 2019




The purpose of this paper is to consider an approximate model of accumulation of microdefects in a material under repeated loading which makes it possible to define theoretical parameters of the fatigue failure (durability, fatigue limit, etc.). The model is involving the relevant law of distribution of ultimate (yield) stresses in the material of these members in combination with the basic characteristics of main mechanical properties of a material (ultimate and yield stresses and associated standard deviations).


The model of fatigue failure of brittle and elastoplastic materials based on the use of the structural-probabilistic approach and up-to-date ideas on the mechanism of material fracture is proposed. The model combines statistical fracture criteria, which are expressed in terms of damage concentrations, with the approximate model of microcrack accumulation under repeating loading of the same level. According to these criteria, the fatigue failure begins with the accumulation of separation- or shear-type microdefects up to the level of critical values of their density.


The failure mechanism is associated with the accumulation of dispersed microdamages under repeated loading. The critical value of the density of the microdamages, which are identified with those formed either by separation or shear under static loading in consequence of simple tension, compression or shear, is accepted as the criterion of the onset of fatigue failure. The fatigue being low-cycle or high-cycle is attributed to accumulation of shear microdamages in the region of plastic deformation in the former case and microdamages produced by separation under elastic deformation in the latter one.


The originality of the paper consists in the following. The authors theoretically define parameters of the fatigue failure (durability, fatigue limit, etc.) using the model in combination with the statistical failure (yield) criteria appearing in the damage measures. The constructed fatigue diagram has discontinuities on the conditional boundary dividing domains with the shear-type and separation-type fractures of structural elements. Such results are supported by the experimental results.



Babich, D., Bastun, V. and Dorodnykh, T. (2019), "Structural-probabilistic modeling of fatigue failure under elastic-plastic deformation", International Journal of Structural Integrity, Vol. 10 No. 4, pp. 484-496.



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